ACID . BASE EQUILIBRIA IN LIQUID AMMONIA The“: for" IIIM Degree GI: Ph. D. MICHIGAFI STATE UNIVERSITY J. J. Lagowski 1957 . . - __._._#.... -Tw‘.,'WV‘—wwwwk _ . .~ . ..m-_ mm "= '= I 'F I“! II T -....7. “—an rr'" ‘ . . . — _ _ . v ”1.. vwfl 1W "Ww If?“ ‘ .__ ‘ _ ‘ ‘ - .__ -_ _._‘x';.'.'-:i_- ‘.~ A... -.., .___.. , m- MICHIGAN STATE UNIVERSITY OF AGRICULTURE AND APPLIED SCIENCE EAST LANSING, MICHIGAN ACID—BASE EQUILIBRIA IN LIQUID AMMONIA By JOSEPH JOHN LAGOWSKI AN ABSTRACT Submitted to the School of Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1957 Approved W 77 W an: _ Joseph John Lagowski ABSTRACT The equilibrium which occurs in a liquid ammonia solution of a strong acid, e.g., an ammonium salt, is expressed by equa- tion 1. NH4+X" :3 NH4+ + X" (1) When a weak acid is dissolved in liquid ammonia, the following equilibria are established. RH + NH3 a NH4+R' (2) NHJR" e NHII+ . R' (5) Equation 2 represents the ionization of the weak acid, whereas 1 and 3 represent the dissociation of an ion pair to free ions. Equilibria l, 2, and 5 were investigated voltammetrically and spectrophotometrically. The voltammetric reduction wave which occurs at a rotat- ing platinum microelectrode in liquid ammonia solutions of acids at -77°C. was found to result from the reduction of ion pairs containing the ammonium ion. Data based on the temper- ature coefficient of the diffusion current, the power depend— ence of the rate of rotation of the microelectrode, and the linearity of the plot of the limiting current versus the con- centration of ammonium salt indicate that the electrode proc- ess is diffusion controlled. The voltammetric method could Joseph John Lagowski not be used to estimate the values of ionization or dissoci- ation constants of acids (equations 1, 2, and 3) in liquid ammonia, because the platinum microelectrodes became coated with a dark deposit which changed the electrode characteris- tics. The deposit was shown to be finely divided platinum, and a mechanism was proposed for its formation. Equilibria 1, 2, and 3 were investigated spectrophoto— metrically using phenolphthalein as an indicator. A method was developed to determine absorption spectra of liquid am- monia solutions at ~77SC. Two procedures were devised to determine the ionization and dissociation constants of indi— cators which behave as monobasic acids. The dissociation constants of several ammonium salts, urazole, and urazine were determined in liquid ammonia solutions. Water, urea, benzamide, acetamide, aniline, and carbohydrazide were not sufficiently acidic in liquid ammonia to effect the color of phenolphthalein. The ionization and dissociation constants of guanazole and thiourea were estimated in liquid ammonia solutions. ACID-BASE EQHILIBRIA IN LIQUID AMMONIA By JOSEPH JOHN IAGOWSKI A THESIS Submitted to the School of Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1957 ToJ ii iii ACKNOWLEDGEMENTS The author wishes to express.his appreciation to Dr. Robert N. Hammer for his guidance and encouragement during the course of this investigation. The valuable suggestions and general interest in this investigation of Professor F. B. Dutton, Dr. James C. Sternberg, and Dr. Andrew Timnick are gratefully acknowledged. In addition, the author would like to thank Mr. Frank Bette and Mr. Forrest E. Hood for their assistance and suggestions in the construction of equipment used for this study. Appreciation is extended also to E. I. du Pont de Nemours and Company whose Predoctoral Teaching Fellowship provided personal financial assistance during the academic year 1956-1957. iv VITA Joseph John Lagowski candidate for the degree of Doctor of Philos0phy Dissertation: Acid-Base Equilibria in Liquid Ammonia Outline of Studies Major subject: Inorganic Chemistry Minor subjects: Physical Chemistry, Mathematics Biographical Items Born, June 8, 1930, Chicago, Illinois. Undergraduate Studies, B. S., University of Illinois, 1948-1952. Graduate Studies, M. 8., University of Michigan, 1952-1954, Michigan State University, 1954-1957. Experience: Teaching Fellow, University of Michigan, 1952-1954; Graduate Assistant, Michigan State University, 1954-1956; DuPont Pre- doctoral Fellow, Michigan State University, 1956-1957- Member of American Chemical Society, Society of the Sigma Xi. TABLE OF CONTENTS INTRODUCT I ON 0 C O O O O O O O O O O O O O O 0 GENERAL HISTORICM’ O O O O C O O C O O O O O 0 PART ONE VOLTAMMETRY IN LIQUID AMMONIA HISTORICAL . . . . . . . . . . . . . . . . . . APPARATUS . . . . L . . . . . . . Electrolysis Cells . Microelectrodes . . . Rotation AssembLy . . Reference Electrodes Thermostat. . . . . . Polarograph . . . . . Ammonia Line. . . . . Preparation of Solutions in Polarography in Liquid Ammonia. Chemicals . . . . . . . . . . . DISCUSSION 0 O O O O O O O O O O O O O O O O 0 SW 0 O O O O O O O O O O O O O O O O O O O (Dooooooo t D‘ oomooooooo O Cog-+0000... '1 0000000000 |_I 00‘40000000 U) oomooooooo I...I PART TWO SPECTROPHOTOMETRY IN LIQUID AMMONIA HISTORICAL . . . . . . . . . . . . . . . ... . EXPERIMENTAL . . . . . . . . . Introduction. . . . Light Absorption Cells. . Spectrophotometer . . . Dilution and Volumetric Fls Thermostats . . Use of the Dilution Flask Indicator Studies . . . . Chemicals . . . . . . . . o 0009).. o o o o 0 We. 0 U) ooHoooooooo oomooooooo col—looooooo PAGE DISCUSSION SUMMARY. . APPENDIX A. APPENDIX B. APPENDIX C. APPENDIX D. APPENDIX E. APPENDIX F. APPENDIX G. APPENDIX H. O O O O O O O O O O O O O O O O O O O O 0 Study of Membrane Materials . . . . . . . The Relationship Between the Analytical Concentration of Ammonium Salt and the Concentration of Ammonium Ions or Ion Pairs O C O O O O O O O O O O O O O O O O The Colors of Various Indicators in Liquid Ammonia and Aqueous Solutions. . . The Visible Absorption Spectra of Several Indicators in Liquid Ammonia Solutions at -77OC0 o o o o o o o o o o o o o o o o o Spectrophotometric Determination of the Equilibrium and Dissociation Constants of A Weak Indicator Acid. . . . . . . . . The Determination of the Dissociation Constant of A Strong Acid . . . . . . . . Determination of the Ionization and Dissociation Constants of Weak Acids. . . Suggestions for Further Work. . