PART I. THE THERMODYNAMIC FUNCTIONS FOR THE FORMATION OF SOME MOLECULAR COMPOUNDS IN SOLUTION PART II. THE IONIZATION CONSTANTS OF SOME PARASUBSTITUTED p ’-DIMETHYLAMINOA ZOBEN ZENES By Russell Wayne Maatman A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry / 1950 ACKNOWLEDGMENT The author wishes to express sincere appreciation to Professor M. T. Rogers for his guidance and assistance which made this work possible. Table of Contents Pag' Part I. The Thermodynamicfunctions for the Formation of ^ome Molecular Compounds in Solution............................... 1 I. Introduction...............................1 II. Summary of Previous Results............... 3 III. The Present Work......................... .65 IV. Conclusions..............................112 V. Summary..................................121 VI. Bibliography.............................122 Part II. The Ionization Constants of Some Para- substituted p '-Dimethylaminoazobenzenes.127 I. Introduction......................... ..128 II. Experimental........................... 139 III. Dismission of Results...................156 IV. Summary................................ 164 V. Bibliography........................... 165 Part I. The Thermodynamic Functions for the Formation of Some Molecular Compounds in Solution. I. INTRODUCTION A large number of compounds are known as addition compounds. The term "addition compound" refers to a method of preparing these substances, there being only one product in an addition reaction. An addition com­ pound may be one of three types: A. Nothing but simple valences exist. An example is ethylene bromide which is the only product formed when hydrogen bromide is added to ethylene. B. The valences that exist represent an extension of the simple valence theory. Ammonium chloride is such a compound because here nitrogen has a valence of four, giving the ion its charge. Oxonium salts are included in this type. C. A third type of addition compound is represented by molecular compounds, which may be divided into three groups: (1 ) complexes which are held together by means of a hydrogen bond; (2) quinhydrones, which are highly colored complexes of quinone or a substance with a similar structure with an aromatic substance like aniline, phenol or hvdroquinone (the hydrogen bond is important here also); (3) addition compounds' of polynitro compounds, or in a few cases, compounds similar to polynitro com­ pounds, with aromatic amines, hydrocarbons, and phenols. The term "molecular compound" will be used to refer -1- only to substances formed from polynitro compounds or similar compounds. The other types of molecular compounds are not discussed in this paper. Use of the term "molecular compound" implies that the interaction leads to compound formation. Since the question of whether or not there is compound formation is part of the principal problem of this paper, this term is used only as a convenient one, and it is not to be inferred that the answer to this problem is assumed. There is no general agreement concerning the nature of the attraction force existing between the components of a molecular compound. (1) It is the purpose of this paper (1 ) to discuss the theories of the nature of this interaction and the evidence for these theories given in the literature and (2) to present experimental evi­ dence intended to clarify certain aspects of the problem. -2- II. SUMMARY OF PREVIOUS RESULTS A. Theories explaining the interaction between the components of a molecular compound. 1. The covalent bond theory. That there is a definite covalent bond involved in molecular compound formation is suggested by several workers. Three different kinds of covalent bonds are postulated; a. Bennett and Willis (2) suggest that one ethylenic double bond in the unsaturated hydrocarbon component is polarized and that the negative carbon atom thus pro­ duced is linked to the nitrogen atom of a nitro group. b. Sudborough (3) postulated a carbon-carbon covalent bond. Later he abandoned this idea for the residual valence theory. (4) Buehler, Hisey, and Wood (5) also suggest this carbon-carbon covalent bond. Bennett (6 ) abandoned his earlier view of the carbonnitrogen bond, and accepted the idea of a carbon-carbon bond or in the case of amines, a carbon-nitrogen bond, as is shown for amines; JJQ 0_ c. ArNH, 2 P A reaction of the ethylenic bond with the oxygen atoms of the nitro groxip was postulated by Hammick and Sixsmith. (7) t -3- Structure I leads to Structure II. Ri 0 0 ' H- Cf?C -H H-C'C-H I II This results from the same ethylenic polarization as presented In (a.) and (b.) According to the theory, the nitro group does not react in this manner unless there is something in R which attracts electrons. Hammick later abandoned this idea for the polarization theory. 2. The residual valence theory. Sudborough (4) elaborates on the theory of Pfeiffer (8) who explains some of the interactions of phenols and amines with quinones and aromatic hydrocarbons. sugp^ests: OgHgtNOgJg Sudborough Ci q H s for the inter action between s-trinitrobenzene and naphthalene. The residual valence of the whole aromatic molecule interacts with the residual valence of the nitro group. This idea was also supported by Kenner and Parkin. (9) Later it was pointed out by Shinomiya (10) that there is another type of residual valence typified by the interaction between naphthylamine and picric acid: C10H7NH2 .•••.HOCgHgCNOg)^. According to Shinomiya this latter interaction does not show a large color change, as contrasted with the noticeable coloration -4- produced by the interaction between s-trinitrobenzene and naphthalene. 3. The coordination theory. Lowry (11) suggests there is a coordination between the components which form molecular compounds. It may be that a hydrogen atom in the hydrocarbon molecule attracts a "lone pair" of electrons on a nitrogen, oxygen, or halogen atom. This view is not clarified further by him. polarization theory. The idea is advanced by several workers that the phenomena observed in molecular compounds may be explained by a polarization interaction between the nitro group and the hydro­ carbon molecule. There are five different views on polarization. a. The aromatic hydrocarbons which form molecular compounds are unsaturated and are polarizable. The permanent dipole of the nitro group induces a dipole in the hydrocarbon molecule. The two molecules together are called a dipole aggregate. This idea is advanced by Briegleb and his coworkers. (12-17) .b. Gibson and Loeffler (18) say that the polariza­ tion is actually an incipient oxidation-reduction reaction. For example, it is polarization that neces­ sarily precedes the reduction of nitrobenzene. This reduction does not occur when an amine such as aniline is mixed with nitrobenzene. -5- There is, however, a polarization interaction, since a color is produced. c. Hammick (19) abandoned his earlier idea of covalent bond formation and accepted the polarization theory. He suggests the interaction is not very different from that between molecules of a liquid, except that there is some orientation in molecular compound complexes. The polarization aggregate that produces color is not, however, the dipole aggregate of Briegleb; with the polarization aggregate there actually is an incipient chemical reaction. d. Pauling, (20) in accepting the polarization theory, ascribes the color so commonly associated with molecular compounds to the stabilization of certain resonance contributions of nitro molecules by a hydro­ carbon molecule. Some of the resonance contributions to picric acid are; He states that coulombic energy is important in ultra­ violet and visible spectra, and that structures having a charge separation, as do those shown, give the com­ pound color.. Since aromatic hydrocarbons are easily polarized, and the hydrocarbon molecule can come within -6- o 3.5 A. of the nitro molecule, the effective dielectric constant in the region around the nitro molecule is greatly increased. The coulombic energy of separation of the charge is therefore proportionately decreased; structixres with separation of charge are stabilized, and color is enhanced. No attempt is made to explain other phenomena of molecular compounds, as electrical properties and equilibrium constants in solution. e. Recently there has been an interesting modifi­ cation of the polarization theory advanced by Sahney and coworkers. (21) They say s-trinitrobenzene has these contributing structures.;.. - 0S. ■ y0 - 0 . “ 0It interacts with naphthalene, which can have the contributing structures: They show the first two to be the actual structures. The molecular interaction is a polarization of the hydrocarbon molecule by the nitro molecule.■ In the molecular compound that is formed the second structure which is the most highly polarized of those shown for -7 s-trinitrobenzene becomes most important, while the third structure of naphthalene which is least polarized becomes most important. 5. The ionization theory. The reaction A -H B — » (AB) -- ^ (A f ( B) ~ is postulated by Weiss. (22) In this equation A is a donor molecule such as an aromatic hydrocarbon or amine, and B is an acceptor molecule such as an aromatic nitro compound. In the reaction there is a transition complex, (AB), which probably forms from A and B through dipole and dispersion interactions. When this complex forms, there is a bond with a large amount of ionic character formed by means of -an electron transfer. The polar molecule thus formed dissociates into ions. The amount of this dissociation depends upon the nature of A and of B and upon the nature of the solvent. solvents favor this dissociation. Ionizing Probably the equili­ brium constant for the formation of the transition complex is always large. B. Discussion of the evidence for the different theories. After one has postulated the nature of the interac­ tion between the components which make up the molecular compound in solution, it is desirable to find one or more physical or chemical properties which prove con­ clusively the postulated interaction. Most properties, however, do not meet this rigid requirement: -8- all but a very few can be consistent with two or more proposed interactions. It is therefore necessary to examine carefully these properties. In this section some of these properties and their significance in relation to the proposed interactions are discussed. 1. The rate of formation of molecular compounds. If the rate of formation of a molecular compound were slow, this fact would be evidence for the existence of a covalent linkage. The only case of a detectable rate of formation of a molecular compound is reported by Hammick and Sixsmith (7) who say that the complex between indene and methyl-4,6,4 *,6 1-tetranitrodiphenate may be formed and deformed at a finite rate in carbon tetrachloride. They determine the rate by titrating with bromine; the amount of bromine used by the solution decreases with time, indicating the ethyl­ enic linkage is inactivated in the complex. They calcu­ late the equilibrium constant from rate data (both formation and deformation) and from experimental data; these values agree within experimental error. would be convincing if valid. This data Hammick (19) later admits there must have been an error, although the experiment was repeated with the same results. In the present paper two reasons are given for questioning these result a. No finite rate of formation is reported in the litera ture for any other molecular compound. Mixing toluene and tetranitromethane at -96° produces color immediately the rate of formation would probably be detectable at this low temperature if a covalent bond were formed, b. Dr. M. T. Rogers (23) who attempted to repeat the early work of Hammick and Sixsmith on the indene complex by noting the color produced found there is no change in total color with time. If it is true, as Hammick states in the earlier work, that the only requirement for covalent bond formation is that there be, in at least some cases, a measurable rate of formation, then it must be concluded there is no covalent bond formation. Whether or not this is the only requirement is no longer of interest, since other properties discussed here show conclusively there is' no covalent bond formed. Since there is no observable rate of formation noted, the nature of the interaction eventually chosen must be such that a rapid rate is possible. It is certainly true that such a rate is consistent with all the polarization and the ionic theories; it may not hold for the residual valence theories. Weiss (22) discusses theoretically the rate of formation of an ionic molecular compound, and he shows the rate will be very rapid except for the case in which the equilibrium constant for the formation of the transi­ tion complex from the initial state is small; he thinks that this may be true in the case of the indene complex mentioned above. -10- 2. Measurements made on the solid state. The primary consideration of this paper is the nature of the molecular compound in solution, but it is necessary to discuss certain properties of the solid state, because they aid in disclosing the nature of the corresponding solutions. It is not necessarily true that a molecular com­ pound can be isolated as a solid if it forms in solution. It may be, as is probably the case with tetranitromethane compounds with aromatic hydrocarbons, that the amount of compound formed is never large enough to exceed the solubility of that compound in any solvent used. This would be true even with mixtures of the pure components in any proportion. There are steric and other factors which aid the formation of a crystal­ line lattice in some cases. Where these favorable factors are absent, the tendency to form a crystalline lattice may also be absent, even though the compound is relatively stable. There may also be instances in which crystals are stabilized principally by these favorable factors. These things confuse the "order of stability" when determined in the solid state. Hammick and coworkers (24, 25) report phase diagrams for several systems in which solid molecular compounds might be expected to form. reported is for interactions between -11- Most of the data 4,6,4 ’,6 *_ tetranitrodiphenate and several aromatic hydrocarbons. The diagrams indicate that in several cases compounds do form, but that in some others they do not. All mixtures in the liquid state give color. This further shows that the conditions favorable for compound formation are not the same as those for solid formation, if it can be assumed color indicates com­ pound formation. The values of the melting points are discussed in the literature. Kronberger and Weiss (26) point out that metal halides which break up into polar mole­ cules, not ions, melt at low temperatures. (27) They suggest that much the same situation exists with mole­ cular compounds which according to their theory, also break up into polar molecules upon melting. The polar molecules subsequently break up into ions to a slight extent. According to Powell and Huse (28) the low melting points of molecular compounds— usually not far different from those of the components— indicate the binding forces in molecular compounds are no stronger than the binding forces of the original molecular crystals. Much higher melting points would be expected, they say, if ionic crystals broke up into ions upon melting. They ignore the above theory of Kronberger and Weiss. It is not easy to predict what the melting point would -12- be for the other types of interaction suggested. If a covalent bond were formed the melting point would be determined by the magnitude of the dissociation and re.combination effects. The crystal structure of molecular compounds has been the subject of some debate. There have been o reported intermolecular distances of the order of 3.2 A, as with p-iodoanillne-s-trinitrobenzene reported by Powell and coworkers. (29) Acenaphthene-2,6-dinitroxylene, which Hertel and Kleu report, (30) has the sodium chloride type face-centered cubic structure. Powell, among others, says that an intermolecular o distance of 3.2 A is too great for covalent bond formation. Powell and Huse (28) discuss the possibility of an ionic bond and reject it not only on the basis of the melting point already cited, but also on the basis of crystal structure, diffuse X-ray spectra, and the falling off of intensity of X-ray spectra with increasing Bragg angle©. In the p-iodoaniline-s- trinitrobenzene compound mentioned above and in the picryl halide-hexamethylbengene compounds described in the later paper the molecular crystal is pictured as one of alternate layers of hydrocarbon and nitro compound; they say this suggests something other than the ionic bond. Weiss points out in referring to the work of Hund (27) that large polarizable ions would -13- tend, to form layer lattices. Intense diffuse X-ray spectra are found In crystals where there are planes held hy weak forces. Such diffuse spectra are found In the plcryl halide molecular compounds examined. The intensity of all X-ray reflections fails off as the Bragg angle, &, increases in such, weak crystals, as is found with the molecular compounds examined. The only objection of Powell and Huse that remains is the structural objection; according to Kronberger and Weiss (26) the presence of the electronegative iodine atom on the donor molecules makes these nontypical cases. Kronberger and Weiss do not discuss the instances in which the iodine atom is- not present. Later Powell concluded (31) that some of the inter­ atomic distances in these molecules are too small for the attracting forces to be van der Waals forces. The objection that X-ray analysis shows there are weak bonds does not seem to be applicable: there is ample evidence that the interaction energy in dilute solution is small, suggesting that the same is true in the crystal. The weak ionic bond postulated is discussed more fully in the section on heats of reaction. More recent work by Saunder (32) shows that there are weak bonds in the molecular crystal of 4,4'-dinitrodiphenyl and 4-hydroxybiphenyl. -14- Essentially the same results as those obtained for the other crystals mentioned are given. The intermolecular distances are considered by Weiss (22) in connection with the ionic theory. Inorganic ions are spherical, while ions of molecular compounds are flat, parallel plates that are much larger than inorganic ions and are, therefore, more polarizable. The interionic distances in molecular compounds are of the same order of magnitude as in some o inorganic crystals of univalent ions--such as 3.15 A for potassium chloride. The existence of the sodium chloride type lattice, for acenaphthene-2,6-dinitrom-xylene is further evidence for the ionic structure. The so-called "radius of action" of the carbon atom is about 1.6 S. The distance between the parallel plates woixld have to be about twice this value. Weiss o points out that the distances actually are about 3.2 A. The radius of the positive ion would be a little less o than 1.6 A. and that of the negative ion a little more. It is apparent that the best Weiss can do in discussing the crystal structure.of molecular com­ pounds is to show that the evidence in the literature is not inconsistent with the ionic theory. This attempt is sometimes labored, but it seems that there is as yet insufficient evidence from crystal data to prove or disprove the ionic theory. -15- 3. The nature of the "donor" and the "acceptor" molecules. There is general agreement that for an interaction of the kind being discussed to take place one of the molecules must tend to give electrons and the other must tend to accept electrons. For the sake of brevity the terms "donor" and "acceptor" molecules are used; it is not intended that these terms should decide the nature of the interaction. Some molecules which tend to give electrons are aromatic hydrocarbons, conjugated unsaturated aliphatic compounds, and deriva­ tives of aromatic hydrocarbons, such as amines in which electrons are donated to the ring by the amino group; those Y/hich tend to receive electrons are aromatic nitro compounds and aromatic compounds which have substituents similar to the nitro group. a. The donor molecule. (1) Aromatic. molecule must have a low ionization potential. The donor These molecules all have loosely bound I f electrons and in some respects they act like metals. London (33) points this out for conjugated, unsaturated aliphatic compounds. It v/ould be expected that the lower the ionization potential, the greater the energy of Interaction. The polarizability of the donor molecule is undoubtedly a parallel function; Briegleb and coworkers (13,14) show the energy of interaction increases as polarizability increases. Polarizability and energy of interaction -16- increase with, for example, increasing number of fused aromatic nuclei in proceeding from benzene to naphtha­ lene to anthracene to chrysene. The number of nuclei in one donor molecule that can interact in solution differs in the various inter­ action theories. Some workers who assume a residual valence theory or a covalence theory, such as Sud­ borough (4) and Bennett and Wain (6), believe that two separated benzene nuclei, as in anthracene and diphenyl, can interact independently of each other. However, as shown in the section on equilibrium measure­ ments, many workers show that equilibrium constants are obtained for the reaction in solution with the assump­ tion there is a 1:1 reaction. In the polarization and ionic theories it would seem more reasonable to expect a 1:1 reaction in most cases since the electron cloud of the whole planar hydrocarbon molecule probably can be acted upon by the acceptor molecule. exceptions. There may be Weiss (22), as well as Kuhn and Winterstein (34), suggests that there may be two separate regions of influence in the same, molecule. This would mean that there is a doubly charged ion which may be either positive or negative, leading to 2:1 compound formation. It must be remembered that solid state evidence given is particularly unreliable -17- in such a question. Spatial arrangements are likely to he more important than a "region of influence". Bamberger and Dimroth (35) obtain much the same result for condensed aromatic hydrocarbons as Brieglebj they measure the solubilities of the molecular compound of picric acid to determine the equilibrium constant. It would be expected that if substituents of the benzene nucleus cause an increase in the electron density of the ring, there would be more interaction. Davies and Hammick (36) use the number of interactions, that is, a number proportional to the equilibrium constant, instead of the energy of interaction, to determine the relative stability of methylated benzenes. They find that in proceeding stepwise from benzene to hexamethylbenzene that the relative stability increases a thousand-fold. Their method is open to question, as is discussed in the section on equilibrium measurements, but their general conclusion undoubtedly is valid, since it is well established that methyl groups donate electrons to the ring. Shinomiya (57, 38, 39) determines the effect of compound stabilit:y in the solid state--measured by melting points and examination of phase diagrams--of fourteen substituents on the aromatic hydrocarbon; half are more active, and half are less active than the parent hydrocarbon. -18- The order of activity is about as expected; the groups which are least active are electron accepting groups, such as the nitro and cyano groups. Briegleb (12) shows that if a side chain on benzene is conjugated with the ring, e. g. styrene, phenyl butadiene, and diphenyl butadiene, there is much greater interaction than with benzene itself; increased conjugation in the side chain increases the amount of interaction. The nitro group, which accepts electrons from the ring, will, however, permit compound formation. Moore, Shepherd, and G-oodall (40) report a pale yellow solid compound of picric acid with a nibronaphthalene;, other similar compounds are nitrobenzene-dinitrobenzene (1:1 ) and nitrobenzene-s-trinitrobenzene (2:1). These are all weak interactions, and probably the nitro group in the donor molecule affects the interaction in no other way than by hindering it. From their work Moore, Shepherd, and Goodall, among others, make the same conclusion concerning the general nature of the donor molecule. The equilibrium concentration of picric acid is determined in the presence of various substituted benzenes. Their methods are discussed in the section on equilibrium measurements. Aromatic amines constitute the strongest kind of donor molecule in molecular compounds, and they react not only with aromatic and aliphatic nitro compounds, but also with nitroso compounds, quinones (41) and liquid sulfur dioxide. (42) Gibson and Loeffler (18) show that an aliphatic amine like o(-phenylethylamine, even though it is a stronger base than aniline, will not react. Amines must be aromatic or, perhaps, conjugated with the ring in order to react. The color observed indicates that methyl groups on the amino nitrogen increase the stability of the'molecular com­ pound. These authors take the viewpoint that the amino group focu.ses the electrons of the ring and the group itself so that the inductomeric polarization is aided. The difference between hydrocarbons and amines is then only one of degree. Weiss (22) thinks that groups like the amino group increase the strength of the electron cloud; this is not a focusing effect. It is difficult to see how the amino group could be said to focus the electrons in the. solid state, where the donor and acceptor molecules probably lie in alternate parallel planes. This does not mean that the amino group could not focus electrons in solution. (2) Aliphatic. If a molecule must be surrounded with an unusually dense electron cloud to be a donor -20- molecule in a molecular compound., it would be expected that some conjugated aliphatic chains would take part in such a reaction. Briegleb (12) points out that every nitro group must be able to interact with all the polarizable bonds; this means not only that the two interacting molecules cannot lie in the same plane, but it also means long chains cannot interact well. Conjugated chains are not as polarizable as ring systems of equal length; and so a short chain would be expected to cause weak interaction, if any. This Briegleb shows to be true for 1,3-butadiene, the energy of interaction, his criterion for stability, between this compound and s-trinitrobenzene being much less than 0.6 kilocalorie. Benzene, which has by far the smallest value of the aromatic hydrocarbons, has an interaction energy of 0.6 kilocalorie with s-tri­ nitrobenzene. b. The acceptor molecule. (1) Aromatic. molecules have a high electron affinity. Such One of the resonance contributions of an aromatic nitro molecule is a structure in which both oxygen atoms of the nitro group carry a single negative charge; in this the nitro group accepts electrons from the ring. The nitro group will aid in this same process by the inductive effect. Ordinarily another part of the same molecule is the source of these electrons. -21- The ionic theory says that in molecular compoLinds there is an outside source of electrons by which the molecule acquires a charge. Substituents other than the nitro group are known to have properties similar to those of the nitro group. It would be expected that substances other than nitro compounds could act as acceptor molecules in molecular compounds. Bennett and Wain (6) have actually observed the color effect typical of mole­ cular compounds in solution for 1,3,5-tricyano’ oenzene and for the acid chloride of trimesic acid which is also symmetrical. The cyano compound gives a color with each of two amines, and the acid chloride with five hydrocarbons and one amine. The number of groups on the aromatic nucleus of an acceptor molecule affects the strength of the molecular compound Interaction. No studies are reported in this connection for groups other than the nitro group. Briegleb and others (13,17,43., 44) show that with a given hydrocarbon the energy of interaction increases with the number of nitro groups.. With acenaphthene or naphthalene, for example, the energy of interaction decreases from s-trinitrobenzene to m-dinitrobenzene. Gibson and Loeffler (18) are unable to find evidence in the literature'of the existence of any -22- mononitro solid molecular compound. some contrary evidence. (45,46) There may be Whether or not a few mononitro solid molecular compounds exist does not alter the general conclusion that'stability of the complex formed increases with the number of nitro groups. As is pointed out elsewhere, solid formation is no absolute criterion of stability, but the compound must have at least a certain amount of stability if its concentration is sufficient to make possible solid formation. It is very likely that all, or almost all, of the mononitro compounds are too unstable to be present in sufficient concentration for the solid to form. It would be expected from the ionic theory that substituents other than the nitro group in the nitro molecule would produce an effect similar to the effect of the nitro group. There are no substituents which can accept electrons as well as the nitro group, but there are some which can receive electrons from the ring in positions ortho and para to a nitro group, making it easier for the nitro group to receive a charge. Picric acid affords the best known example of a nitro compound in which another substituent plays a role in molecular compound formation. The compara­ tive stability of picric acid-aromatic hydrocarbon -23- compounds is well known. The reaction is not an acid- base reaction, but one in which the hydroxy grouptends to receive electrons from the positions which are ortho and par-a to the three nitro groups. It is possible for picric acid to act as an acid in reactions involving strong bases, but this reaction does not represent molecular compound formation. However, the hydroxy group does not aid this process much, since it does not accept electrons well. Buehler and others (47,48) show that the presence of the hydroxy group in the ortho or para position stabilizes the molecular compound only slightly in comparison with the nitro compound which has no substituent. They also report the effect of several other substituents on the stability of the molecular compoxmd formed from the nitro compound. The substituent in the.most stable compound is given first: Cl, Br, OH, H, CH,j, NHg. The nature of these groups is well known and the order of stability is what would be expected if the stability depends upon the ease with which the nitro group can accept an electron. (2) Aliphatic. It is not necessary that, the nitro compound be aromatic. Tetranitromethane (12,49) is well known to give deep color with many donor molecules, although no solid compounds have been isolated. The colored solutions have been studied at -24- length, and there is no doubt that the interaction is that which is characteristic of molecular compound formation. This is not restricted to tetranitromethane Will (50) reports that hexanitroethane imparts a yellow color to benzene or to toluene, as well as forming a red compound with naphthalene. The relation between aromatic and aliphatic nitro compounds in molecular compound formation is discussed by Briegleb (12) who concludes that since the stability of tetranitromethane complexes is smaller than polynitro aromatic compound complexes, the difference is due to the freedom of the nitro groups. The freer they are with respect to each other, the greater the interaction with donor mole­ cules. He does not prove, mathematically that the interaction energy (which he calculates theoretically, as well as obtaining it from experiment) decreases as the nitro groups become closer to each other. If the energy of interaction is to be explained by the ionic theory, it is also possible to explain the difference between aliphatic and aromatic nitro compounds. It is much easier for nitro groups to donate electrons to the ring than to donate electrons to the carbon atom in tetranitromethane. In both cases the received electron would oscillate between several nitro groups; this is much easier where the nitrogen-oxygen bond is conjugated with the ring. -25- (4) The color of molecular compounds. Molecular compounds are known to have a deep color In solution, and this is usually, although not always, carried over to the solid state. The color produced is always deeper than that of the components. Since the absorp­ tion of light is undoubtedly closely connected with the interaction between donor molecules and acceptor molecules, a close examination of color phenomena should be important in the study of these compounds. The observed color, reported in many papers and in this work, is usually not given adequate treatment. Hunter and coworkers (51) dismiss the cause of the color with the remark, "Colour is produced by deforma­ tion which throws absorption into the visible region." The actual nature of this "deformation" (of the electron cloud) is of interest, and it has been discussed at .length in a few papers. No absorption peaks characteristic of the mole­ cular compound have been observed. This probably indicates the color observed is merely a shift of the absorption of at least one of the components towards the red. These, solutions vary from a faint yellow to a deep red. There seems to be no correlation between the absorption shift of either component and the stability of the molecular compound formed (measured by equilibrium constants and heats of interaction). -26- According to Weiss, (22) ions are formed having an odd number of electrons. This means there is an unoccupied energy level, and only a small excitation energy is required for absorption. Mullikan (52) says that resonance structures, such as these, which have a separation of charge, have strong visible absorp­ tion. Weiss (53) also makes a comparison of molecular compounds of aromatic hydrocarbons with s-trinitrobenzene and the molecular compounds of some fully conjugated ketones with s-trinitrobenzene. These ketones show deep color when protonated due to large loss of electrons on the part of the ketone. of electrons is ion formation. This loss Since these ketones also give a deep color with the formation of molecular compounds, this is certainly consistent with, but not proof of, the ionic theory. Weiss describes the interaction in systems in which there are separated spheres of influence. 1:2 compounds may form. Here First one region of influence reacts to give a 1:1 compound, and this compound acts as a donor or acceptor molecule and reacts to form a doubly charged ion. Such a doubly charged ion has an even number of electrons, and it is not as deeply colored as the free-radical-like ion of the 1;1 com­ pound, which has an odd number of electrons. -27- Briegleb (12) associates the loosely bound, electrons,, which in his theory, are polarized by the nitro compound, with the visible absorption noted. Hammick and Yule (19) point out that there are known dipole interactions, such as those in which different nitro compounds are mixed with each other, which do not produce color as would be expected according to the theory of Briegleb. It is pointed out by Hammick and coworkers (54) that even in some cases in which molecules repel each other color characteristic of the molecular interaction is produced. Methyl-4,6,4 *,5', - tetranitrodiphenate and mesitylene, for example, separate into two colored liquid layers; apparently a small amount of each component dissolving in the other forming some molecular compound. Hammick (55) does, however, state there is no covalent bond formation, and accepts the idea of an absorption shift of the nitro compound. This does not invalidate his criticism of the work of Briegleb. Gibson and Loeffler (18) conclude that the nitroso group in the nitro molecule is the seat of the observed absorption since nitrosobenzene is at least as capable of bringing about deep color with aromatic hydrocarbons as is nitrobenzene, and since the absorption shift would have to be too large if the hydrocarbon were responsible. -28- Hydrocarbons such as benzene and. toluene, the hydrocarbons which would have the greatest shift, would have an absorption shift o of 1500 A., but it is observed with anthracene-tetranitromethane and acenaphthene-tetranitromethane that the shift in absorption is this great, no matter which compound is affected. The possibility that it is a shift in the absorption of the hydrocarbon cannot be ruled out for the reason given by Gibson and Loeffler. Pauling (20) ascribes color to the stabilization of color-producing separation of charge resonance structures of the molecule. This stabilization is brought about by the effective increase in the dielec­ tric constant caused by aromatic hydrocarbon molecules, since the coulombic force between separated charges is inversely proportional to the dielectric constant. The effective increase in dielectric constant is due to the large polarizability of the donor molecules. According to Pauling, picric acid owes its color to the structures which have a separation of charge. There is some dispute in the literature as to whether or not pure undissociated picric acid is colored, but the assumption of Pauling that it is colored is consistent with the inability of the present author to obtain colorless picric acid, jn Table 1 in the experimental section it is seen that there is some -29- absorption by picric acid at the lower edge of the visible region when It is dissolved in carbon tetra­ chloride. It is difficult to believe that the picrate ion could be responsible for absorption in such a solvent; it can only be concluded that undissociated picric acid is faintly yellow, indicating the ideas of Pauling may be correct. A decision as to the origin of the color of molecular compounds must rest upon the nature of the compounds, each theory of interaction affording a different theory of color. It is not possible to use color as a means of deciding between the covalent, ionic, and polarization theories. If it can be shown that one of the proposed theories is the correct one, then the corresponding color theory must be accepted. There apparently has been no work on the infrared absorption of molecular compounds. Studies in this region of the spectrum could prove' fruitful, as it seems likely intermolecular vibrations, which could be measured in the infrared region, would be dependent upon the nature of the interaction. In general, the amount of interaction in solution is found to be small, and is most often estimated quantitatively by the amount of color produced. Hunter and coworkers (51) conclude that the extent of inter­ action (in several typical molecular compound systems) -30- is at the most very small. However, examination of their data shows that the interaction in, for example, the naphthalene-picric acid system may he fairly large. They suggest that the deviations observed are of the same order of magnitude as deviations expected from a change of solvent. The inference that the observed effect is a solvent effect is probably not true, but the work of many others confirms the idea that the amount of molecular compound formed in solution is small. Further discussion of the use of color in making quantitative measurements is given in the section on equilibrium measurements. 