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . vi 91 131 132 156 159 144 154 161 168 174 176 vii LIST OF FIGURES Figure Page 1 Stopcock electrolysis cell . . . . . . . . . . . . 16 2 Diaphragm electrolysis cell- . - ~ . . - . . . . . l8 5 Modified diaphragm electrolysis cell . . . . . . . 21 4 Detail of aluminum ring clamp. . . . . . . . . . . 22 5 Electrolysis cell. . . . . . . . . . . . . . . . . 25 I 6 Electrolysis cell. . . . . . . . . . . . . . . . . 25 I 7 Electrolysis cell. . . . . . . . . . . . . . . . . 27 I 8 Microelectrodes. . . . . . . . . . . . . . . . . . 28 9 Ground glass electrode shaft and bearing . . . . . 29 10 Electrode compartment. . . . . . . . . . . . . . . 33 ll Ammonia handling system. . . . . . . . . . . . . . 36 12 Weighing vessel. . . . . . . . . . . . . . . . . . 57 15 Apparatus-for polarography in liquid ammonia . . . 59 14 Diffusion current versus concentration of supporting electrolyte . . . . . . . . . . . . . . 42 15 Diffusion current versus concentration of ammonium salt for various ammonium salts . . . . . 49 16 Diffusion.current versus concentration of ammonium salt for various ammonium salts . . . . . 50 1? Dependence of diffusion current upon the rate of rotation. . . . . . . . . . . . . . . . . . . . 53 l8 Log id versus log v for various concentrations 19 20 of ammonium perchlorate. . . . . . . .......55 Current versus voltage for the reduction of ammonium perchlorate . . . . . . . . . . . . . . . 5? Current versus voltage for the reduction.of ammonium perchlorate . . . . . . . . . . . . . . . 58 21 22 23 24 25 26 27 28 29 50 31 52 '53 34 35 56 37 58 39 ‘40 Low temperature light absorption cell. . . . . . . Low temperature light absorption cell. . . . . . . Spectrophotometer. . . . . . . . . . . . . . . . . Detail of absorption cell compartment. . . . . . . Volumetric flask . . . . . . . . . . . . . . . . . Dilution flask . . . . . . . . . . . . . . . . . . Optical density at 585 mu versus concentration of 2,4-dinitroaniline in strong base . . . . . . . Optical density of 2, 4-dinitroaniline at 585 mu and 555 mu in liquid ammonia . . . . . . . . . . . Optical density of 2, 4-dinitroaniline at 585 mu and 555 mu versus concentration of potassium amide Optical density of 2,4—dinitroaniline at 585 mu and 555 mu versus concentration of ammonium perchlorate. . . . . . . . . . . . . . . . . . . . Optical density of penitroacetanilide at 540 mu in liquid ammonia. . . . . . . . . . . . . . . . . Optical density of phenolphthalein at 575 mu versus concentration of ammonium perchlorate . . . Optical density of phenolphthalein at 575 mu versus concentration of potassium amide. . . . . Optical density of phenolphthalein at 575 mu versus concentration of phenolphthalein. . . . . Optical density of phenolphthalein at 575 mu versus concentration of ammonium perchlorate . . Optical density of phenolphthalein at 575 mu versus concentration of ammonium iodide. . . ... Optical density of phenolphthalein at 575 mu versus concentration of ammonium.bromide . . . Optical density of phenolphthalein at 575 mu versus concentration of ammonium.chloride. . . Optical density of phenolphthalein at 575 mu versus concentration of urazine. . . . . . Optical density of phenolphthalein at 575 mu versus concentration of urazole. . . . . . viii 75 74 80 80 82 85 96 98 99 102 104 105 . 106 . 110 . 111 41 42 43 45 46 47 48 49 50 51 52 53 54 55 56 57 58 - 59 6O 61 62 ix Log dissociation constant of acid versus concentration of acid. . . . . . . . . . . . . . . 116 Log dissociation constant versus concentration Of aCid. O O 0 0 O O O O O 0 O O O O O O O 0 O O O 117 Optical density of phenolphthalein at 575 mp versus concentration of thiourea . . . . . . . 118 Optical density of phenolphthalein at 575 mu versus concentration of guanazole. . . . . . . . . 119 Absorption spectra of phenolphthalein in liquid ammonia C 0 O O O O O O O O O O O O O O O O 124 Optical density of phenolphthalein at 575 mp versus concentration of benzamide. . . . . . . 125 Optical density of phenolphthalein at 575 mu versus concentration of acetamide. . . . . . . . 126 Optical density of phenolphthalein at 575 mu versus concentration of urea . . . . . . . . . 127 Optical density of phenolphthalein at 575 mu versus concentration of aniline. . . . . . . . 128 Optical density of phenolphthalein at 575 mu versus concentration of carbohydrazide . . . . . . 129 Apparatus to test electrical resistance of membrane materials . . . . . . . . . . . . . . . . 155 1 Absorption spectra of 2,4-dinitroaniline . . . . . 145 Absorption spectra or p—nitroacetanilide . . . . . 146 Absorption spectrum of phenolphthalein. . . . . . . Ill-7 Absorption spectra of tropeoline CO. . . . . . . . 148 Absorption spectra of methyl violet. . . . . . . . 149 Absorption spectra of thymcl blue. . . . . . . . . 150 Absorption spectrum of grnitroacetanilide. . . . . 151 Absorption spectra of brom cresol purple . . . . . 152 Absorption spectra of methyl orange. . . . . . . . 155 NOmograph. . . . . . . . . . . . . . . . . . . . . 166 Nomo 8r aph C Q C O O O O O O O O O O O C C Q C O C O 167 Table II III IV VI VII VIII IX XI LIST OF TABLES Page Equilibrium constants of acids in liquid mom a O 0 O O 0 O 0 O O O O 0 O O O 0 0 I 0 O 9 Indicator data on urea and its derivatives. . . 11 Summary Of analyses 0 o o o o ‘o o o o o o o o 0 4‘0 Concentration of various species present in solutions with constant ammonium salt concentration . . ._. . . . . . . . . . . . . . 45 Temperature coefficient for diffusion current . 52 Qualitative observations on potential acids in liquid ammonia . . . . . . . . . . . . . . . 65 Critical angles at the interface between Plexiglas and other media . . . . . . . . . . . 76 Summary of analyses . . . . . . . . . . . . . . 89 Extinction coefficient of phenolphthalein in basic solution . . . . . . . . . . . . . . . 109 The limiting values of ED for strong acids. . . 120 The ionization and dissociation constants of thiourea and guanazole. . . . . . . . . . . . . 125 INTRODUCTION The use of liquid ammonia as a reaction medium and its pr0perties as a solvent have been studied extensively since the pioneer work of Franklin and Kraus (l, 2, 5, 4, 5, 6). Several investigators (7, 8, 9, 10) have determined the relative acidities in liquid ammonia of compounds which ex- hibit weakly acidic or basic prOperties in.water. The basic character of liquid ammonia, as compared to water, enhances the acidity of acids and makes this solvent well suited for studying the acid strengths of weak acids. Compounds Which are weakly acidic or not acidic in water become more notice- ably acidic in liquid ammonia. Kraus and his students (10, 11, l2, l5, 14, 15, 16) haVe shown that electrolytes in liquid ammonia are not dis- sociated completely, although these compounds may be completely ionized. Bjerrum developed a theory (17) which accounts for the conductance datapin solvents with.low dielectric constants by considering the interaction of ions at short range. The 1' =4“ 62 cut) (1) T I'C‘CCDET dissociation constant, 5, for the equilibrium.between the ion.pair and its ions is expressed.by equation.l,‘where'g 2 is aDk ,,fl is Avogadro's number, g is the electronic charge, Q is the dielectric constant of the medium, 5,13 the Boltz- mann constant, and a is interpreted as the distance between centers of charge of the ions in the ion pair when the ions are in contact. The values of the function C(b) have been computed for h from one to 80 by Bjerrum (l8) and by Fuoss and Kraus (19). In view of these findings, it becomes ap- parent that the phrase "strong electrolyte" must be used with caution when considering solvents with low dielectric con- stants such as ammonia which has a dielectric constant of 22.7 at -50°C. (20). In these solvents, an electrolyte could be "strong" in the sense of being completely ionized but "weak" in the sense of being incompletely dissociated. The solvated proton in liquid ammonia is the ammonium ion; hence ammonium salts are strong acids, i.e., completely ionized, in liquid ammonia solutions. When an ammonium salt, NH4X, is dissolved in liquid ammonia at a given temperature, an equilibrium (equation 2) exists between the ion pairs NH 4X",-.em-I*'+X" (2) 4 (NH#+X-) and the free ions. Equivalent concentrations of different ammonium salts will not give the same concentration of ammonium ions, because the dissociation constant for equa- tion 2 varies with the size of the ion X. (equation 1). As the analytical concentration of the ammonium salt is increased, equation 2 no longer describes the equilibrium in solution, because ion associations of higher order occur. It has been found experimentally (10, 11, 12, 13, 14, 15, 16) that if the analytical concentration of solute is l x 10-5 M or less, the formation of higher ion aggregates is negligible, and . only ion pair formation need be considered. Two equilibria must be considered for a solution of a weak acid in liquid ammonia. RH + NH3 :2 NH4+R- (5) NH4+R" s.- NH4+ + R- (4) The ionization of the weak acid is represented by equation 5 and the equilibrium between the ions and ion pairs by equa- tion 4. This investigation was undertaken to develop a method which could be used to measure ionization and dissociation constants of acids in liquid ammonia. GENERAL HISTORICAL Ammonium salts are considered to be acids in liquid ammonia solutions. Reasoning from the oxygen system of compounds in which water is the parent substance, Franklin (21, 22, 25) derived a system of nitrogen compounds based on ammonia. For example, alcohols may be derived formally from water by replacing a hydrogen atom with an organic radical; similarly, amines may be derived from ammonia. Acid amides, metal amides and imides, metal nitrides, anilines, ammonium ions, and amide ions may be considered the nitrogen analogs of carboxylic acids, metal hydroxides, metal oxides, phenols, hydronium ions, and hydroxyl ions, respectively. The ammonium ion has many of the characteristics of the hy— dronium ion but exhibits electrical prOperties comparable to other ionic species in liquid ammonia (24). Bergstrom (25) and Divers (26, 27) have reported the action of liquid ammonia solutions of ammonium salts on metals to yield metallic salts. The acidic prOperties of acid amides are indicated by the isolation and characterization (28) of metallic salts of these compounds, which are prepared by reaction between an acid amide and a metal or metal amide in liquid ammonia. Bronsted (29) has suggested that the acidity of a solution should be measured by the activity of the hydrogen ion in that solution, and the dissociation constant of an acid in dilute solutions should be a measure of its acid strength. The acidity, ite., the hydrOgen ion activity, of a solution is influenced by the presence of neutral salts, but the value of the thermodynamic dissociation constant is independent of these effects. Electrometric (50, 51), colori- metric (52, 55, 54, 35), and kinetic (50, 56) methods have been used to determine the acidity of various solutions and the dissociation constants of acids in a variety of solvents. The results of these methods depend on certain assumptions, and each method must be calibrated in terms of an arbitrary reference standard. With proper attention to definitions and reference standards, the three methods should give the same results (50). The electrometric method depends on measurement of the potential of a cell