5. Equilibrium me a sur ement s on molecular compounds in solution. The problem of determining the position of the equilibrium in the interaction which forms molecular compounds has been the subject of wide interest. Although there are some who prefer other criteria, it is generally assumed that the" equilibrium constant may be used as a measure of the stability of molecular compounds. Although workers who advance one of the polarization theories imply that calculated equilibrium constants have no meaning, a search of the literature reveals that no one states flatly that there are no true equilibrium constants. a. Reversibility. There is 110 doubt, however, that the molecular interaction is reversible. -31- ^ibson and Loeffler (18) cite a few proofs: (1) Mixtures of aniline and nitrobenzene give a deep color; if dilute hydrochloric acid is added the color disappears, apparently because the anilinium ion is formed. the acid is removed, the deep color returns. If (2) If the aniline-nitrobenzene mixture is frozen, the color disappears, but returns upon melting. There is also other evidence in the literature to prove reversibility. b. The problem of true equilibrium. It may be that these reversible interactions do not represent true equilibria, a problem which is not discussed adequately in the literature. Those who assume that true equilibrium exists apparently do not give much consideration to any other possibility, and those who seem to doubt that a true equilibrium exists do not give a discussion of the problem.. Experimental results are given in the literature with the assumption that the answer to this question is known. Experimental results intended to decide this question are given in this paper, and the conclusion is reached that there is a ' true equilibrium. Gibson and Loeffler (18) explain the phenomena observed for so-called molecular compounds without assuming a small amount of chemical compound formation. By a chemical bond they mean a covalent bond. They discuss neither the possibility of an ionic bond nor -32- equilibrium constants. However, they do state that only a certain fraction of molecules take part in the interaction at a given moment. Whether or not this fraction can give a true equilibrium constant would seem to be an important question. They merely describe the interaction without discussing their "probability of interaction" in a quantitative manner, as an inductomeric polarization. Although they do not make themselves clear on this point, apparently they consider the interaction to be one that is stronger than ordinary dipole interactions. If they mean that the interaction Is a dipole interaction, and that, therefore, no equilibrium constant is calculable, then the data presented in this paper is not in agreement with their postulate. These data show an equilibrium constant which is constant over a very wide range of concen­ tration. There are two other difficulties which may arise even though the calculated equilibrium constant appears to be a true one. There may be a difficulty similar to that encountered with strong electrolytes for which an apparently consistent dissociation constant can be calculated, although in actuality dissociation is complete at all concentrations. This anomaly arises from the use of concentrations instead of activities for strong electrolytes, since even in -33- fairly dilute solutions the electric field surrounding each ion is large. In the molecular interactions studied, this difficulty does not arise because the components--except in some special cases— are always non-electrolytes dilute enough so that concentrations may be substituted for activities, and the molecular compound (or its ions) produced is so dilute that substituting concentrations for activities is per­ missible, even if ions are formed. Since it seems likely that concentrations may be used to calculate an equilibrium constant, it is.probable that the constant obtained is a true one. The other difficulty which may lead to a false conclusion from the constancy of the calculated equilibrium constant concerns a change in the constant measured spectrophotometrically with a change in the wavelength. This might arise if the shift in absorp­ tion of, for example, the nitro molecule depended upon the degree of interpenetration of the interacting moleoules, and if this degree of interpenetration were not always the same. Then the pairs of molecules which penetrate each other most would give absorption at the lowest wavelength and, since such interpenetra­ tion would be least likely, the lowest intensity. The experimental facts show an absorption completely different from this, and the equilibrium constants -34- calculated (given in the present work) do not vary with wavelength. This possibility of a change in equilibrium constant with wavelength is ignored by those who use color to calculate the constant, as in almost all cases the values given are obtained at only one wavelength. Gibson and Loeffler (18)- attempt to prove their polarization mechanism by studying the effect of pressure and heat on the color produced by molecular compounds. They find that the color increases with increase in pressure at constant temperature. The color increases with increase in temperature if the pressure is increased in such a way that the volume is held constant. The color increases or decreases with an increase in temperature at constant pressure; the tendency to decrease with an increase in temperature is smaller at higher pressures. All these measure­ ments were made on mixture of pure liquids such as nitrobenzene and aniline. They assume a picture of the liquid state (56-59) in which one molecule oscillates in a cage of stationary molecules. They show that thei3? experimental results are consistent with their theory of liquids. However, these results can also be consistent with a kind of interaction in which a true equilibrium constant may be calculated. Weiss (22) states, assuming the ionic theory, that they really -35- measure the effect of pressure on the equilibrium A -H B — » (AB) ^=^ A -t B' The phenomena noted above may all be explained in terms of some kind of equilibrium: (1) Even though there is an increase in volume on mixing, the interaction in which AB is formed may in itself cause a decrease in volume, and this would have a positive pressure coefficient. (2) The increase in absorption as the temperature is increased at constant volume may also be considered as an increase in color with an increase in pressure at constant volume. Increasing the temperature at constant pressure causes the amount of interaction to decrease slightly while increasing the pressure at constant temperature markedly increases interaction. Noting changes at constant volume merely combines these two effects, and it is to be expected that the larger effect of pressure predominates. (3) The temperature effect on color at constant pressure may be the resultant of several effects, as is discussed more fully in the section on the heat of reaction. Either a positive or a negative temperature coefficient is possible if there is equilibrium established. None of these phenomena permit a decision on the nature of the molecular interaction. 'The first two above are consistent with the polarization theory -36- and the theories that presume a chemical equilibrium, '■^'he third may be inconsistent with the polarization theory that Gibson and Loeffler postulate, but it is not inconsistent with all polarization theories. c. Methods of obtaining equilibrium, constants. (1) Hammick and coworkers (39,49) have obtained quantities which are proportional to equilibrium constants. equilibrium They do this colorimetrically for the A B C ; the equilibrium constant may be expressed by: c .k (¥p? ' where a,b represent the initial number of moles of A and B in volume v and c/v represents the equilibrium concentration of the molecular compound G. Then; c k = _________ (a-c)(b-c) and /6 c \ a-c____ a+-b~2c+v/k \3"’E/a,v If the amount of molecular compound is small, then c<^ a+-b-2c. Then, by approximation: ( & c \ _ Since d = Elc/v -37- ak where d is the optical density, E is the extinction coefficient of the molecular compound, and 1 is the cell thickness, a,v v El Rearranging: This last equation is slightly different in their paper (49) due to an algebraic error which Hammick acknowledges in a later paper (39). Thus, if several different solutions of A and B. are made in such a way so that b varies while a and v are constant, plotting d vs. b should give a straight line whose slope involves the product of k and E, as well as known constants. Hammick and coworkers report kE for molecular compounds involving tetranitromethane and many aromatic hydrocarbons. They assume that the extinction coefficient is approximately the same for the various molecular compounds they report, and that the kE values are then indicative of relative stability in the same way that equilibrium constants indicate stability. Discussion of these relative stabilities is included in the section on the nature of the donor and the acceptor molecules. -38- The assumption that the extinction coefficient does not vary from one molecular compound to another when the aromatic hydrocarbons may be substances as dissimilar as benzene and be, but is not, proved. -methylnaphthalene should In order to shorn' that this assumption is logical they compare their relative stabilities with equilibrium constants reported by Dimroth and Bamberger (discussed below) for the molecular compounds of some of the same hydrocarbons with picric acid. Even if the work of Dimroth and Bamberger in itself were not open to serioxis criticism, the use of such an analogy would permit only the most general of conclusions to be made. It is likely that picric acid and tetranitromethane would act in the same way, but is better to prove this than to assume It. According to them this treatment is necessary because equilibrium constants are not obtainable. It is shown later in this paper that they are obtain­ able, and their assumption concerning the constancy of the extinction coefficient is compared with the results obtained in this work. Only in a very general way may their relative stabilities be accepted. In the above derivation it was assumed that a small amount of molecular compound is formed. Only in such cases, if d is plotted against b, is a straight line obtained. A non-linear curve Is reported for the mesitylene-tetranitromethane compound, and they -39- derive an equation which may be used in this special case: Af in i) _ V ^ej 3Tb -k v Here the equilibrium.constant is obtainable if a plot of lnj^d vs. b gives a straight line, for mesitylene <3b it does give a straight line, and the.equilibrium constant they report is 0.07. For the concentrations given this gives a value of c which is about three percent of b and about two-tenths of one percent of a; apparently c is small enough to meet the conditions of the first derivation and the authors are greatly in error for some reason. They report complexes of tetranitromethane with naphthalene, ^ -methylnaphthalene, 2, 4-dimethylnaphthalene, and ^-naphthol which have a much greater relative stability measured by kE, than the mesitylene compound and they do not find it necessary to give these compounds the special treatment given to the mesitylene compound. The concentrations they use are usually very small, but with the benzene-tetranitromethane compound the concentration of benzene varies from 0.70 M to 2.78 M; the tetranitromethane is 0.42 M. In the present.work tetranitromethane-benzene mixtures of similar concentrations in carbon tetrachloride, the solvent which Hammick uses, are studied, and it is found that no simple relation such as the one they -40- assume exists. It may be that concentrations may not be substituted for activities in solutions as con­ centrated as these. It is difficult to iinderstand how these workers are able to obtain a straight line when plotting d vs. b in solutions concentrated with'respect to benzene. One of the aromatic hydrocarbons they use with tetranitromethane is hexamethylbenzene. In the present work data for the same two components in the same solvent, carbon tetrachloride, show that after the color is produced, it diminishes in intensity rapidly enough so that its intensity is about half its ori­ ginal value in twenty-four hours. It is difficult to imagine that any impurities could bring about such a loss of color, or in the case of the compounds Hammick uses, such a prevention of loss of color. This puts the work of Hammick in further doubt. Among those using colorimetric methods are von Halban and Zimpelman (44) who determine equilibrium constants colorimetrically for several systems involving acenaphthene and anthracene with a few aromatic nitro compounds. (2) The solubility of the components and of the molecular compound formed has been tised to determine the equilibrium constant by Behrend (60), Kuriloff (61), and Bamberger and Dimroth (38). Bamberger and Dimroth determine the concentration of free picric -41- acid, in water in equilibrium with the other compound and the molecular compound formed. Weiss (22) points out that they really assume, in calculating an equilibrium constant, that Henry’s Law holds for each component and the molecular compound formed. This, says 'Weiss, is not true for picric acid because it reacts with water. It is also true that some saturated solutions may be such that concentrations cannot be substituted for activities. (3) Moore, Shepherd, and Goodall (40) mixed aromatic hydrocarbons with picric acid in the solvent chloroform and determined the free picric acid by noting its concentration in a water phase in equili­ brium with the chloroform phase. (This requires knowledge of the distribution coefficient of picric acid between water and chloroform.) Hammick and Young (49) point out that this method measures not only the chemical effect which causes color, hut also dipole effects, introducing error into the results. (4) Brown (62) determines the equilibrium constant of naphthalene-picric acid and naphthalenes-trinitrobenzene in nitrobenzene as solvent by measuring the freezing point depression. (5) Bronsted (63) reports the free energy of reaction obtained from electromotive force measure­ ments. Bronsted made measurements on the system naphthalene-picric acid-KCl-ECl-water. -42- The measurements are made with solid naphthalene and picric acid. 6. The heat of formation of molecular compounds in solution. When components are mixed to form mole­ cular compounds, there is a heat effect. For example, this can be observed in dilute solution by measuring the■temperature coefficient of color. The heat effect is of the order of magnitude of two kilocalories per mole. Weiss (22) points out that the heat of interaction is actually a very complex quantity; he shows that if ions are formed, the heat of formation of the mole­ cular compound AB, AH/ = A H is given by the exact equation: - Qa - Qb ■+ Q^g - IA -+- Eg -+■ U c -+• Up •+■ U D r* U R where the Q, terms refer to the heats of solution of A, B, and AB; 1^ is the ionization potential of the donor molecule, and Eg is the electron affinity of the acceptor molecule (both in the gaseous state); U c is the coulombic attraction energy; Up is the energy due to polarization forces; Ug is the energy due to dispersion forces, and Ug is the repulsion potential. Weiss is incorrect in stating that the formation of molecular compound increases with an increase in temperature. He seems to be confused in the signs of AH and the Q terms. If measurements were made in the gaseous state, the first three terms would be omitted, but prediction -43- of the heat of formation would still be very difficult. Weiss criticizes the measurement Briegleb (discussed below) makes on the heat of formation in solution because it loses its significance when complicated by the heats of solution. Hovtfever, measurement in inert solvents, such as carbon tetrachloride, which Briegleb often uses, should remove this difficulty becaij.se then the three Q values are probably small enough to be neglected. Experimentally, it is shown to be true by Hammick and Yule (19) that if a solvent is not inert values are affected considerably. AH They use a spectrophotometric method along with the determination of Ek values discussed in the section on equilibrium measurements. They measure the optical density (used to determine k values, also) at different temperatures, and they apply the equation derived in earlier paper (49). In this derivation they assume that there is no appreciable change In the volume of the solvent over the range of temperature with which they are concerned, 15-60° G. This is not warranted at all, and it probably introduces an error, since the change in optical density due to -44- the change In the amount of molecular compound formed at the different temperatures is small. Hammick and Yule report A H values for tetra­ nitromethane with naphthalene, o^-methylnaphthalene, and ^-metbylnaphthalene and for diphenylamine with mono- and dinitrochlorobenzene; all these are measured in several solvents; some are measured in as many as ten solvents. The four Inert solvents are carbon tetrachloride, ethylenedichlor_i.de, n-hexane, and % tetrachloroethane, which all have low dielectric constants. In all cases the heat of formation is negative, as expected. The reaction Is exothermic. The six polar solvents are methylphenylketone, cyclohexanone, acetone, n-propyl alcohol, ethyl alcohol, and methyl alcohol; in all. cases A H is more positive than in the inert solvents. Where tetranitromethane Is the nitro molecule all A H values are positive; in..the diphenylamine systems all AH values are negative, but are less negative than when measured In the inert solvents. Hammick and Yule offer an explana­ tion of the solvent effect. An explanation of non-solvent terms in the expression for A H is of greater interest. While Weiss discusses the theoretical value in terms of his ionization theory, Briegleb (17) actually calculates the energy of interaction assuming that the interaction -45- is one in which a permanent dipole (of the nitro molecule) induces a dipole in the polarizable aromatic hydrocarbon. This is described in some detail for the inter­ action between p-dinitrobenzene and naphthalene. He assumes that the two planar molecules lie super­ imposed one on another in parallel planes about 3 £. apart. This distance is about twice the so-called "radius of action" of the carbon atom;, the regions of action of the two molecules thus are assumed to touch one another. The induction energy, AH, for this interaction is given by: AH = * 2 m2 E where c*. is the polarizability of the carbon-hydrogen -24 bond (0.65 x 10 ) or of the carbon-carbon bond -24 (1.06 x 10 ), and E is the field set up by the dipole. o( is calculated from a knowledge of the index of refraction; E is calculated from a knowledge of the permanent dipole moment one nitro group gives to p-nitrobenzene and from geometrical considerations. This is discussed with the aid of adjacent figures. The effect of the two nitro groups on each bond in the hydrocarbon is calculated, and the sum of all such effects is the interaction energy which is the same as the heat of reaction in the gaseous state. -46- The figure on the left is a planar representation of the quantities involved in the polarization of one naphthalene bond as shown on the right. All the distances and angles are known if the interplanar o distance of 3 A. is assumed; values must be known. Ev and Ev , the components of E, may then be calculated: Jrk. X E„ - M (3 cos2£>, X — 5~ ' Ev x- 3* sin d, cos g~ 1) - sq (3 c o s ^ 3^ — sin ©, cos &, rl - 1) — 7” -r r2 (These equations are the corrected ones reported in errata, Z. phys. Ghem., B27, 474 (1934).) The sum of the A H values obtained is the energy of interaction. ■The interaction energies Briegleb obtains in this way are of the same order of magnitude as those he obtains spectrophotometrically; the predicted value differs from the experimental value by as much as fifty per cent. As predicted, compounds which have a higher <* (polarizability) value bring about an interaction that evolves more energy. -47- The general agreement which Briegleb obtains between calculated and experimental values is ho proof of his polarization theory. This might be sufficient proof if his calculated values were very close to the experimental values. The absolute values of the energy of interaction are all small and it is difficult to differentiate between the effect of change of solvent, the heat of reaction (if there is a chemical reaction), and the interaction energy of the polarization effect (if the polarization theory holds). It is very likely that similar values for the energy of interaction could be calculated on the basis of the other theories. For example, Briegleb shows that the energy of interaction increases, as the polarizability of the hydrocarbon increases,which agrees with experimental results. A detailed analysis- of the quantities in Weiss’ equation for A H (see above) would reveal that several of these quantities would be greatly affected in changing from a less to a more polarizable hydrocarbon (such as proceeding from benzene to naphthalene). Briegleb admits that due to the difficulty introduced by omitting the heats of solution, the absolute values are not significant. He gives meaning only to the changes noted with a change in one component. It Is likely, as Hammick and Yule (19) point out, that the -48- energy of interaction is far too small for an ordinary / ° (presumably covalent)v bond length of 1 - 2 A . ; the force involved varies with the reciprocal of the power of the distance, and this requires a much greater bond energy for a bond of such a length. Instead of the energy of interaction Gibson and Loeffler (18) discuss the color coefficient of tem­ perature. According to thermodynamics, the heat of reaction for the formation of the compound is negative if the equilibrium constant for compound formation, of the color produced, decreases with an increase in temperature; this decrease must be independent of the corresponding volume change of the solvent. By considering the structure of the liquid, they explain that the color coefficient of temperature may be either positive or negative. They postulate a cage of stationary molecules containing an oscillating molecule of the other component which produces color when it collides with the wall of the cage. Increasing the temperature at constant pressure has two effects: the "free volume" of the oscillating molecule increases and the number of collisions decreases, vmile the kinetic energy of the oscillating molecule increases and the number of collisions is proportional to the intensity of the color produced If the temperature.coefficient of color at constant pressure is positive, the latter effect predominates; if it is negative, the former predominates. This theory is made more plausible by showing that if the volume of the solvent is kept constant (by increasing the pressure from 1 to 1000 bars) while the temperature is increased from 25° to 85°, the temperature coefficient of color is always positive, as contrasted with the variable nature of the temperature coefficient when the pressure is kept constant. These phenomena may be explained by both the polarization and the chemical reaction theories. Other experimental findings reported in this work and supported by similar evidence in the literature, are evidence against the polarization theory of Gibson and Loeffler. If there is a chemical reaction, it may be accompanied by a decrease in volume and an evolution of heat. It also may be that the effect of increased pressure which Gibson and Loeffler use to maintain constant volume greatly offsets the corresponding increase in temperature. This would explain why they always obtain a positive temperature coefficient at constant volume, which is the same as a positive pressure coefficient at constant volume. But it may also be that the effect of increased pressure does not offset the effect of increased temperature and that the color coefficient of temperature -50- is negative at constant volume. No data of Gibson and Loeffler show this, but the possibility exists from chemical reaction theory. The heat of reaction data in this paper show that such situations do exist. The volumes of the solutions studied are not kept constant, but a correction is applied so that the heat of reaction reported is that for constant volume. The heat values obtained are usually nega­ tive, corresponding to a negative temperature coef­ ficient of color at constant volume. The heats of reaction Briegleb and others report are often -3 or -4 kilocalories; the correction for the change of volume of the solvent over the temperature interval used (usually less than thirty degrees) would not be sufficient to change the sign of the heat of reaction. A negative heat of reaction under these conditions is not possible according to the theory of Gibson and Loeffler. There is a question as to whether or not the relative heat of reaction values are a measure of the stability of the compound or the polarization aggre­ gation formed. It is certain that the experimental error involved Is much larger in the heat measure­ ments than in equilibrium constant measurements. Often the former values lose their meaning when they are compared with one another, the limit of error -51- being too large. Free energy, or equilibrium constant, measurements are also more significant because they take into account the entropy changes accompanying reactions. The necessity for such a treatment in equilibrium calculations for molecular compound associations is noted by H e r (64). Others, as von Halban and Zimpelman (44) report values of the heats of formation of molecular compounds from color data. ^• Electrical and magnetic properties of mole­ cular compounds. a. Dipole moments. One of the principal arguments for the ionic theory offered by Weiss is the existence of dipole moments of certain molecular compounds. If molecular compound formation consists of an electron transfer, this should give rise to a permanent dipole moment in the molecular compound. Since the molecular compound and its components are slightly soluble in solvents used and the amount of molecular compound formed is very small, it would seem likely that no measurable moment nvould be observed in solution. Weiss (22) reviews the subject and points out that several workers are able to make significant measurements under more favorable conditions (16, 65,66,67). s-trinitrobenzene and p-dinitrobenzene are each dissolved in carbon tetrachloride and -52- chloroform. In all cases there is no permanent dipole moment. Each of these same two nitro compounds Is also dissolved in benzene and molten naphthalene; in all cases^t is between 0.7 and 1.0 Bebye unit. b. Ions in solution. Possible evidence for the ionic theory is available from the electrical proper­ ties of certain solutions of molecular compounds. If the ionic theory holds, solutions of molecular com­ pounds should have a measurable conductance if an ionizing solvent is used, and if the amount of mole­ cular compound formed is fairly large. Several such observations are recorded. Kraus and Bray (68) show that both s-trinitrobenzene and dinitrobenzene dissolve in liquid ammonia to give a deep color. Apparently ammonia is a donor molecule and colorless (NHg)"*" forms. The nitro compound accepts an electron causing the deep color. Garner and coworkers (69,70) show that these solutions may be electrolyzed with migration of the nitro anion to the anode. They also show by measuring the color that the conductivity is proportional to the ion concentration, if the ion concentration may be measured by the color produced. This proves that some nitro compounds which form molecular compounds with aromatic hydrocarbons and amines, form ionic molecular compounds with liquid ammonia. -55- Weiss (22) reports he is able to prepare a deeply colored, compound of s-trinitrobenzene and other nitro compounds with alkali metals like potas­ sium and sodium by making an ether solution of the nitro compound with the finely divided alkali metal. It is also possible to show that the donor molecules can form positive ions under favorable conditions. Walden (71) shows that anthracene dis­ solves in liquid sulfur dioxide to give a yellow color to a solution that has measurable conductivity. He also shows that some amines have a much deeper color in liquid sulfur dioxide, and that the equi­ valent conductance of the amine solution is much higher than that of an anthracene solution at similar concentrations. The difference in the conductivity is due to the difference in the number of ions formed. In these solutions the SOg molecule accepts an electron; + in anthracene solutions the (C^H-^q ) ion forms. Weiss (22) points out that sxich aromatic hydro­ carbons can also accept an electron from a metal. Compounds as anthracene and naphthalene can form addition compounds with sodium or potassium. Thus, these hydrocarbons are amphoteric. Several salts of aromatic hydrocarbons have been prepared. In all cases the hydrocarbon molecule becomes the cation. perchlorate. Weiss (72,73) prepares anthracene The composition of anthracene perchlorate -54- is proved by elementary analysis. It is dark brown, conducts current in and is very soluble in acetone, and there is a deposit at the cathode in electrolysis. Other salts reported are the perchlorates, sulfates, and pyrophosphates of coronene, 1,2-benzperylene, 3,4-benzpyrene, and anthracene. None of the above evidence is for the class of molecular compounds discussed in this paper. It is true that solutions of naphthalene with picric acid and anthracene with s-Lrinitrobenzene dissolved in liquid sulfur dioxide have a measurable conductivity, but it is possible that this is due to the reaction of the hydrocarbon molecule with the solvent. These facts show that the ions postulated by Weiss for molecular compounds can form under favorable conditions. The evidence for the formation of such ions in inert solvents is not sufficient. It cannot be supposed that the existence of these ions in ionizing solvents, such as liquid ammonia and liquid sulfur dioxide, proves their existence in inert solvents. Hydrogen chloride, for example, is covalent when dissolved in benzene, but largely dissociates into ions when dissolved in water. However, the - existence of these ions under certain conditions shows that they may exist in Inert solvents. c. compounds. Magnetic susceptibility of solid molecular Kronberger and Weiss (30) state that if -55- >Tf electrons are transferred in molecular compound formation, the magnetic suseptibility of the compound is less than the sum of the magnetic suseptibilities of the components; this is a negative deviation. They relate the same phenomenon to a decrease in polarization. With the formation of s-trinitrobenzene-perylene there is a great 4ecrease an magnetic suseptibility. (Positive deviations are possible; there is a slight increase with the formation of quinhydrone, the molecular compound formed by the addition of quinone to hydr-oquinone (74, 75).) According to Kronberger and Weiss, these results are predictable from polarization measurements. Sahney and coworkers (21,76) report the magnetic susceptibility of many molecular compounds and their components; the nitro compounds are s-trinitrobenzene, 2,4-dinitrophenol, and 2,4-dinitro-l-chlorobenzene; some of the donor molecules are naphthalene, phenanthrene, anthracene, q ( -nitronaphthalene,o< -naphthol, and aniline. Of the twenty-one molecular compounds reported, sixteen have large negative deviations; one molecular compound, benzidine-s-trinitrobenzene, has no deviation; and 2,4-dinitro-l-chlorobenzene with p-naphthol,©(-naphthylamine and aniline; 2,4-dinitro­ phenol with aniline have positive deviations. For example, the magnetic susceptibility of naphthalene —6 is 91.77 x 10 units; of s-trinitrobenzene, -56- -6 -6 74.81 x ?_C units the sum is 166.58 x 10 units, and the observed value for the molecular compound is -6 -6 163.03 x 10 units, a decrease of 3.55 x 10 units, -6 The largest decrease, 14.19 x 10 units is that observed for fluorene-s-trinitrobenzene; the largest -6 increase, 17.93 x 10 units is that observed for aniline-2,4-dinitro-l-chlorobenzene. There is no noticeable trend among the deviations; they appear to be distributed between the two extremes in a random manner. Sahney and coworkers interpret these results in terms of the various resonance structures of the two components. They conclude that the wide deviations from additivity indicate the differences are not due to any chemical linkage, including ionic, and that the deviations are too large to be due to weak van der Waals forces. They say that there would be no deviation if the polarization idea of Briegleb were valid. They calculate the magnetic susceptibilit;/ for each of the different resonance structures of each component according to a method outlined by &ray and Gruickshank (77). This makes it possible to determine which resonance structiires predominate. If there is a positive deviation, they conclude that the most highly polarized (representing a separation of charge) resonance structures of the nitro compound which have the highest magnetic susceptibilities become the most important, structures of the nitro compound when the molecular compound forms. If there is a negative deviation, they conclude that the non-polarized structures of the donor molecule, which have the lowest magnetic susceptibilities, become the most important structures of the donor molecule when the molecular compound forms. These effects take place simultaneously, but they are usually unequal. They find that deviations are parallel to the amount of "internal ionic character", or the possibility of structures in which there is a separation of charge. They do not explain the actual nature of the bond or the nature of the interaction between the components. In neither of the papers by these workers is there a clear explanation of their theory. There is no explanation of the mechanism by which the non-polar forms of the donor molecule or the polar forms of the acceptor molecule become more important. There is an obvious need for theoretical work in the magnetic susceptibilities of molecular compounds. Their experimental results do not agree with the prediction of Kronberger and Weiss in the three places that the data are comparable. With the molecular compounds of s-trinitrobenzene with phenanthrene, anthracene, and benzidine, the magnetic susceptibility deviations are negative and the dielectric polarization deviations are positive. Kronberger and Weiss expect the two -58- deviations to have the same sign. d. Dielectric polarization of solid molecular compounds. The dielectric molar polarization of mole­ cular compounds is related to the magnetic suscepti­ bility in that it also depends upon the polarizability of the electron cloud of the molecular compound. Kronberger and Weiss (30) report the dielectric constants for some molecular compounds and their components, and they discuss the polarizations calcu­ lated from these. If there is an ionic bond, there would be two principal effects: (l) The molecule that becomes the negative ion becomes more easily polarized because of the increase in the electron cloud and (2) the molecule that becomes the positive ion becomes polarized with more difficulty because the electron cloud becomes fixed. These effects are termed the "softening" and the "hardening" effects, respectively. Kronberger and Weiss obtain polarizations for molecular compounds which are either higher or lower than the sum of the polarizations of the components; this they attribute to the predominance of either the hardening or softening effect. This is formally related to the explanation of magnetic susceptibility deviations given by ^ahney (see above). It is probably presump­ tuous to assume that the observed deviations can only be due to the formation of an ionic bond. It must be remembered that in the few places in which molar -59- polarization data and magnetic susceptibility data are comparable, they do not agree as to the expected sign of the deviation if the ionic theory is assumed. 