in which the electromotive force is a function of the hydrogen ion activity. An example of a cell which may be used for this purpose is 0.1 N KCl ngcl2 Salt bridge Solution 3 H89 Pt, H2 where S is a solution containing a given hydrogen ion activ- ity. The electromotive force of this cell is expressed by RT E e ‘E0 ' If’ln a‘Hi’ n. where the symbols are defined,in the usual manner. To deter— mine §H+ from a measurement of the electromotive force of this cell, E0 must be fixed, and a method for correcting liquid junction potentials must be devised or defined. E0 represents the electromotive force of the cell when the hydrogen electrode dips into a solution of unit activity, hence an arbitrary assumption must be made to define this solution. The hydrogen ion concentration can be determined kinetically by calibrating the velocity of an acid catalyzed reaction in terms of solutions of known or defined hydrOgen ion concentration and then using the velocity of this reaction to determine the hydrogen ion concentration of the unknown. The colorimetric method requires a reference hydrogen ion solution in order to determine the equilibrium constants of the indicators under investigation; the hydrOgen ion activity of an unknown solution, or the equilibrium constant of an acid, can be evaluated with the aid of these indicators. In each of these methods, the ultimate standard is a solution of a strong acid. Ionization constants of Weak acids in aqueous solutions can be determined from the degree of ionizationq a, using the Ostwald dilution expression, equation 5. The degree of K:f-’—§‘T (5) ionization can be obtained from conductivity data using the Onsager modification of the Debye-Hfickel equation (57) for strong electrolytes, Aer — (A + BAOWE (6) where 1; is the equivalent conductance of the electrolyte at concentration g, 110 is the limiting equivalent conduct— ance, and A and B are constants dependent on the solvent and temperature. In the case of a weak acid, ionized to extent cx at a given concentration, the DebyeoHfickel-Onsager equation becomes A. A A0 .. (A + Mon/m (7) where lL' represents the equivalent conductance of free ions at concentration q, and 41 is expressed byAA//\'. Although A' and a are unknown quantities, they may be evaluated by a series of approximations. If o< is set equal to the con- ductance ratio, /\//\0, as a first approximation, a value for /\' can be calculated from expression 7; a is then set equal to /M/A', using the previously calculated value of A' and a new value of /\' calculated. This process is re— peated until /\' and NH4I ) NH4NO5 ’ NH4Br ’ NH4C1. The relative acid strengths of carbohydrazide, semi- carbazide, and urea have been determined by Corwin and Reinheimer (8) using an indicator technique and the prin- ciple that a base will displace a weaker base from its conjugate acid. Sodium salts of indene (yellow), fluorene (yellow), and triphenylmethane (red) were used as indicators, and the color of liquid ammonia solutions containing carbo— hydrazide, semicarbazide, or urea and each of the indicators was observed. The results of this study are summarized in 11 Table II. The pK values of the indicator acids in ether solutions were obtained by Conant and Wheland (54), and the TABLE II INDICATOR DATA ON UREA AND ITS DERIVATIVES (8) w“ ‘— “:— #_-~ I I * Indene Fluorene Triphenyl- Compound pK 21 pK 25 methane PK 53 Urea --~ yellow colorless semicarbazide --- yellow colorless Carbohydrazide yellow colorless colorless same values were used in liquid ammonia solutions by Corwin and Reinheimer. Carbohydrazide will not decolorize a soluti of sodium indyl, but it will decolorize a solution of sodium fluoryl or sodium triphenylmethyl. Thus, carbohydrazide is a stronger acid than fluorene or triphenylmethane but weaker than indene, and its acid strength, i.e., the value of the dissociation constant, must lie between those of indene and fluorene. The relative acid strengths of the compounds studied were determined to be carbohydrazide > semicarbazide > urea by a similar process of reasoning. THESIS vb. l ‘I I IL? ,I I I I 12 Watt and coworkers (55) have deduced the relative acid strengths of a series of urea derivatives in liquid ammonia by potentiometric titrations with standard potassium amide solutions. Comparison of the potentiometric titration curve: gave the following decreasing order of strengths. NH s 9 NH“ 'Nd-NH“ HNCNH . HNCN‘H » 4 ’ H2 " 3 ’ 2 ' " 2 2 ' "‘ 2 NH IT" (IT I IIH H2N-C-NH2 ’ H2N-C-NH- . HZN-C-NH . HzN-C-NH > RH2 PART ONE VOLTAMMETRY IN LIQUID AMMONIA HISTORICAL The polarographic method has been used extensively for Ithe analysis of numerous substances in aqueous and non- aqueous media; the theory and techniques of polarography have been thoroughly discussed by Kolthoff and Lingane (56). Voltammetry is a term which has been applied to polarographi techniques employing Solid microelectrodes in.place of the conventional drOpping mercury electrode. The surface of a solid microelectrode is nonrenewable, and this electrode tends to be less reproducible than a drOpping mercury elec— trode. The surface characteristics are an important con— sideration in the use of solid microelectrodes; consequently a reproducible cleaning procedure is a major factor. Howeve: the greater sensitivity of rotating or vibrating microelec- trodes to low concentrations of electroactive species is a distinct advantage. Polarographic studies have been conducted in liquid ammonia solutions of ammonium nitrate (Divers‘ solution) at 0°C. (57, 58). Laitinen and coworkers (59, 60, 61, 62, 65) and Nyman (64) have investigated the polarographic reduction of some common ions in liquid ammonia solutions at -56°C.; the lower temperature limit for polarography in this solvent . ".th 14 is the freezing point of mercury, -58.9°C. The half-wave potential for the reduction of the ammonium ion occurs at -l.59 volts versus the lead--0.l N lead nitrate electrode (62); the reduction.product at a dropping mercury electrode is implied to be free ammonium which is stabilized by amalgam formation. Hammer (65) observed that solutions of ammonium salts in liquid ammonia exhibit a reduction wave at a rotating platinum electrode at -78°C. This wave, which is character- ized by a half-wave potential at approximately 0.6 volts versus an electron electrode, is assigned to the reduction of ammonium ions; hydrogen gas is presumably the reduction product. The results of these studies suggest that voltammetric methods could be used to characterize acids in liquid ammonia to give an indication of acid strengths based on the concen— tration of ammonium ions. —.-.'.:€.---=.-II...."' '_ —-'..—-l-II-a-. .- APPARATUS Electrolysis cells The electrolysis cells employed at various stages of this investigation were adapted from.the conventional H—type cell which is frequently used in aqueous polarography. One leg of the cell contained the reference electrode, 31g; ipfgg, while the other leg was the working compartment. The working compartment was constructed from a Pyrex graduated cylinder and the gaseous ammonia inlet from a 5 ml. graduated pipette. In this manner a series of reference marks was established, and the volume of the working compartment was determined with water introduced from a calibrated burette. The female member of a 14/58 standard taper ground glass ' joint near the t0p of the working compartment permitted the introduction of solids while the cell was in operation. The overall width of each electrolysis cell was 15 cm. or less, which allowed the cell to be placed in a one gallon wide- mouth Dewar flask. The first electrolysis cell which was constructed had the working and reference compartments separated by a 4 mm. vacuum stOpcock (Figure 1).. The working compartment was constructed from a 100 ml. Pyrex graduated cylinder and had a maximum useable volume of 75 ml. and a minimum useable volume of 50 ml. Both the working and reference compartments contained small auxiliary platinum wire electrodes which 16 5 m1 pipette m m a w \ llllllllllllllll Illlll lllllllllllllllll'll IIIIIIIIIIIIIOIII 2 mm To exhaust STOPCOCK ELECTROLXSIS CELL FIGURE 1. 1? permitted pro—electrolysis of solutions. The auxiliary electrode in the reference compartment was used to remove sodium metal electrolytically from the solution.which was adjacent to the stopcock. The liquid levels in the working and reference compartments were equalized by condensing ammonia in the electrolysis cell with the stopcock opened. Equilibration of the liquid levels was necessary to prevent mass transfer of solution when the stOpcock was reOpened to conduct an electrolysis. The inability to obtain a stopcock lubricant which would function satisfactorily under the conditions of the electrolysis led to the abandonment of this design. Using Dow Corning Silicone greases (numbers 5 and 55) as lubricants the stopcock turned with difficulty at 40°C. and became immovable at ~77°C. Frequently bubbles of noncondensable gases became trapped in the arms of the st0pcock and intro- duced a large resistance into the circuit. These gases presum- ably were either hydrOgen or nitrOgen. HWdrcgen is a product of the decomposition of sodium metal solutions in liquid ammonia, and nitrogen was used to agitate the solutions before elec— trolysis. To eliminate the difficulties inherent in an electrolysis cell with a stOpcock, a second cell, shown in Figure 2, was designed which incorporated a center compartment separated from the reference and working compartments by semipermeable nembranes. The addition of a drOp of water to the center :ompartment insured that no sodium metal diffused from the 18 1. N2 m MI) is 2mm ‘;rstopcock-\r1 DIAPHRAGM ELECTROLYSIS CELL FIGURE 2. l9 eference compartment into the working compartment which ontained reducible species. The working compartment, con- tructed from a 100 ml. Pyrex graduated cylinder had a max- mum useable volume of 75 ml. and a minimum useable volume f 50 ml. The membrane material was stretched over both ends of he center section and held taut with rubber bands. The enter section was attached to the cell exhaust by Silastic lbing and to the reference and working compartments by a dyer of polyethylene or rubber tape. A coating of Glyptal‘ asin was applied to the tape and allowed to dry. SaranI, >lyethylene, surgical rubber, and CelIOphane films were Ivestigated as membrane materials (Appendix A). .Specially reated Cellophane was found to have characteristics suited > its use as a semipermeable membrane in liquid ammonia. The diaphragm cell tended to leak at the points of .ncture between the working or reference compartments and e center compartment. A leak could be detected by the pearance of a reduction wave characteristic of Cellosolve by the appearance of a small "mushroom-like" growth in a bath liquid at the point of the leak. This growth was :umed to be ammonium carbamate, the reaction product of ;onia and carbon dioxide. * Manufactured by the Chemical Division of General :tric, Pittsfield, Massachusetts. r Trade name for polyvinylidene chloride manufactured Iow Chemical Company, Midland, Michigan. 