8. Other properties of molecular compounds. a. Optical rotation. Leslie and Turner (78) resolved the optically active 2,4-dinitro-2-methyldiphenyl with , o brucine, and they found an optical rotation ofxl8.7 . When dissolved in alcohol with benzene, conditions for molecular compound formation are favorable. They noted that the rotation decreases toi;7.8° in the presence of benzene. Hammick and coworkers (54,79) obtain the d-acid by resolution with d-c(-phenylethylamine, and the rotation they observe is +89.8°. This indicates incomplete resolution in the compound pre­ pared by Leslie and Turner. The optical rotation of the d-acid of Hammick and coworkers does not change in the presence of benzene. There is no other evidence in the literature that optical rotation changes with compound formation. Since the mirror images in the nitro compound mentioned above result from hindered rotation, it may be that covalent bond formation would cause a decrease in rotation. It is unlikely that a donor as weak as benzene would bring about enough of an interaction to cause a measurable change in optical rotation. According to the ionic theory there are both polar molecules and free ions. -60- If ions predominated, no change in optical rotation would be expected. b. Hardness. No work has been done on the hardness of molecular compounds, but it has been shown (80) that some organic crystals are similar to ionic crystals, although the relationship is complex. C. General discussion of the problem. The major purpose of the previous discussion is to show that most phenomena cited in the literature offered in support of one particular theory of interaction can be shown either to be consistent with two or more theories, or to be applied incorrectly to the problem. There are two kinds of data available for the solution of a problem such as this. The first is chemical data (equilibrium measurements, etc.) and it is a purpose of the present work to determine some chemical data to aid in the eventual solution of the problem. The second is physical data, which include crystal structure and X-ray diffraction data, color, electric and magnetic data, -and molar polarisation. The position taken here is that ultimately some physical data will have to decide the nature of the interaction, but that there is not enough reliable physical evidence now available to make this decision. Some chemical evidence can aid in the solution to this problem, but it would seem that a decision concerning the nature of the chemical bond or interaction must depend upon certain kinds of physical evidence. -61- It is possible, however, to discuss these theories and indicate what may be the eventual solution. Probably the only theories which need be considered are the covalent, ionic, and polarization theories. There is, of coiirse, the possibility that molecular compounds actually represent some new bond type, but here it is assumed that only these three theories need be considered. All the covalent theories would seem, to be incorrect because ordinarily bond energies much larger than those obtained for molecular compounds are associated with covalent bonds. These larger bond energies are for bonds much shorter than those determined for molecular compounds in the solid state. What is usually meant by the covalent bond cannot very well be the bond existing between the components of a molecular compound. The ionic theory seems to be too extreme a solution of the problem in that it postulates a complete transfer of an electron in solvents which are usually non-ionizing solvents. It would seem that there is no conclusive evidence for this theory, while there may be some evidence against it. It is one thing to postulate the formation of a polar molecule, but quite another to say that this polar molecule breaks down into ions. Some evidence offered to substantiate the ionic theory does not -62- apply to the conditions under discussion; other evidence offered could just as well be consistent with a theory postulating a polar molecule which does not dissociate into ions. The polarization theories vary, but it may be that the actual interaction is that of the formation of a polarization aggregate which is the same thing as a polar molecule, with the shortest distance o between the two components 3-3.5 A. No one who postu­ lates one of the polarization theories attempts to prove that a true chemical equilibrium exists in solution (Briegleb does calculate some equilibrium constants, but does not prove there is a true equilibrium). In the present work it is shown that there is such an equilibrium. Thus, if there is a polarization it is not one in which there are not specific interactions between pairs of molecules, contrary to the ideas of Gibson and Loeffler. If there were a polarization aggregate, or a polar mole­ cule, then the calculations of Briegleb can explain the low interaction energy and the Ideas of Pauling (and others) can explain the color. The existence of an equilibrium and other chemical evidence (including stability) given earlier is in harmony with the idea of Briegleb and Pauling that there are specific interactions between pairs of molecules, not general interactions, as is probably the case with the ions -63- of strong electrolytes. Such a polar molecule would have a permanent dipole moment. It would be difficult to predict the magnetic susceptibility and the molar polarization, but there can be no definite conclusions made from the confusing data on these properties cited above. A problem similar to the one being discussed is the nature of the interaction between iodine and benzene or benzene derivatives, discussed by Benesi and Hildebrand (81). They say that there is an acid-base reaction in the Lewis sense with benzene, an electron donor, a Lewis base and iodine, electron deficient, a Lewis acid. Substituents on the benzene nucleus which tend to increase the electron density in the ring strengthen the compound formed, as would be expected if the aromatic compound acted as a Lewis base. It will be seen that the compound formed here probably is similar to the one formed between tetranitromethane and aromatic hydrocarbons. Tetra- nitromethane is an electron-deficient molecule and it is possible that the polar molecule described above actually is the product of a reaction between a Lev/is acid and a Lewis base. -64- III. THE PRESENT WORK A. The purpose of this work. There are six principal reasons for undertaking this work. -^e determination of the ratio of the com­ ponents in the compounds. Since the methods described below used for the determination of the equilibrium constant utilize measurements made over a much wider concentration range than previously reported, it is also possible to state with greater certainty than was possible earlier the ratio of the components in the compounds. It is also possible to utilize the method of continuous variations, a method used frequently in determining the ratio of reacting substances in solution, on the color of molecular compounds. The use of this method is not reported for these compounds in the literature. determination of whether or not a true equilibrium constant exists. The question of whether or not a true equilibrium constant exists is an important one. The fact that the same constant is obtained over a wide range of concentration and other reasons cited earlier in the section on equili­ brium measurements show that there is a true constant. 3. compounds. The determination of the stability of molecular The equilibrium constants which are -65- determined, not only afford conclusions concerning the questions suggested in the first two points, but they also permit an estimate of the stability of molecular compounds to be made. This is reported for several molecular compounds; all but a few are compounds of tetranitromethane with aromatic hydrocarbons. These results are obtained from spectrophotometric measure­ ment s. 4. The determination of the energy of interaction. The energy of interaction is not useful as a measure of relative stability because the experimental error is far too large, and the entropy of reaction is ignored. It does, however, make possible an estimate of the stability of a whole class of compounds such as the tetranitromethane molecular compounds. The energy of interaction is also necessary for the calculation of the entropy of reaction. The temperature coefficient of color at constant volume can be used to calculate the energy of inter­ action at constant volume, but this coefficient is used as such in the discussion of the polarization theory advanced by Gibson and Loeffler. 5. The determination of the entropy of reaction. Prom the equilibrium constant and the heat of reaction the entropy of reaction is calculated. 6. The determination of the ultraviolet spectra of mixtures containing molecular compounds. -66- It is desirable to determine the nature of the ultraviolet spectra of a few representative solutions containing molecular compounds. An appreciable change in the ultraviolet spectra accompanying molecular compound formation would be of particular interest, since it might indicate the existence of a strong interaction. Lack of such a change would indicate a weak interaction. B. Experimental. 1. Spectrophotometry. All the results listed in the previous section are based upon spectrophotometric measurements; these were all made on a Model DU Beckman Spectrophotometer. Either Sorex (glass) or silica cells which have one centimeter light path were used. Occasionally cells in a set vary so that the cells used for solutions are not identical with the cell used for the solvent alone. All the cells used have been calibrated in order that this correction may be applied. With a few systems the optical densities changed with time. The color produced by mixing hexamethyl- benzene and tetranitromethane in carbon tetrachloride decreased to less than one-half its original intensiiy in twenty-four hours. No calculations could be made with any data of the hexamethylbenzene complex. The reason for this decrease in color is not understood, but it is probable some reaction is followed by molecular compound formation. -67- This phenomenon was not observed by Hammick, as is mentioned in an earlier section. There was also a slow change in the optical densities of mixtures of phenanthrene and acenaphthene with tetranitromethane in carbon tetra­ chloride. However, equilibrium constants and approxi­ mate heats of reaction could be calculated in these cases. Anthracene in solution slowly dimerizes in the presence of light, and the dimer is colored. This was avoided by keeping all anthracene solutions in the dark and by measuring the absorption of these solutions as quickly as possible. To measure the temperature coefficient of color, temperature control in the spectrophotometer was necessary. A suitable attachment to the spectropho­ tometer was not available commercially; so one was built. One half of this attachment is shown in Figure 1. An aluminum plate, g-" thick, was placed on each side of the cell compartment. (It is pos­ sible to insert plates such as these on the DU Spectrophotometer.) The opening in the center allows the light to pass through. Water of the desired temperature enters at A and leaves at B. The dotted lines show possible routes the water may travel. The side of the plate that faces the cells was painted black to avoid any possible light reflection. other side of the plate was separated from the -68- The Te m peratu re C o n t r o l Pl a t e \~ H I E Z 1 |i Drill 4-Ho l e s l-2Sctq X IOc/YfjcI4.5cw A l u mi n u m Plate instrument by a sheet of asbestos for the purpose of insulation, although there is little danger that the rather small temperature differentials used would affect the instrument. Screws which connect the phototube housing to the main part of the instrument were replaced with longer screws to take care of the thickness of the plates. The water was circulated by means of an ordinary water pump from a refrigerated bath. Since tetra­ nitromethane freezes at 13°, and the solid is much less soluble in carbon tetrachloride, the solvent used, the temperature in the cells was kept above 13°. Usually, the highest temperature used was about 28°. Where picric acid was used the lowest temperature was about 6°. To avoid condensation of water vapor at these temperatures, since often the dew point is only a few degrees below room temperature, the cells were kept' in the cell compartment until all the measure­ ments at all the temperatures were completed, by sealing the cell compartment, and by keeping ‘ Uri.erite in the cell holder in place of one of the cells. All the readings could be taken in a few hours because the bath temperature could be changed three or four degrees in about fifteen minutes. The compartment was sealed at the top by use of a weighted rubber cover and by use of stopcock grease which was used -69- at all possible openings of the-compartment. Since the solutions were kept in the cells for a few hours, it was necessary to prevent loss of the volatile substances. As no glass stoppered cells were available when this work was done, the cells that -were used had their loose fitting covers sealed on by means of a wax. The temperature in the cells was determined by ascertaining the temperature difference between the bath and the cells at different temperatures under the conditions of the experiment. A thermometer was placed In the cells (which were then covered) and the temperature difference between the cells and the bath was noted. A 0-50° thermometer calibrated in tenths was used for all measurements. There may be a small error in the absolute values of the temperatures obtained in this way, but only the relative values are needed, and these are undoubtedly more accurate than necessary, since there is greater error in the optical densities measured. 2. Materials. The solvents used were d.p. grade. The hydrocarbons were recrystallized several times from ethanol or benzene, except 1,2-benzanthracene, which was recrystallized from a mixture of acetic acid and ethanol. Picric acid was recrystallized from water; a glass fritted filter was used to avoid the formation of addition compounds with filter paper. -70- The purity of the hydrocarbons was determined by the constancy of the melting point; the melting points of sucessive recrystallizations were determined simultaneously to minimize errors. All the melting points were in good agreement with those found in the literature. The purity of the picric acid was assayed by neutralization with alkali, using methyl red as indicator (82). It was found to be slightly less than 99% pure, the impurity probably being water which could not be removed. The melting point agreed well with that found in the literature. It Is certain that the small amount of water impurity would have no appreciable effect upon the optical measurements made. The tetranitromethane used was prepared according to the method of Chattaway (83). Fuming nitric acid (the anhydrous fuming nitric acid recommended by Chattaway was found not to be necessary) was mixed with acetic anhydride and kept in an ice bath for several hours; care was taken not to agitate the mixture for several days. At the end of a week the product separated with the addition of a large excess of water. The oily liquid was washed with water and dilute sodium carbonate and dried over sodium sulfate. The product was purified by fractional o distillation at 15-25 mm. of mercury at 25-30 to prevent decomposition below 125°, the boiling point. -71- The color of all lots was fairly yellow, Hammick and Young (49) report the preparation of colorless tetranitromethane, but recent work that has been done very carefully by Nicholson (84) shows that the colorless compound probably cannot be prepared, Nicholson very carefully prepared pure tetranitromethane and he reports physical constants which are probably more reliable than others in the litera­ ture, The freezing point he reports, 13.8°, is o higher than any other given; some are as low as 12.5 , He found that the method of preparation of Chattaway (the method used in this work) could yield a pure product only with many distillations. '^he physical constants of the substance he prepared by another method with very laborious purification are compared with those of the substance used in the work of the present author. The refractive index he reports at 20° for the D-line of sodium is 1.4384; for the substance of this work, all lots had refractive indices between 1.4376 and 1.4381. This is signi­ ficantly lower than Nicholson’s value. The density / obtained by Nicholson is 1.630 g/ml. at 25° ; one lot of the tetranitromethane of this work had a density of 1.622 at 25°. The tetranitromethane prepared here was distilled in a six plate column after drying. It may be that the product was.impure, but it is not believed that the results of the work are seriously affected. -72- Nicholson suggests that the chief impurity may be trinitromethane. It would seem that this substance would act in a manner similar to that of tetranitro­ methane in molecular compound formation. To prepare tetranitromethane whose purity approached that of the substance prepared by Nicholson would be pro­ hibitively difficult, since he was only able to prepare a few samples of one milliliter each, while a few hundred milliliters were used in the present work. The optical densities of tetranitromethane and of picric acid in the visible region are given in Table 1. C. Treatment of the data. 1. Equilibrium constants. In order to achieve the aims set forth it is necessary to be able to calculate a true equilibrium constant over wide ranges of concentrations. The method of obtaining this constant follows. Let the reaction represent the reversible formation of a molecular compound AB from components A and B. Let c-^ anb. Cg be the initial molar concentrations of A and B, respectively, and Xj the equilibrium molar concentra­ tion of AB. Then the equilibrium constant K is given by -73- We assume xj, the amount of molecular compound formed, is small; this is justified, since it is found to be true with the use of this assumption. 2 Then Xj may be ignored in comparison with c^x-j- or CgX^., since either c^ or Cg or both always are much larger than x^-. (2) Then K (°1c2“clxI“c2xl) = xi Dividing both sides of this equation by Kx^ Cl°2 Xj “ Ci - c2 - 1 K The optical density at a given wavelength, d, may be defined for this solution in terms of E, the molar extinction coefficient, (4) dj = XjE dj is the observed optical density when the molecular compound formed is the only colored substance. In some instances one of the components absorbs slightly in the region of interest. The absorption calculated to be due to a component is subtracted from the observed absorption. This approximation is justified because it always produced results consistent with those obtained where the correction was unnecessary. Substituting in the above, Solving for E, (6) E = dI c2 ^ dI °1 1 K dI °lc2 d of another solution of the compounds can be measured, giving a similar equation. Then ci becomes c^, cg becomes c^, and d^ becomes d^^. (?) E = dH + Then dII + _ L _ c4 c3 K dII C3C4 The right hand sides of these two equations can be equated and these two solutions can be chosen so that the concentration of A changes while the concentra­ tion of B remains constant; therefore, c^ may be substituted for c . 