20 A modification of the diaphragm cell is illustrated in Figure 5. The center compartment was machined from a poly- ethylene rod; a Pyrex ball and socket joint was heat-sealed to the exhaust portion of the center compartment. Cellophane diaphrag s were clamped between the machined faces of the center compartment and the polyethylene face pieces on the working and reference compartments. The face pieces were attached after first being softened in boiling water. They were then forced over glass tubes sealed to the reference and working compartments, and hose clamps were applied while the face pieces were still hot. The face pieces and the center compartment were held together by aluminum ring clamps (Figure 4). The auxiliary electrode which was sealed orig— inally through the bottom of the working compartment, as illustrated in Figure 2, was replaced by a platinum wire sealed through a 5/20 standard taper ground glass joint near the t0p of the working compartment. After thermal equilibrium had been established between the refrigerating bath and the cell, the ring clamps were retightened to compensate for any contraction which may have occurred upon cooling. Leaks develOped occasionally around the polyethylene-CeIIOphane seals. To eliminate the possibility of leaks occurring around the CelIOphane diaphragm,eulelectrolysis cell, Figure 5, was constructed which did not require a pressure seal to keep the diaphragms in position and the cell liquid tight. The center compartment of the cell illustrated in Figure 5 was - "42‘: m;;E-_" ' ._ 21 To NH5 and N2 / supply 1 I I l I l l I ' l l I l l ’ i l I l. I i I J O. I I I l I I I l I I l I I l I. I. \ I I i I II $5.. MODIFIED DIAPHRAGM ELECTROLYSIS CELL FIGURE 3 . Aluminum Polyethylene Aluminum bolt FIGURE 4. DETAIL OF ALUMINUM RING CLAMP 22 -‘ M1“ '3' 23 EZ§ W ”30 ”‘5": a "”3 EXHAUST ,/ EZMM STOPCOCK FIGURE 5 . ELECTROLYSIS CELL 24 replaced with a ground glass joint. A CellOphane diaphragm was stretched over the flanged end of the male member of the joint and held taut with rubber bands. A No. 2 rubber stopper containing a short length of 12 mm. glass tubing with one end flared constituted the support for the second Cellophane diaphragm; CeIIOphane was stretched over the flared end of the glass tubing and held in position with rubber bands. This assembly was inserted between the center compartment and the working compartment into a position.pre- determined during calibration of the working compartment. All rubber items used in this construction were boiled in two changes of 0.1 E sodium hydroxide and boiled in four changes of distilled water. The working compartment was constructed from a 250 ml. Pyrex graduated cylinder. After the electrolysis cell was assembled, the ground glass joint was wrapped with either polyethylene tape or latex rubber tape. A fifth cell, Figure 6, was designed and built, which precluded the possibility of contamination of the solutions by Cellophane. Fine fritted glass disks 50 mm. in diameter separated the working and reference compartments from the center compartment. An ammonia gas inlet tube allowed the center compartment to be filled with liquid ammonia to any desired level, eliminating the necessity of waiting for the liquid levels to equilibrate by mass transfer through the glass frits. The majority of measurements reported in this investigation were made with this cell. . éA—‘u—u __.‘ __ H ' —l-\.--—-n._ 25 .ZMM STOPCOCK % tum“ fl - F d GRADUATED CYLINDER 250 ML J .. \30 MM.)' FINE FRITS <— ISCM. :# D FIGURE 6. ELECTROLYSIS CELL 26 The design of the electrolysis cell which was used. for exploratory investigations of the current-voltage curves of compounds which were potential acids in liquid ammonia is illustrated in Figure 7. A fritted glass disk separated the working compartment from the reference compartment. Microelectrodes The various platinum wire microelectrodes employed in this investigation are illustrated in Figure 8. All elec- trodes were constructed on the end of a female 7/25 standard taper ground glass joint to make them interchangeable on the shaft, Figure.9, of a glass bearing carrying the male member of this joint. The platinum wire which formed the electrode, or more usually a 00pper wire silver soldered to it, was passed through the shaft of the bearing and sealed through a wax plug. The wax plug was formed in a glass tube attached to the shaft of the bearing by a short length of rubber pressure tubing Which served as a flexible coupling between the motor and the bearing shaft. Electrical contact to the polarOgraph was made through a nichrome wire dipping into a short column of mercury resting on the wax plug. A majority of the current-voltage curves were determined using electrodes a or b, Figure 8. Electrode a was a con- ventional wire microelectrode made from platinum wire 0.018 inch in diameter. The exposed portion of the wire was 4 mm. long. Electrode b was identical with electrode g, except that the wire was cut off close to the glass, and the whole 2'? ELECTROLYSIS CELL FIGURE 7. 28 1% \L I, \\ \\ >3 \L K / y w _ SI. LLLLLL *1/PLUG I::I I:-<—Pt DISK TEFLON Aa/ d FIGURE 8. MICROELECTRODES 29 WAX PLUG \% g—RUBBER TUBING PRECISION GROUND SURFACES / I IN“ NIZ'B (ngh as I FIGURE 9. GROUND GLASS ELECTRODE SHAFT AND BEARING P BO electrode was ground to give a circular cross section. Electrode 2, while easier to clean and less fragile than electrode a, had the disadvantage of a smaller limiting current. Electrode g was an attempt to obtain a ring electrode. It had the desirable characteristics of electrode b, and in addition a larger area and hence a larger limiting current. The electrode was constructed by fusing a 100p of platinum wire around a soft glass tube. While electrode 9 did give higher limiting currents than b, it was highly strained and cracked after a few immersions in liquid ammonia. Electrode g was constructed to eliminate the unfavorable strain char— acteristics of g. The surfaces of the platinum disk which were in contact with the glass shaft of the electrode and the Teflon plug were coated with unpolymerized silicon é rubber‘, and the electrode was assembled. After the Silastic had polymerized, the entire assembly was ground to a circular cross section. Ekctrode g was not satisfactory, because the Teflon plug could not be tightened sufficiently to elimp inate leakage of the solution around the platinum disk. The design of electrode 2 permitted the investigation of various electrode materials. A wire made of the material under investigation was sealed through a Silastic plug formed in a glass tube carrying the female member of a standard taper ground glass joint. Occasional leakage was encountered . * Marketed by Dow-Corning Corporation, Midland, Michigan, under the trade name Silastic. 51 with this electrode design, but this could be avoided if care was exercised in forming the Silastic rubber plug. Usually, the microelectrodes were cleaned before use by rubbing the platinum surface with scouring powder. After a distilled water rinse, they were immersed in hot, concentrated nitric acid for one to two minutes, rinsed a second time with distilled water, and dried with an absorbent tissue. Rotation Assembly In experiments involving variations of the rate of rota- tion of the microelectrode from 200 - 1200 r.p.m., a Sargent cone—drive stirrer with a hollow chuck was used. The stirrer assembly was modified by the addition of a larger cone to extend the rate of rotation to 2400 r.p.m. A stroboscope was used to determine the rate of rotation of the electrode before and after a current-voltage curve was made. A system of pulleys was constructed and adapted to the stirrer assembly for experiments involving a constant rate of rotation of 1200 r.p.m. The rate of rotation for this system was determined periodically, and it was found to be constant to £10 r.p.m. over a period of six to eight weeks. Refergnce Electrodgg An electron electrode (60), a platinum sheet electrode, and a lead-lead chloride electrode were used as reference electrodes in liquid ammonia. A sheet of bright platinum suspended in a solution of the supporting electrolyte did not have the characteristics of a reference electrode, because 52 the potential of this electrode was dependent on the current which passed through the circuit. A lead-lead chloride electrode suspended in a saturated solution of sodium chloride in liquid ammonia was unsatisfactory, because lead chloride is appreciably soluble in liquid ammonia. The current-voltage curve of ammonium chloride, using sodium chloride as a sup— porting electrolyte and a lead-lead chloride reference elec- trode, exhibited two reduction waves in addition to the ammonium ion reduction wave. After one electrolysis, the platinum microelectrode was coated with a black deposit. The two additional reduction waves were presumably due to the two step reduction of lead ions. The electron electrode consisted of a sheet of platinum suspended in a solution of sodium metal in liquid ammonia. The concentration of the reference solution was found to be variable over relatively wide limits without a change in the potential of the electrode. In general, the solution was prepared by dissolving a 0.5 cm.5 piece of sodium in approx- imately 40 ml. of liquid ammonia contained in the reference compartment of the cell. Laitinen and Nyman (60) have shown that the process of solution of electrons in liquid ammonia from a platinum electrode is reversible. W When using the electron electrode with the cell illus- trated in Figure 7, it was necessary to eliminate the pos- sibility of the reduction of the solution in the working compartment by the reference solution. The electron elec- trode was prepared in a separate compartment, Figure 10, .35 WM??- 3 42 \ Pressure equilibration L hole 7 [J gm Platinum EZZZZZZ .b‘———— Fine glass frit FIGURE 10. ELECTRODE COMPARTMENT 34 which was inserted into the reference compartment of the cell. This arrangement converted the cell containing a single glass frit to a three compartment cell. Thermostat The thermostat for the electrolysis cell consisted of a one gallon, wide-mouth Dewar flask containing Cellosolve’ as a heat transfer medium and powdered Dry Ice as the re- frigerant. A temperature of -77°C. was insured by keeping an excess of Dry Ice in the Dewar flask. As the bath liquid accumulated moisture, the lower temperature limit of the bath increased. The bath liquid was replaced after a one or two degree increase in the lower temperature limit; replace- ment usually was required after a four week period. A stream of dry air was used to agitate the contents of the Dewar flask. Temperatures other than -77°C. were obtained by the addition of warm Cellosolve. These temperatures could be maintained within *0.5°C. by periodic addition of small quantities of Dry Ice. The temperature of the bath was determined with a calibrated toluene thermometer. Polarograph A Sargent Model XXI recording polarograph was used to determine all current—voltage curves. * Trade name for ethylene glycol monoethyl ether. 55 Ammonia Line The basic system used to handle ammonia gas is illus- trated in Figure 11. To condense a quantity of ammonia in the electrolysis cell sufficient to determine a current- voltage curve, the following procedure was employed. After attaching the cell to the gas handling system by means of standard taper ground glass joints (not shown), the entire system was evacuated and then filled with either ammonia gas or oil-pumped nitrOgen. The system.was kept under a slight positive pressure of nitrogen to eliminate contamination by air. Synthetic ammonia gas from a tank, a, was passed into . vessel b and condensed over sodium metal using a DryIce-- -f Cellosolve cooling mixture. All gases which subsequently : passed into the system were dried by bubbling them through I this solution of sodium metal in liquid ammonia. A one I gallon Dewar flask containing Dry Ice—-Cellosolve was used to condense anhydrous ammonia gas in the electrolysis cell, 2. Manometers g and d were used to follow the condensation of liquid ammonia and to adjust the rate of flow of ammonia gas to the rate of condensation. The safety valve g protected ._ .-._-..