4 <8 ) dI . dI c2 + C1 Then 1 dl K clc2 - dH C2 , dH r C3 ^ Rearranging, (9) 1 / dI ^ ^clc2 dII \ c2 c 3 J dII , dII c2 °3 Rearranging further, . . dTTdn (10) = K dT °1 Dividing as shown, (H) dII°2 dI°2 0, ~ c, 3 1 _1_ _ d II C3 dII~ dI - K ' dI _ dII C1 c3 -75- c2 dI °2 1 dI C1 dH c 2c3 This is one of the desired equations. When Cg is small and K is also small, Cg may be neglected, ‘ ^'his is usually the case, but there is no difficulty when this approximation is not made. The equilibrium constant could be calculated from (11) if the d values could be known with suf­ ficient accuracy. However, in practice the difference between d^/c-^ and dj^/c^ is small in comparison to the absolute values, and so the inevitable error in the optical measurement leads to a very large error in the equilibrium constant. Wo consistent results were obtainable by comparing the K values obtained from different pairs of solutions. Equation (11) could be used if d^. and d ^ were accurately known. No improvement could be affected by taking an average of several measurements, but it was found possible to use equation (5) C1C2E _Ci _ c2 - dI 1 K to obtain more accurate values of d^ and Equation (5) may be rewritten (12) 1 dj 1 _ fl_ °2 K “ cgE + CgE If the concentration of B is kept constant while A is varied, then c^ changes to c3, c&, c7, etc, -76- and cg remains constant. If c-j/dj, Cg/d^, cg/djjj, etc., are plotted against c^,Cg,Cg, etc., a straight line whose slope is l/CgE and intercept is C g + l/K should be obtained. bince °2E experimental data does give a straight line under these conditions, equation (11) may be used by selecting "ideal" values of dj and d ^ from the straight line obtained from (12). One such linear plot is given in Figure 2. The accuracy of the data does not warrant using the tedious least squares method of obtaining the best straight line through the points that are plotted. Values from the extreme ends of the straight line were chosen to increase the differences, and hence the accuracy, in (11). The equilibrium constant was calculated from four to eleven different wavelengths for the systems studied, and the average of these values for each system was determined. The concen­ trations, observed optical densities, and calculated equilibrium constants are included in Tables 2-19. The range of concentrations used is as wide as the solubilities, usually in carbon tetrachloride, permit. The constants are determined in solutions in which one component is much in excess; six to nine different solutions are ixsed. These solutions are made up so that the most concentrated is nine times as concentrated as the most dilute (where nine -77- solutions are used). Where possible the same experi­ ment was performed at concentrations such that the other component was present in excess. This could be done except with the higher condensed hydrocarbons. In only two instances could no calculation of K be made. Concentrated benzene with dilute tetra­ nitromethane and concentrated mesitylene with tetra­ nitromethane give results wholly different from all other results. The amount of tetranitromethane was held constant as the benzene or mesitylene concen­ trations increased. Optical densities increased much more rapidly with increasing benzene or mesitylene concentration than would be expected if there were a 1:1 interaction. However, the interaction is very weak and high benzene or mesitylene concentrations (1-6 M) must be used. It is very likely that acti­ vities are very far from molarities in this range. It is also true that there is essentially a change of solvent, and change of solvent in Itself affects absorption. In Tables 2-19, containing the data for the equilibrium constants, the equilibrium constant calculated for each wavelength is given. The average of these values is also given with the average deviation. The average deviation is large because of the difficulty of using optical methods for the determination of a very small equilibrium constant. -78- C ^ M o l r r if y O f T e r R R R /r & O M c r H G N e ) i An attempt to measure the equilibrium constant of 1,2-benzanthracene with tetranitromethane was made, but the low solubility of the hydrocarbon gave small optical densities. The equilibrium constants calcu­ lated for 1,2-benzanthracene vary widely and they are wholly unreliable. The free energy of reaction, ^ F ° } is recorded in Table 32. It is calculated from the relationship AF° = -RTlnK. Since K is given in all cases within a few degrees of 25°, and the range of change of K with temperature is small, all values are assumed to o be at 25 . 2. Heat of reaction. Since the heat of reaction is related to the change of the equilibrium constant with temperature, it is possible to make measurements used for the equilibrium constant at different tempera­ tures in order to get the heat of reaction. it is known that 1 ir = C1C2E - T f ~ ° i - °2 Rearranging, __JL — °1C2E K (14) K _ cldI — c2di 1 ciCgE cl - c2 dI It is well known from thermodynamics that (15) In K _ - A H RT~ + -79- M M Prom (5) where dH is the heat of reaction and Ivl is an integra­ tion constant. Combining (14) and (15), (16) Prom this the heat of reaction may be determined, since plotting In/ 1 2 against l/T at one wavelength gives a straight line whose slope is A H/R. d is now a variable; it is the optical density at temperature T. The concentrations, c^ and Cg, change slightly with temperature due to the change in the density of the solvent. calculated at each temperature. These are The density of carbon tetrachloride as a function of temperature in the range used, 5-30°, is well known and the values used are recorded in International Critical Tables. There is not general agreement concerning the density of ethylene dichloride as a function of temperature, but the values recorded at various temperatures in the literature are consistent enough to permit their use. The experimental error is larger than the error in using these density measure­ ment s i In this way the heat of reaction determined is the heat of reaction at constant volume. The results are then comparable to those of Gibson and Loeffler, who use different conditions. -80- In order to make the linear plot indicated above, it is necessary to know E, the extinction coefficient of the molecular compound at the desired wavelength. It is assumed that E is constant over the small temperature range used. The value used is determined from the equilibrium constant data. E - + J4_ °Q C1 may be rearranged to give Equation (6) + _1_ _^I_ K clc2 In the equilibrium constant data d values are given for concentration c^,c3,c5, etc., while Cg is held constant. Since 1/K is constant, E may be determined for each d value measured at a given wavelength. The average of these values is used in (16). The heat of reaction, or heat of molecular compound formation, is determined in each of two different concentrations at. four different wave­ lengths for each molecular compound studied. The average of the eight values thus obtained is reported. E values are given in Table 20. than those needed for given. E values other A H calculation are also A H values and the data used for their calcu­ lation are given in Tables 21-31. -81- The error in the heat of reaction is expressed in the large average deviation. The order of magni­ tude is all that can be significant in the heat of reaction values. With each table in the heat of reaction calcu­ lation are given three concentrations. One is for the dilute component, and the other two are for the two different concentrations used for the concentrated component; each of these two is used for an inde-. penent determination of the heat of reaction. The concentrations given are for the highest temperatures given, but in the calculations all concentrations were determined for all temperatures. In the columns giving the optical densities, the first column under each wavelength gives the optical densities of the smaller of the two concentrations of the more con­ centrated component, and the second column gives the optical densities for the larger of these two concentrations. 3. Entropy of formation. Prom the free energy of reaction and the heat of reaction the entropy of reaction may be calculated from (18) AS = AH - AF T A S values are given in Table 32 along with the A F and the A H values. Since these quantities are all measured near 25°, and they change only slightly -82- with temperature, T is assumed to be 298° k. in all cases. 4. The ultraviolet and visible spectrum of a mixture of the components of molecular compounds. No peak due to the formation of a molecular compound has been found. There is appreciable absorption in the visible region, and it is this absorption that is used for the determination of the concentration of the molecular compound in the calculation of the equilibrium constant and the heat of reaction. If there is a weak interaction between the components of the molecular compound, little or no effect on the ultraviolet absorption spectra would be expected. The ultraviolet optical densities of benzene, naph­ thalene, picric acid, tetranitromethane, and the four 1:1 mixtures which can form molecular compounds are given in Table 33. Ethanol is used as a solvent because it is transparent in this spectral region. The average of the densities of the components is also given. It is seen that the difference between the observed and the calculated (average) values becomes smaller in proceeding from the visible region to the low ultraviolet region. The difference that is usually small in the ultraviolet region may be due to experimental error. It is certain, however, that the absorption peaks in the solutions in which there is molecular compo\md formation are where they -83- are expected to be. This shows only that there is no large effect in the ultraviolet region, since the highly absorbing components account for almost all the observed absorption in the mixtures. 5. compounds. The ratio of the components in the molecular The ratio of components is assumed to be 1:1 in the calculation of the equilibrium constant and this assumption is probably correct when a plot of c^/dj, c3/dI3;, C5/<^III» etc., against ox, c , c5, etc., is linear. However, further confirmation is desirable and this is made possible by the use of the "method of continuous variations" originated by Job (85) and developed by Vosburgh (86). The method of continuous variations is applied to the determination of the ratio of the components in molecular compounds in the following manner: equimolar solutions of components A and B were mixed in varying proportions such that the sum of the volumes used of the solutions of A. and of B was constant. The optical densities of these solutions were measured at several wavelengths. A plot of optical density against concentration of one component was made for each wavelength of each solution. The data for all the molecular compounds studied are in Tables 34-37. Only typical curves for each mixture are given in Figures 3-5, since the curves omitted are similar to those given. -84- ' a vS Hi I 5 vS ! ! I 6- f1 t Ui s >1 k <0 £* S £ 0 C 53 .0596 490 .048 .093 .149 .203 .251 .301 .350 .392 .0560 500 .132 .162 .197 .224 .252 .0760 510 .087 .107 .132 .142 .161 .1404 Ave. K ^ .095 + .032 -88- 2.30 .143 Table 3. Spectra of concentrated naphthalene-dilute —3 tetranitromethane Tetranitromethane, 8.28 x 10 mole/l. naphthalene 410 420 430 440 450 460 0.0949 .101 .099 .091 .086 .066 .051 .1898 .193 .185 .170 .147 .125 .100 .2847 .284 .277 .253 .220 .187 .150 .3796 .382 .366 .341 .303 .255 .196 .4745 .470 .448 .421 .371 .312 .243 .5694 .554 .535 .496 .441 .373 .290 .6643 .642 .611 .574 .503 .424 .344 .7592 .733 .705 .658 ' .585 .487 .398 .8541 .809 .763 .722 .634 .538 .437 K .113 .122 .140 .154 .131 .116 Ave!. K = .13 ± .01 Table 4. Spectra of dilute anthracene-concentrated -3 tetranitromethane Anthracene, 2.74 x 10 mole/1, mmu c of TNM 500 510 520 530 540 550 0.5310 .121 .114 .107 .100 .090 .082 .4965 .180 .172 .160 .149 .137 .123 .6620 .232 .220 .204 .191 .174 .158 .8275 .257 .244 .228 .212 .193 .176 .9330 .315 .300 .284 .264 .244 .216 1.324 .393 .372 .352 .525 .302 .269 K .282 .322 .270 .297 .231 .270 Ave. K = .28 ± .02 -89- Table 5. Spectra of dilute phenanthrene-concentrated -3 , tetranitromethane Phenanthrene, 1.42 x 10 moles/1, mmu c of TNM 410 420 430 440 450 460 470 .1655 moles/l. .127 .095 .081 .074 .064 .056 .050 .3310 .224 .165 .143 .128 .112 .098 .086 .4965 .309 .226 .194 .175 .151 .132 .114 .6620 .390 .284 .245 .217 .190 .164 .144 .8275 .461 .333 .288 .252 .221 .195 .168 .9330 .525 .377 .321 .283 .249 .216 .188 1.159 .580 .411 .352 .309 .270 .233 .202 1.324 .644 .457 •.393 .345 .301 .262 .228 K .472 .539 .595 .661 .659 .702 .652 Ave . K = .61 ± .06 Table 6. Spectra of concentrated phenanthrene-dilute tetranitromethane Tetranitromethane, 0.01655 moles/l. mmu c of phenanthrene 430 440 450 460 470 .02322 moles/l. .101 .087 .066 .050 .041 .03483 .136 .118 .094 .074 .060 .04644 .188 .164 .129 .099 .078 .05805 .221 .193 .155 .123 .098 .06966 .271 .237 .190 .149 .120 .08127 .313 .272 .221 .174 .138 .09288 .347 .301 .247 .195 .156 .10449 .390 .340 .277 .220 .176 1.306 .776 .868 .211 .453 K Ave. K = -90- 0.72 £ •oi Table 7. Spectra of dilute chrysene-concentrated tetranitromethane / Chrysene, 3.93 x 10"■4 moles/l. mmu c of TNM 420 430 440 450 460 .3310 moles/l. .071 .067 .063 .057 .049 .4965 .090 .089 .078 .069 .055 .6620 .116 .102 .095 .084 .069 .8275 .139 .122 .110 .095 .079 .9330 .161 .136 .125 .107 .089 1.159 .175 .150 .138 .119 .099 1.324 .198 .169 .153 .132 .113 K .315 .771 .619 .784 .632 Ave. K r .62 ± .13 Table 8. Spectra of dilute benzene-concentrated tetranitromethane Benzene, 0. 337 M mmu 455 420 425 430 1.324 .179 .098 .051 1.986 .263 .150 .080 .043 2.648 .354 .203 .104 .061 3.310 .444 .255 .135 .078 .041 3.972 .535 .313 .165 • .094 .051 c of TNM 440 No K value could be calculated; this is explained in the text. -91- Table 9. Spectra of concentrated benzene-dilute tetranitromethane Tetranitromethane, 0.827 M mmu c of benzene 430 1.12 .124 .079 2.24 .307 .194 .095 .062 .564 .365 .184 .119 .058 4.48 .871 .575 .297 .193 .097 .061 5.60 1.228 .829 .436 .290 .152 .095 6.72 1.664 1.158 .640 .422 .226 .143 7.84 1.499 .850 .564 .309 .197 8.96 1.904 1.118 .756 .423 .275 3.36 . 434 440 444 450 454 No K value could be calculated; this is explained in the text. Table 10. Spectra of dilute mesitylene-concentrated tetranitromethane Mesitylene, 1.44 x 10~^ mole/l. mmu c of TNM 430 440 450 460 470 480 .3310 .281 .202 .140 .090 .053 .030 .4965 .417 .301 .208 .135 .081 .047 .6620 .549 .396 .273 .174 .105 .062 .8275 .670 .483 .333 .213 .127 .076 .9330 .800 .580 .401 .255 .153 .090 1.159 .914 .660 .454 .291 .174 .101 1.324 1.023 .745 .510 .328 .196 .115 .110 .284 .225 .108 .171 .075] K Ave. K = 0. 16 ± .07 -92- Table 11. Spectra of concentrated mesitylene-dilute tetranitromethane Tetranitromethane, .01655 M mmu c of mesitylene______ 460_____470____480____490____500 0.718 .218 .129 .072 1.436 .451 .271 .156 .084 2.154 .677 .415 .242 .133 .071 2.872 .901 .560 .332 .185 .097 3.590 1.151 .716 .4-34 .247 .134 4.310 1.407 .889 .544 .315 .173 5.025 1.639 1.030 .632 .370 .208 5.740 1.803 1.200 .751 .446 .255 6.460 2.12 1.352 .857 .515 .299 No K value could be calculated; this is explained in the text. -93- Table 12. Spectra of dilute acenaphthene-concentrated tetranitromethane Acenaphthene, 1.58 x 10"^ moles/l. mmu c of TNM 510 520 530 540 550 560 570 580 590 .1655 .206 .177 .147 .119 .100 .076 .060 .044 .033 .3310 .413 .355 .295 .239 .197 .150 .115 .086 .4965 .618 .531 .441 -.356 .292 .225 .171 .126 .092 .6620 .790 .674 .573 .467 .375 .290 .221 .165 .120 .8275 .999 .851 .721 .588 .466 .364 .278 .206 .149 .9330 1.179 1.007 .850 .692 .552 .4-27 .327 .243 .175 .063 1.159 1.333 1.153 .969 .795 .634 .494 .375 .281 .204 1.324 1.508 1.305 1.089 .903 .720 .560 .424 .318 .230 1.490 1.627 1.425 1.186 .988 .780 .608 .460 .345 .249 K .125 .0934 .0785 ,0554 .1185 .0714 .1208 .0966 .1144 Ave. K = .09? - *02 -94- Table 13. Spectra of concentrated acenaphthene-dilute tetranitromethane Tetranitromethane, 0.01655 mole/l. c of mmu acenaphthene 4-70 460 480 490 500 510 520 .05270 .114 .105 .099 .089 .081 .070 .060 .1054 .230 .213 .199 .179 .162 .143 .123 .1581 .342 .318 .297' .272 .244 .216 .186 .2108 .454 .424 .389 .355 .319 .284 .245 .2635 .565 .530 .485 .450 .400 .356 .307 .3162 .677 .633 .579 .535 .476 .423 .365 .3689 .779 .724 .669 .612 .550 .486 .420 .4216 .866 .805 .745 .681 .611 .544 .466 .4743 .997 .928 .855 .783 .703 .627 .543 K .155 .0776 .111 .0769 .1052 .0746 .044; Ave. K = .092 2: .02 - -95- Table 14. Spectra of dilute fluorene-concentrated tetranitromethane mmu c of^TNM 410 Fluorene, 1.71 x 10 -•3 moles/l. 420 430 440 450 460 470 .3310 .161 .111 .094 .080 .067 .056 .046 .4965 .224 .153 .128 .109 .091 .073 .058 .6620 .283 .191 .160 .137 .114 .091 .073 .8275 .337 .224 .188 .162 .135 .110 .090 1.159 .437 .283 .237 .203 ■ .167 .135 .106 1.324 .482 .312 .260 .222 .185 .150 .118 K .342 .465 .502 .479 .573 .632 .602 Ave. K = .51 ± .07 Table 15. Spectra of concentrated fluorene-dilute tetranitromethane mmu c of fluorene 410 Tetranitromethane, 0.008275 mole/l. 420 4-30 440 450 460 470 .0673 .115 .098 .085 .074 .063 .052 .041 .1009 .166 .143 .125 .109 .094 .077 .063 .1346 .22,0 .190 .163 .145 .124 .102 .083 .1682 .267 .234 .203 .180 .152 .125 .104 .2019 .315 .276 .242 .213 .182 .151 .124 .2355 .364 .318 .282 .245 .213 .175 .144 s' .2692 .415 .361 .320 .282 .244 .202 .167 .3028 .463 .407 .359 .316 .273 .278 .190 K .796 .413 .144 .282 .223 .217 .106 Ave. K - .31 i .17 -96- Table 14. Spectra of dilute fluorene-concentrated -3 tetranitromethane Fluorene, 1.71 x 10 moles/l. mmu c of TNM 410 420 430 440 450 460 470 .3310 .161 .111 .094 .080 .067 .056 .046 .4965 .224 .153 .128 .109 .091 .073 .058 .6620 .283 .191 .160 .137 .114 .091 .073 .8275 .337 .224 .188 .162 .135 .110 .090 1.159 .437 .283 .237 .203 ■ .167 .135 .106 1.324 .482 .312 .260 .222 .185 .150 .118 K .342 .465 .502 .479 .573 .632 .602 Ave. K =• .51 ± .07 Table 15. Spectra of concentrated fluorene-dilute tetranitromethane mmu c of fluorene 410 Tetranitromethane, 0.008275 mole/l. 420 4-30 440 450 460 470 .0673 .115 .098 .085 .074 .063 .052 .041 .1009 .166 .143 .125 .109 .094 .077 .063 .1346 .220 .190 .163 .145 .124 .102 .083 .1682 .267 .234 .203 .180 .152 .125 .104 .2019 .315 .276 .242 .213 .182 .151 .124 .2355 .364 .318 .282 .245 .213 .175 .144 .2692 .415 .361 .320 .282 .244 .202 .167 .3028 .463 .407 .359 .316 .273 .278 .190 K .796 .413 .144 .282 .223 .217 .106 Ave. K ~ .31 -96- t. .17 Table 16. Spectra of dilute fluoranthene-concentrated -3 tetranitromethane Fluoranthene, 1.70 x 10 mole/l. mmu c of TNM 410 420 430 440 450 460 470 0.1655 .169 .126 .104 .086 .070 .055 .042 .3310 .276 .2,07 .173 .144 .116 .092 .071 .4965 .370 .280 .230 .191 .155 .119 .092 .6620 .452 .339 .281 .233 .191 .149 .116 .8275 .530 .399 .331 .274 .221 .174 .135 .9330 .608 .446 .372 .310 .250 .196 .149 1.159 .662 .489 .411 .343 .278 .219 .169 1.324 .722 .516 .428 .353 .283 .223 .171 K .671 .723 .783 .697 .800 .874 .835 Ave. K z: 0.77 ± .06 Table 17. Spectra of concentrated fluoranthene-dilute -3 tetranitromethane Tetranitromethane, S. 28 x 10 moles/l. mmu 440 450 460 .05936 .121 .096 .077 .060 . .08904 .182 .144 .116 .093 .1187 .238 .190 .150 .118 .1484 .289 .231 .185 .145 .1781 .352 .282 .226 .177 .2078 .404 .322 .257 .203 .2374 .457 .369 .296 .235 .2671 .507 .411 .330 .262 K .424 .269 c of fluoranthene Ave. K := .28 i .08 -97- .289 470 .144 Table 18. Spectra of concentrated naphthalene-dilute picric acid in carbon tetrachloride / Picric acid, 4.05 x 10 -4 mole/1. c of mmu naphthalene 400 405 410 4-20 415 425 430 435 440 .2188 .158 .148 .135 .122 .109 .103 .086 .074 .058 .3282 '.199 .186 .167 .154 .140 .126 .104 .095 .077 .4376' .240 .224 .203 .184 .166 .149 .125 .111 .093 .5470 .258 .241 .218 .198 .180 .160 .133 .120 .098 .6564 .280 .269 .244 .219 .208 .181 .154 .129 .109 .7658 .309 .292 .266 .236 .210 .197 .166 .140 .117 K 2.08 1.86 1.96 2.56 3.09 1.81 1.82 2.34 1.97 Ave. K = Table 19. 2.16 ± 0.33 Spectra of concentrated naphthalene-dilute picric acid in ethyl ene dichloride Picric acid, 4.10 x io"4 mole/l. c of mmu naphthalene 400 405 410 415 420 425 430 435 .1570 .088 .076 .073 .069 .063 .063 .053 .041 .2324 .106 .100 .091 .084 .082 .072 .065 .054 .3139 .140 .132 .123 .112 .106 .095 .085 .070 .3924 .157 .146 .137 .126 .119 .105 .091 .078 .4709 .166 .157 .144 .137 .123 .107 .099 .081 .5494 .190 .176 .168 .155 .138 .121 .111 .089 .6278 .193 .184 .171 .161 .146 .131 .116 .095 K 2.30 1.80 1.74 1.70 2.07 2.44 2.10 2.03 Ave. K 2.02 + .21 -98- Table 20. E for various molecular compounds Dilute acenaphthene1 420 430 ____ ___ 440 450 460 470 430 ______________________ Concentrated acenaphthene Dilute fluoranthene 1444 1348 1245 603 501 Concentrated fluoranthene Dilute fluorene 442 369 Concentrated fluorene Dilute naphthalene 416 337 264 203 881 705 564 446 317 264 212 169 438 377 321 2649 2349 1999 1664 1319 1008 Concentrated naphthalene 943 881 776 656 521 405 Dilute phenanthrene 695 597 530 463 403 350 Concentrated phenanthrene 342 298 241 190 151 Dilute chrysene 921 831 721 602 692 621 726 306 Dilute anthracene Dilute 1,2-benzanthracene Dilute mesitylene 199 Concentrated naphthalene-dilut e picric in GCI4 631 Concentrated naphtha1ene-dilute picric in CH0C1CHPC1 633 503 128 78 459 1. Tetranitromethane is the nitro component where no other is indicated. -99- 45 Table 20 (continued) 490 500 Dilute acenaphthene Concentrated ac enaphthene 510 520 530 540 550 560 9522 84-0 722 606 496 398 309 1139 1021 906 782 Dilute naphthalene 498 Concentrated naphthalene 226 437 398 359 320 Dilute anthracene Dilute acenaphthene 2. 570 580 590 600 255 175 127 92 Limits of error are about one per cent. -100- Table 21. Spectra for trated tetranitromethane of dilute naphthalene-concen-2 Naphthalene, 1.87 x 10 mole/1.; tetranitromethane, 0.3310, 1.324 moles/1, mmu T 470 480 490 500 28.2 .280 1.035 .208 .768 .142 .530 .095 .351 23.5 .287 1.085 .207 .790 .146 .552 .095 .361 21.3 .291 1.104 .212 .802 .147 .558 .098 .365 19.1 .295 1.097 .213 .799 .150 16.3 .298 1.105 .216 .811 .150 .567 .100 .374 14.2 .301 1.115 .220 .823 .153 .576 .101 .377 AH 448 579 Ave. Table 22. 628 .564 .097 .369 560 517 AH r -546 ± 51 cal. Spectra for AH of dilute anthracene- concentrated tetranitromethane Anthracene, 2.73 x 10 —3 mole/l.: tetranitromethane, 0.8275, 1.159 moles/1, mmu 550 T 540 560 550 27.1 .216 .268 .198 .244 .178 .220 .157 .194 21.2 .223 .275 .203 .251 .182 .226 .162 .201 17.5 .225 .278 .205 .255 .186 .230 .166 .204 13.4 .230 .283 .209 .259 .189 .234- .168 .207 AH 423 531 360 497 414 517 Ave. AH rs -481 ± 7 0 cal. -101- 626 Table 23. Spectra for of dilute phenanthrene- concentrated tetranitromethane phenanthrene, 1.42 x 10 “3 mole/1.; tetranitromethane, 0.9930, 1.324 moles/l. mmu T 440 460 450 470 24.2 .240 .322 .200 .269 .166 .223 .133 .180 21.7 .241 .318 .201 .268 .164 .220 .135 .180 18.6 .244 .322 .205 .271 .168 .225 .136 .182 15.7 .247 .328 .206 .274 .171 .228 .137 .185 13.8 .248 .329 .208 .277 .171 .230 .139 .186 A H 362 704 438 Ave. Table 24. 743 A H = -560 Spectra for trated tetranitromethane 392 846 - 153 cal. 480 514 of dilute chrysene-concen—4 Chrysene, 3.93 x 10 mole/l.; tetranitromethane, 0. 8275, 1.159 mole/l. mmu T 430 440 450 460 27.3 .120 .150 .108 .137 .096 .120 .079 .100 21.8 .120 .150 .109 .138 .096 .122 .080 .101 18.9 .122 .151 .110 .138 .096 .122 .080 .101 14.4 .121 .152 .109 .139 .097 .123 .082 .103 A H -320 -126 59 -172 -291 -212 Ave. A H := +138 + 111 -102- 49 -89 Table 25. Spectra for A H of dilute 1,2-benzanthracene- concentrated tetranitromethane 1,2-benzanthracene, 3.09 x 10-4 mole/l.; tetranitromethane, 1.159, 1.324 moles/l. mmu T 440 445 450 455 22.1 .079 .088 .075 .083 .071 .078 .066 .074 19.3 .080 .089 .074 .084 .070 .078 .068 .078 14.5 .081 .089 .076 .086 .072 .081 .068 .078 Ave. Table 26. A Spectra for H = 0 of dilute mesitylene- concentrated tetranitromethane Mesitylene, 1.44 x 10 mole/l.; tetranitromethane, 0.9930, 1.324 moles/1. 450 T 27.6 470 4-80 .376 .484 .242 .311 .143 .187 .081 .106 21.5 .391 .502 .246 .319 .147 .191 .082 .109 17.7 .401 .515 .256 .331 .152 .197 .086 .113 .407 .523 .259 .336 .156 .199 .087 .113 14.3 A H • 460 ' 798 754 753 Ave. 843 1104 -812 ± 127 -103 500 935 Table 27. Spectra for A H of dilute acenaphthene- concentrated tetranitromethane 10" Acenaphthene, 1.58 x mole/l.; tetranitromethane, .3310, 1.159 moles/l. mmu T 540 560 530 600 24.4 .224 .728 .139 .454 .079 .260 .037 .134 22.7 .219 .722 .140 .457 .079 .263 .041 .137 20.5 .226 .741 .139 .459 .081 .267 .041 .137 18.6 .233 .756 .136 .456 .082 .270 .040 .138 16.4 .234 .760 .146 .475 .085 .277 .038 .158 14.5 .238 .774 .149 .481 .085 .281 .042 .144 923 AH 725 1089 Ave. Table 28. A H — -940 Spectra for 828- 1032 837 ± / 1148 128 cal. of dilute fluorene-concentrated —3 Fluorene, 1.71 x 10 mole/l.; tetranitromethane aH tetranitromethane, 0.9930, 1.324 moles/l. mmu T 440 460 450 470 27.1 .186 .243 .159 .207 .134 .173 .106 .139 25.2 .187 .246 .161 .211 .134 .176 .108 .141 22.0 .190 .248 .164 .212 .136 .175 .109 .140 18.7 .193 .254 .166 .215 .137 .179 .112 .144 15.8 .197 .257 .169 .219 .141 .182 .114- .148 13.3 .198 .258 .171 .221 .143 .184 .116 .149 1028 1143 1072 AH 729 886 871 777 Ave . AH = -926 -104- ± 117 900 Table 29. Spectra for A H of dilute fluoranthene- concentrated tetranitrometh.ane fluoranthene concentra-3 tion 1.70 x 10 mole/l.; tetranitromethane concentration 0.8275, 1.324 moles/l. mmu T 440 450 460 470 ' 26.5 .287 .428 .240 .355 .194 .287 .152 .227 23.7 .288 .431 .240 .357 .194 .288 .153 .228 21.0 .294 .439 .244 .363 .197 .294 .155 .231 18.9 .295 .442 .247 .369 .199 .298 .156 .233 16.5 .297 .445 .247 .371 .200 .300 .157 .235 13.8 .299 .448 .249 .373 .202 .303 .158 .237 369 1097 566 1130 532 AH 572 Ave. Table 30. 532 929 A H = -716± 252 cal. Spectra for A H of concentrated naphthalene' dilute picric acid in carbon tetrachloride Picric acid, 4.35 x 10-4 mole/l. ; naphthalene, 0.5500, - 0.8800 mo le/l. mmu 425 T 430 435 440 25.1 .192 .248 .166 .217 .143 .188 .121 .160 23.0 .197 .248 .173 .219 .149 .190 .127 .164 16.6 .212 .261 .185 .230 .158 .197 .133 .169 12.8 .226 .274 .195 .235 .168 .206 .142 .176 7.7 .243 .294 .212 .258 .182 .224 .153 .191 5720 5980 5720 5460 7260 5430 AH Ave. A H = -5930 ±460 cal. -105- Table 31. Spectra for <4H of concentrated naphthalene- dilute picric acid in ethylene dichloride Picric acid, 4.10 x 10“^ -mole/l.; naphthalene, 0.3924, 0.5494 mole/l. mmu T 415 420 425 430 22.4' .108 .137 .099 .125 .087 .111 .072 .092 19.9 .110 .146 .097 .130 .088 .117 .077 .103 16.6 .112 .151 .102 .136 .091 .124 .079 .106 13.6 .120 .158 .106 .141 .097 .127 .083 .110 9.4- .130 .167 .120 .162 .106 .135 .092 .118 6.2 .137 .175 .125 .152 .111 .140 .099 .123 AH 3830 4290 4140 3540 4020 4-340 4640 4770 Ave. A H = -4200 ± 330 -106- Table 32. Summary of the thermodynamics of the formation of molecular compounds from the components K® 6 P° 4H° Dilute naphthalene^________ 0.095____1395 -546 4S° -6.52 e.u. Concentrated naphthalene .13 Dilute anthracene .28 750 -481 -4.13 Dilute phenanthrene .61 291 -560 Concentrated "phenanthrene .72 282 138 -0.48 very small Dilute 1,2-benzanthracene .62 un­ certain Dilute benzene small Dilute chrysene -2.85 Dilute mesitylene .16 1083 -812 -6.36 Dilute acenaphthene. .097 1383 -940 -7.81 Concentrated acenaphthene .092 Dilute fluorene .51 398 -926 -4.45 Concentrated fluorene .31 Dilute fluoranthene .77 154 -716 -2.92 Concentrated fluoranthene .28 Concentrated naphthalenedilute picric in CCI4 2.16 -456 -5930 -18.40 2.02 Concentrated naphthalenedilute picric in CHQC1CHPC1 -417 -4200 -12.70 1. Tetranitromethane is the nitro compound and carbon tetrachloride is the solvent where no other is named. o 2. All quantities are at 25 G. Table 33. Ultraviolet and visible absorption spectra of some molecular compounds and their components compound mmu 250 TNM^ Picric^ .880 .715 260 .652 .457 270 .500 .257 280 .379 290 Benzene'""' Naphth.^ Benzene-TNM^ Obs. Calc. .046 .120 .518 .463 .222 .367 .340 0 .279 .257 .250 .191 0 .228 .191 .190 .272 .193 0 .107 .140 .136 300 .189 .232 0 .015 .101 .095 310 .123 .313 0 0 .075 .062 320 .090 .439 0 0 .063 .045 330 .066 .618 0 0 .063 .033 340 .067 .820 0 0 .077 .033 350 .065 .970 0 0 .086 .032 360 .054 1.011 0 0 .072 .027 370 .945 0 0 380 .840 0 0 .028 1. -4 8.28 X 10 * M.. tetranitromethane • 2. 8.52 X 10-5 M. picric acid. 3. 1.12 x 10"4 M. benzene • 4. 1.32 x 10"5 M. naphthalene. 5. This and succeeding mixtures are mixtures of equal volumes of the solutions of the components given in columns 2-5, The calculated values are determined by assuming the density is the average of those of the two solutions. -108- Table 33 (continued) compound Benzene-picric Naphthalene-TNM Naphthalene-picric Obs. Gale. Obs. Calc. Obs. Calc, mmu ' 250 .387 .380 .425 .500 .418 .503 260 .234 .242 .448 .437 .337 .339 270 .128 .127 .402 .389 .265 .268 280 .091 .095 .312 .303 .203 .210 290 .092 .096 .198 .190 .145 .150 300 .118 .116 .115 .102 .125 .123 310 .167 .156 .076 .065 .170 , .156 320 .238 .219 .057 .043 .239 .219 330 .337 .309 .045 .033 .338 .309 340 .442 .410 .048 .033 .443 .410 350 .522 .4-85 .048 .032 .528 .485 360 .540 .505 .041 .027 .549 .505 370 .502 .472 .508 380 .444 .420 .452 -109- .472 .420 Table 34. Continuous variations for naphthalene- tetranitromethane, 0. 0823 mole/l. mmu c of TNM 420 430 4-40 450 460 470 480 .0082 .098 .083 .072 .063 .052 .040 .029 ,0164 .152 .132 .112 .098 .079 .061 .045 .0246 .185 .161 .139 .119 .096 .072 .052 .0328 .225 .197 .168 .141 .113 .086 .062 .0411 .236 .204 .174 .145 .116 .089 .065 .0492 .217 .188 .162 .134 .109 .034 .060 .0574 .208 .178 .147 .129 .102 .082 .061 .0656 .158 .136 .111 .098 .077 .062 .048 .0738 .092 .077 .062 .057 ,044 .037 .028 Table 35. ac enapht hene ■ Continuous variations for : tetranitromethane, 0.0825 mole/l. mmu c of TNM 430 440 450 460 470 480 490 500 510 520 .0082 .109 .101 .095 .088 .078 .075 .067 .062 .053 .047 .0164 .173 .164 .153 .145 .132 .124 .111 .099 .088 .078 .0246 .221 .207 .198 .188 .171 .159 .145 .132 .117 .101 .0328 .259 .245 .233 .217 .202 .137 .172 .153 .133 .114 .0411 .262 .248 .236 .219 .206 .191 .175 .155 .134 .116 .0492 .247 .234 .222 .207 .196 .181 .166 .147 .128 .111 .0574 .224 .208 .198 .188 .173 .160 .148 .128 .114 .096 .0656 .164 .154 .146 .139 .128 .118 .110 .095 .084 .071 .0738 .089 .080 .078 .074 .067 .062 .059 .049 .044 .036 -110- Table 36. Continuous variations for mesitylene- tetranitromethane, 0.4110 M mmu c of THM 450 460 470 480 490 0.0411 .447 .288 .167 .096 .053 .0822 .737 .507 .297 .168 .092 .1233 1.020 .654 .387 .218 .118 .1644 1.161 .755 .443 .253 .137 .2055 1.200 .775 .458 .258 .140 .2466 1.148 .743 .435 .246 .132 .2877 1.015 .643 .387 .219 .116 .3288 .758 .482 .238 .163 .087 .3699 .440 .282 .169 .096 .051 Table 37. Continuous variations for benzene _ tetranitromethane, 8.270 M. mmu 440 445 450 455 460 0.827 .747 .448 .259 .151 .084 1.654 1.150 .694 .404 .233 .129 2.481 1.340 .800 .467 .268 .148 3.308 1.369 .825 .473 .274 .155 4.135 1.292 .763 .435 .249 .141 4.962 1.109 .644 .364 .207 .117 5.789 .868 .504 .288 .162 .091 6.616 .558 .320 .180 .101 .056 c of TNM -Ill- IV. CONCLUSIONS A. Proof and significance of a true equilibrium. Whether or not there is a true equilibrium in solution is an important question in the field of molecular compounds. It is believed that this question is not answered satisfactorily in the literature. If there is a chemical reaction, it should be possible to show there is a true equilibrium; if there is a polarization of the kind that Gibson and Loeffler postulate, then a true equilibrium would not be observed. Those who postulate a polarization are either vague or noncommittal on this point. If there is a true equilibrium, then either one of the chemical reaction theories or some modification of a polarization theory which includes the idea of an equilibrium must be the correct theory which explains the phenomena observed for molecular compounds. It Is shown elsewhere that the chemical reaction theories (an ionic or a covalent bond form) are improbable. The experimental evidence offered in this paper shows there Is a true equilibrium. Thus, strong--but not conclusive--evidence for the existence of the polarization aggregate discussed earlier is given. That there is true equilibrium is deduced from the fact that the curve obtained from plotting c/d against c is linear, as supposed; the equilibrium constants - 112 - determined at wide extremes of concentration are the same, within rather large limits of error; the extinction coefficients at extremes of concentration are close enough to indicate the;y are probably of the sarae compound. Although the equilibrium constants determined at extremes of concentration are sometimes not close . (e.g. 0.77 and 0.28 for dilute and concentrated fluoranthene, respectively) the limits of error can be seen to be so large that no conflict with the existence of a true equilibrium can be deduced. It is believed that the cases in which there is good agreement (naphthalene, acenaphthene, phenanthrene) are not accidental. It is particularly significant that calculation of the extinction coefficients -at these extremes of concentrations shows the best agreement where there is the best agreement between the two equilibrium constants (acenaphthene-tetranitromethane). In Table 20 it is seen that the E values for this molecular compound agree to within five per cent at the three wavelengths for which measurements were made at both extremes of concentration; this is true in spite of the fact that E is very sensitive to the value of K \ised ('-i-'he two K values differ by about this amount.), and in spite of the fact that E values at the extremes are theoretically not exactly the same -113- (this is discussed below). The difference between the extinction coefficients calculated at each extreme can be seen to be appreciable where the equilibrium constants become farther apart, as would be expected. It is true, however, that this difference always is in the direction it would be expected to be from a consideration of the equilibrium constants. 3. The factors affecting results There are four principal reasons for the error observed: 1 . The equilibrium constants are small; the calculations described earlier are such that large equilibrium constants could be determined much more accurately. 2. The error in the optical measurements is high compared to other physical measurements, and this introduces a large error in small equilibrium constants. 3. In some cases, as with 1,2-benzanthracene, the solubility is very low and only a small amount of color is produced. There is a large error in measuring low optical densities with the Beckman instrument. For this reason no constant could be calculated for 1,2-benzanthracene-tetranitromethane. 4. There is a slight change of solvent in going from, for example, a tetranitromethane concentration of 0.1655 M - 1.490 M, as recorded in Table 12 for concentrated tetranitromethane-dilute acenaphthene. This could introduce an error, since absorption spectra change with a change of solvent. -114- It is not possible to calculate equilibrium constants with concentrated benzene and concentrated mesitylene solutions, but this is not due to experi- . mental error or to the lack of a true equilibrium. Examination of the data given in Tables 9 and 11 shows that the concentration ranges are 1.12 M - 8.96 M and 0.718 M 6.46 M for benzene and mesitylene, respectively These represent concentrations much higher than those of other solutions, and in the benzene and mesitylene solutions there is again actually a change of solvent; the most dilute of these solxitions contains almost ten percent hydrocarbon. In such solutions the activities of the components are altered, and the absorption spectrum changes due to a change of solvent. It is difficult to determine the equilibrium constant in the dilute benzene-concentrated tetranitro­ methane solution because the nitro compound is very concentrated (1.324 M - 3.972 M) and because the constant is very small. That the constant is small is evident from the data and from the conclusions of other workers (Hammick, Briegleb, and coworkers). It might be expected that the ratio of the extinction coefficients calculated at the two extremes of concentration would at least be constant at different wavelengths, even if the extinction coefficients calcu­ lated at the two extremes are not the same. not true for two reasons: -115- This is 1. E is only approximately, but not exactly, proportional to l/K. 2. There is at least a small change of solvent in going from one extreme to the other; in concentrated tetranltromethane solutions there is always at least five per cent tetranitromethane. The ratio of the extinction coef­ ficients is therefore not constant for different wave­ lengths where the two equilibrium constants are not very close to each other. If, however, optical densities are compared for solutions at extremes of concentration, then the first of these objections does not hold. Since the other objection does hold, actual calcula­ tions reveal that the ratio is not perfectly constant with a change is wavelength, in contrast to the constant ratio obtained between optical densities of two different solutions which have nearly the same concen­ trations of components. The values obtained for the heat of reaction are only approximate because of some of the same reasons cited for K and E value inaccuracies; it is also true that the temperature coefficient of color is small and the extinction coefficient, which is not accurately known, must be used for the calculation. No calculations could be made in the case of benzene-tetranitromethane because the density as a function of temperature of these mixtures was not determined. The data of the method of continuous variations confirm some of the results obtained from the -116- determination of equilibrium constants. The components of the molecular compounds of tetranltromethane'with naphthalene, acenaphthene, and mesitylene are seen to be in a ratio of 1:1 from Pigs. 3 and 4; Pig. 5 shows benzene-tetranitromethane to give results from which no conclusion can be made; neither a 1:1 nor a 1:2 complex is indicated. It would be expected that benzene-tetra- nitromethane would behave in an irregular manner because of the change in solvent which occurs here. Careful examination of Pigs. 3 and 4 reveals the curves to be slightly asymmetric, even though 1:1 com­ pounds are indicated. Experimental error will cause the peak to be moved slightly,/ and this is in accordance with the conclusions made by Kingery and Hume (87). C. The stability of molecular compounds. Some generalizations concerning stability can be made from the data given in this paper. 1. The stability of all. tetra- nitromethane molecular compounds, whether measured by the equilibrium constant or by the heat of reaction, is much less than the stability of the corresponding compounds formed by picric acid and (according to Briegleb and others) s-trinitrobenzene. This is in accordance with the view of Briegleb (discussed earlier) that aromatic nitro compounds form molecular compounds which are more stable than those of aliphatic nitro compounds. 2. The molecular compounds of both tetranltro­ methane and of picric acid are weak. -117- This is shown not only by the small equilibrium constants and the small heats of reaction, but also by the nature of the ultra­ violet absorption spectra of four of these compounds given in Table 33. It is seen that the presence of a molecular compound does not alter the ultraviolet spectra. For a noticeable difference in the ultra­ violet spectra the molecular compound would have to be present in fairly large concentration, and its spectrum would also have to be appreciably different. Molecular compounds do not meet these conditions. 3. The relative stability of molecular compounds of tetranltromethane can be determined from the equili­ brium constants, but because the limits of error are wide, the heats of reaction cannot be used for such a comparison. As Briegleb and others indicate, increasing aromaticity increases molecular compound stability. This seems to be true if the equilibrium constants of compounds of benzene, naphthalene, anthracene, chrysene, and phenanthrene are considered; the constants increase in the order given. The methyl groups of mesitylene bend to donate electrons to the ring, and they therefore make the ring more aromatic (better electron donor); accordingly the equilibrium constant for the formation of the mesitylene compound is much higher than that of the benzene compound. Hexamethylbenzene should form an even stronger complex than mesitylene. Although the equilibrium constant -118- could not be measured, It is of Interest to note that hexamethylbenzene-tetranitromethane solutions were observed to have a very deep red color. The deep red color probably indicated a strong interaction (in comparison with the yellow color of the benzene and mesitylene mixtures), but this is by no means certain. Acenaphtherie, fluorene, and fluoranthene have the structures indicated. . Acenaphthene Fluoranthene Fluorene It might be expected that acenaphthene, a derivative of naphthalene which is partly aliphatic, would form molecular compounds of greater stability than naph­ thalene. Their equilibrium constants are very close, however, and this expectation is not realized.. Fluorene and fluoranthene appear to be much better electron donors in molecular compound formation than acenaphthene. 4. In the one example given (naphthalene-picric acid) it seems apparent that carbon tetrachloride is a slightly better solvent for stability than is ethylene dichloride. Both are inert solvents, but the dielectric constant of ethylene dichloride is five times that of carbon tetrachloride. This may indicate that a smaller interaction energy is necessary for formation of the molecular compound in the solvent of higher dielectric constant, as is expected. -119 5. In the calculation of the heat of reaction, the correction for the change of the volume of the solvent with temperature was made. Thus, the heats of reaction obtained are for the condition of constant volume. All but one of the heats determined has a negative value, indicating a negative color coefficient of temperature at constant volume and showing, as pointed out earlier, that at least part of the polarization, theory of Gibson and Loeffler is incorrect. 6 . -^11 the entropies of formation of molecular compounds are negative. This indicates that there is an orientation effect in the formation of a molecular compound. If there are Ions formed from the inter­ mediate polar molecule, it would be difficult to predict the sign of A S. -120- V. SUMMARY A. 'The formation of molecular compounds of tetranitromethane with aromatic hydrocarbons has been studied at different temperatures by a spectrophotometric method. B. Equilibrium constants and free energies of formation have been calculated from the data. 0. Heats and entropies of formation of the com­ pounds have been calculated. &. The stabilities of the compounds have been correlated with the nature of the constituent molecules. E. The various theories concerning the nature of the interaction between the components of a molecular compound have been discussed in the light of the data obtained in the present and in the earlier work, and a modification of a polarization theory has been suggested to represent the true nature of the interaction - 121 - VI. 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'-'hem., £>27, 11 (1934). 66. G. G. Lefevre and R. J. W. Lefevre, J. Ghem. Soc., 1955, 957. 67. H. 0. Jenkins, J. Ghem. Soc., 1956, 862. 68. G. A. Krauss and W. C. Bray, J. Am. Ghem. Soc., 35, 1315 (1913). 69. M. J. Field, w. E. Garner,- and G. c. Smith, J. Chem. Soc., 127, 1227 (1925). 70. W. E. Garner and H. P. Gilbe, J. Ghem. Soc., 1928, 2889. 71. Walden, Z. phys. Ghem., 45, 385 (1903). 72. J. Weiss, Nature, 147, 512 (1941). 73. J. Weiss, Nature, 145, 744 (1940). 74. K. S. Krishnan and S. Banerjee, Phil. Trans., 234, 265 (1935). 75. S. Banerjee, Z. Krist♦, A100, 316 (1939). 76. B. Puri, R. C. Sahney, ■M. Singh, and S. Singh, G* Ind. Ghem. Soc., 24, 409 (1947). 77. P. W. Gray and J. H. Cruickshank, Trans. Parad. Soc., 31, 1491 (1935). 78. Ml. S. Lesslie and E. B. Turner, J. Chem. Soc., 1950, 1758. 79. D. LI. Hammick and R. B. Williams, J. Ghem. Soc., 1955, 1856. 80. G. Kochendorfer, Z. Krist., A97, 263, 280; z* Physik, 108, 264 (1937). 81. H. A. Benesi and J. H. Hildebrand, Jh_ Am. Ghem. Soc., 71, 2703 (1949). Ghem. Soc., 69, 724 (1947). -125- 82. St. Minovici and C. Kollo, Bull, de l'Acad. Bourn., 3, 61-71, 7-15-1914. 83. P. 0. Ghattaway, J. Ghem. Soc., 97, 2099 (1910). 84. A. J. G. Nicholson, 85. P. Job, Arm. Chtm., (10), 9, 113 (1928). 86. W. G. Vosburgh and G. R. Gooper, J. Am. Ghem. Soc. 63, 437 (1941). 87. W. D. Klngery and D. H. Hume, J. Am. Ghem. Soc., 71, 2393 (1949). J. Ghem. Soc., 1949, 1555. -126- Part II. The Ionization Constants of Some Parasubstituted. p 1-Dimethylaminoazobenzenes. I. INTRODUCTION For many years the structure of dyes and of the Ions they form in solution has been a subject of much discussion in the literature. These structures are discussed in connection with dye color. It might be expected that the only valid conclusions would be those made since the inception of modern ideas concerning resonance and molecular structure, but some ideas advanced earlier are helpful in understanding the present problem. The dyes to be discussed in this paper are azo dyes of the type I. where Y may be Cl, I, H, CH3, C(CH3 )3, SCN, SeCN, 0CH3, or NOg. The parent substance, where Y H, is well known, and its structure is discussed by several workers Including Prideaux who in 1917 (1) postulated the following structure for the free base: The dots (....) indicate "subsidiary” valence while the unbroken lines indicate "primary" valence. alkyl group. The free base is yellow. R is an In the presence of an acid, HX, the proton adds to the azo nitrogen farthest from the amino group, and the "primary" valence between R and the azo nitrogen is broken. According to the theory of. Prideaux, X adds to this same R group, -128 and now this R group is connected to the amino nitrogen with a primary valence. Acid solutions of (I) are red. According to Hantzch and Burawoy (1950) the structure of the "salt” form should be slightly dif­ ferent (2 ): in. / This they conclude from an examination of the spectra of the base in alcohol, in dilute acid, and in concen­ trated sulfuric acid. subject of dispute. The ideas of Hantzch became the However, it is not necessary to give more than a representation of the early ideas on the subject here. The ideas the early workers had on the origin of the color of these dyes were rather vague and uncertain. Prideaux (ibid.,.p. 82) refers to light absorption as being due to the vibration of atoms or valency lines of force; this is seen to be related to modern ideas on molecular spectroscopy if the infrared spectrum is included in the term "light absorption". He says it seems that at least some great changes of color are due "...to very fine adjustments of vibrations within the molecule..." Balv (3) suggests that the self-neutralized affinities on the molecule may be opened up by light or the residual affinity of the solvent. He says an increase in the residual affinity 129 of the solvent displaces the absorption band toward the red. In this connection it must be noted that the work of Purvis (4) shows that in high dilution some substances absorb about the same as their vapors. ^aly later elaborated on this theory (5). While our modern ideas on the nature of the chemical bond are much clearer and more useful than the ideas expressed in II. and III. above, our modern ideas on the origin of the color of these molecules are not clear, well-defined, and universally accepted. Lewis and Oalvin (6) in a review article on the color of organic molecules suggest that a separation of charge in a molecule makes possible a low energy electronic transition; this corresponds to absorption of light of longer wavelength than would be absorbed if there vi^ere no separation of charge. With molecules that absorb strongly in all or nearly all of the ultraviolet region, as do these dyes, absorption of the free base and of the ions-formed in acid soLution is moved into the visible region. The same idea is-used by Pauling (7) to explain the yellow color of the picric acid molecule and the color of the other molecules. There are a large number of other effects discussed in modern spectroscopic literature; it is not the purpose of this paper to discuss at length the spec­ troscopy of these dyes. The purpose of this paper is -130- to use the color of the nine dyes 'which have the general formula (I) and their ions in acid solutions as a means of analysis in calculating ionization constants. It is intended that these constants should make it possible to determine the relative importance of various resonance contributions to the dye molecule by comparing the effect of different substituents. The effect of these substituents on the basicity of the dyes is discussed. These nine dyes are all weak bases which can take on two protons. The number of protons which add on, and the nitrogen atoms to which they add, are other results of this investigation. It is stated in the literatr.re (8) that the parent dye of this group, p-dimethylaminoazobenzene takes on two protons, but quantitative evidence is not given. The first proton adds to the free base in acid solutions dilute enough so that the pH is measurable by ordinary means. The second proton adds to the singly protonated base in strong acid solutions which may be between 10^ and 80^ sulfuric acid. These facts are easily observed by the marked color changes which accompany the first and the second addition of a proton. The ionization constant corresponding to (A) BB where B is the free base, can be measured by methods -131- by which the ionization constants of ordinary acidbase indicators are measured. It can be easily shown that, (1) pKn j- pH - log ..S.R) f - log — (EH^) fBH. which is a form of the Henderson-Hasselbach equation, where K^ is the ionization constant for (1) and where (B) and(BH+) represent concentrations and fR and f„TT+ ■D ±311 represent activities; for the corresponding ionization of the doubly protonated ion Kg is used. Since both the free base and the ion have characteristic absorption bands, it should be possible to use Beer's law to evaluate pK-^ in solutions of known pH by the use of (1). It would be possible to calculate (B) and (BH+) directly if the free base and the ion absorbed in mutually exclusive regions. Bince there is no wave length at which one of the two species (free base and first ion), does not absorb while the other does absorb, certain' modifications must be made (9). The combined Beer-Lambert law, (2) E - "loS I/Io cl where E is the absolute extinction coefficient, -log l/IQ is the optical density, c is the concen­ tration of the colored substance, and 1 is the length of the light path, may be written as -132- (3) -log I/Ic = (Eb ob - E ^ o g g j l where Eg and. Egg--#- are the absolute extinction coef­ ficients for the free base and the first ion, respec­ tively, and Cg and Cgg-f- represent the molar concentra­ tions of these substances. The substitution of the terms in parentheses in (3) for the product Ec in (2) is seen to be justified when it is remembered that a measure of the color observed is Eg EbH'+ if the solution is 1 M with respect to both species; Cg and CgH+ are weighting factors. (4) -log l/l0 = (2) may also be written as E(cg +- cBH*)l Equating the right hand sides of (3) and (4), (5) Ecg f Ecgg-r = EgCg +- EgH+ cBH+ Rearranging, it may be seen that (6) CB __ CBH‘#" E ~ EBH* EB - E Equation (1) becomes (7) pE^ = pH - log E - Egg+EB - E c -log 'f fg bh+ E is the "apparent extinction coefficient" calculated from,observed optical densities at known total concen­ tration of Cg CgH+; Egg+ and Eg represent the same quantity calculated when the first ion and the free base, respectively, are present alone. The use of this equation in the xjr,®sent work is explained later. -133- The determination of the ionization constant for the reaction + BH + (B) H + can be calculated only if the hydrogen ion activity is known and if suitable spectrophotometric measure­ ments can be made. For each of these conditions a modification of the above method must be made. The second proton adds to the singly protonated dye molecule only in strong acid solutions, and here there is no way to measure hydrogen ion activity. Hammett and ueyrup (8) report a function which is a measure of the acidity of strong acid solutions; it cannot, however, be said to be the hydrogen ion acti­ vity. They measure the tendency of a strong acid to protonate a weak, uncharged.base, and for several acids they report HQ, a measure of the tendency of a strong acid to protonate an uncharged base. H. is an anal- ogous function, and it is a measure of the tendency of a strong acid to protonate a base which has a single positive charge. It is this latter function which should be used in the present work, but the values of H+ have never been determined. The results obtained in this wor.-.c show that HQ and H+ are not the same. It is not necessary, as will be seen, to know H+ at various acidities to compare the various dyes. HQ can be used for this comparison. cussed more fully later. -134- This is dis­ Hammett and j-'eyrup determine HQ by making spectrophotometric nieasurements on strong acid solu­ tions of bases which, can take on only one proton. For such a solution pK, where K is the ionization constant, is given by (8) pK = -log aH+°B „ _ -logSnfB . 1o aBH"t' CBH+ ^BH"b where c is the concentration and f is the activity coefficient. The activity coefficient term drops out in dilute aqueous solutions, since concentrations and activities are identical in such solutions. They determine pK from (8) for a base which adds a proton in dilute aqueous acid. It is true that if two bases, B and C, are compared in any solution (9) pK-n - pKp = - log -JL CH^ _ log They assume throughout this work that (10) fB fBH+- _ fG fCH + for any two weak bases. Then pK„ - pK_ may be deterSD 0 c o mined- if B and __£H+ are known, since the last CBH-»°G term of the equation drops oirfc. These may be known from spectrophotometric data, as pointed out above. If pKg Is known (for substance B (8) may be used) then pKq may be Known even if the measurements for the use of (9) are made in a solution in which the pH -135- is not measurable. (9) may then be used in comparing bases C and D, even though D is a weaker base than C; in this manner the pK value of a very weak base, which adds a proton only in 90-95 per cent sulfuric acid, may be known if several bases of intermediate strength such as are described above are used in a series of comparisons. It must be remembered that pK values obtained in this way are referred to a dilute aqueous solution as a reference standard. We may rewrite (8) for any weak base: pK = -log _JL_ BH+ - log a + M This is rewritten sothat (11) pK « - log CB -fcBH+‘ H ° which defines the acidity function, H . It is seen J * o that H o is notthe pH, ■ since oalso takes into account the substitution of concentration for activities. However, if (10) is valid, then H the weak base used. is independent of HQ may now be known for any acid solution in which a weak base whose pK is known takes on a proton. ■Once H q is known for acid of a given strength, the pK of a weak base which adds a proton in acid of that strength may be calculated. This is done in the present work; details concerning this are discussed later. -136- It was mentioned earlier that pK's of very weak bases could only be measured if suitaole spectrophotometric measurements can be made. It is true that both the first and the second ion have characteristic colors in all the dyes studied here, but a difficulty arises in evaluating; the lop; E "*EBH^ term. - E_, E, B and .Er^.+ must be calculated from solutions which must of necessity be very different in acia strength. This means that there is essentially a change of solvent, and the absorption of a given species changes with a change in solvent. The log term mentioned above cannot be evaluated correctly unless the three extinc­ tion coefficients are calculated from the same medium. Plexser, Hammett, and Dingwall (9) disciiss two methods, the least squares and the isobestic point, by which this difficulty may be eliminated: they shorn1 from experiment that the two methods give the same results. In this work the isobestic point method is used exclusively. If the absolute extinction coefficients of two species in equilibrium are identical at some wavelength, then all possible mixtures of these two species should also have the same apparent extinction coeffi­ cient (10) at this wavelength. The absorption curves of all mixtures should intersect at a point if there is no medium effect; this point is called the iso­ bestic point. In the determination of the first -137- ionization constant of the dyes in this work it was noted that there is such an isobestic point; there is therefore no medium effect in these solutions. But in the determination of the second ionization constant (for reaction (B) ) it is seen that, although all absoriotion curves obviously should intersect at a point, they do not do so. Hammett and coworkers assume that there would be a true isobestic point if there were no medium effect, and they correct for the medium effect by using this assumption. They shift all absorption curves laterally so that they all do inter­ sect at one noint. The curves are shifted so that two which apparently are close to the middle of the ioniza­ tion region are nob moved. The use of this procedure assumes that the medium effect is one in which there is only a lateral shift in the absorption curve, not one in which the height or shape is altered. Since this treatment gives good agreement with the least squares method of correcting for the medium effect in the determination of the pK for acetophenone, and the p K ’s calculated vary with wavelength only in a random way, Hammett and coworkers conclude that this assumption is a valid one. -138- FIG. I PK. fo* Y * G H 3 CURVE 6. 75 3.53 L o g Is . I 1.96 NORMRUrv Z.O