-::._ - —: -_. I - the system from excess pressure but permitted evacuation of the apparatus. The maximum allowable pressure in the system .. was varied by adjusting the mercury leveling bulb, g, to the fig Proper height. Ammonia was absorbed by passing the exit gas : stream into a large carboy of water (i). A second carboy, h, served as a safety trap in the event of a suddtn pressure 56 .o<> fifiamwm GZHQQ24N mpg “ago .9” gang .7, 0.0 ouch-.030 nouaooao £5.85. Hawanopom 634.994 ”00 O O O _ _ _ _ m.o _ m o m H mtno . . . . a In} 1 H .. m L n 1 v 1 m 1 m 1 K. 1 m i m igomcm CON-H I. OH 16sz a. 2.0 1. e 1 - d 0.8 S mica M mmzw ° due 1! ‘ guezmo Current. p amp, 22 20- 18- 16- 14- 12- 10 - 1.6 1.2 0.8 58 ’_ 11114010,, = 1.78 x 10'5 11 11.0104 = 0.1 y ! 0.4 0.0 .0.4 Potential 3g electron electrode FIGURE 20. CURRENT VERSUS APPLIED POTENTIAL FOR THE ‘ REDUCTION OF AMMONIUM PERCHLORATE 59 the same limiting current which was observed prior to the formation of the dark deposit. Often the cleaned electrode gave current—voltage curves with a reproducible half-wave potential at approximately 1.0 volt even though the limiting current was not reproducible. ' The coating on the microelectrode was formed by prolonged use of the electrode as a cathode in the voltammetric reduc- tion of ammonium ions or by electrolysis at a constant po- tential using a stationary or rotating microelectrode. The potential which was applied to the microelectrode to obtain a deposit was sufficient to permit the reduction of ammonium ion.pairs but not large enough to cause electron dissolution. Nb deposit was observed when a platinum sheet electrode, one centimeter square, was used to electrolyze a solution which gave a deposit on a platinum wire or a microelectrode. The formation of the deposit is evidently a function of current 'density. In some experiments, the dark deposit adhered tenaciously to the microelectrode and could’be removed only with scouring Powder, whereas at other times the deposit could be removed by Wiping the electrode with an absorbent tissue or by immer— sion in a gently boiling liquid. The deposit was insoluble in hot concentrated nitric, hydrochloric, and sulfuric acids. Platinum was not detected (84) in any of the solutions used to test the solubility of the deposit. A-minute quantity of the dark dePOSit was Obtained by repeated electrolysis of liquid ammonia solutions of ammonium 6O ‘Salts with a microelectrode and was subjected to X-ray dif— fraction analysis. The diffraction patterns of a sample of 1 the deposit, a platinum wire which was coated with the depos- it, and a clean platinum wire were identical. The reduction of an ammonium salt at a platinum microelectrode evidently causes a disruption of the platinum surface to form finely divided platinum. A rotating platinized platinum microelec- trode gave very poorly defined reduction waves when it was used to electrolyze solutions of ammonium salts in liquid ammonia containing sodium perchlorate as a supporting elec- tmlyte. Several of the current;voltage curves resembled curve Q 0f Figure 20 in their general appearance. Coustal and SPindler (85) observed that electrodes used in the elec— trolysis of anhydrous liquid ammonia are coated with a dark dePosit. These investigators further reported that copper, silver, and gold are reduced to fine powders which yield ammonia and the metal upon heating; an analogous reaction Occurs with platinum. A search of the literature has reveal— ed no conclusive evidence for the existence of a platinum- ‘ hydrogen compound, although platinum does absorb hydrogen to an appreciable extent above room temperature. The hydrogen, absorption depends on the state of subdivision of the plat- inum (86). The processes occurring at a platinum microelectrode acting as a cathode in the electrolysis of a solution con— taining an ammonium salt and a supporting electrolyte can be summarized by equations 16 through 19- 61 Pt + N345C- +. e' as (P12311115) + x" (16) Pt + 11114? + 'e = (PtH) + x‘ + NH (17) 3 2 (PtHNHa) a: 2 Pt + H2 + 11115 (18) (P11111133) + ruff + e‘ e.- Pt + m5 + X‘ + H2 (19) After the diffusion of the ion pair to the electrode surface, reduction may occur according to equation 16 or 17. Equation 16 represents the reduction of the ion pair to free ammonium, whereas equation 17 represents the reduction product as hy- drogen. In either case, the reduction product may form a metastable compound of unknown composition at the platinum surface which is sufficiently stable to cause a rearrangement of the surface when it decomposes according to equation 18 or 19. The formation of free ammonium as the reduction product is a distinct possibility. Laitinen and Kolthoff (80) have Shown that the reduction of hydrogen ions to hydrogen gas in aqueous solution occurs at a more negative potential when using a bright platinum microelectrode than with a platinized platinum microelectrode. If it is assumed that a bright platinum microelectrode is platinized or partially platinized by electrolysis of liquid ammonia solutions of ammonium salts, the reduction wave g of Figure 20 represents the reduction 0f ammonium ion pairs at a bright platinum electrode, and waves 2, g, or d represent the reduction at a platinized electrode. Platinizing the electrode had the effect of mov— 62 ilf-wave potential to more negative values for the of acids in liquid ammonia. This is the reverse ier observed by Laitinen and Kolthoff and implies reduction process in liquid ammonia is not the same lich occurs in aqueous solution. Equation 16 repre- alternative possibility, i.e., the reduction of ior pairs, or ammonium ions, to free ammonium. The of the original wave into two more or less distinct gure 20, could be attributed to the simultaneous 1 of ion pairs at two different electrode surfaces. exploratory study of the electrode characteristics silver, and nichrome was made. The ammonium ion uction wave was not reproducible, although a deposit ‘ s to that formed with platinum was not observed with “ these electrode materials. A series of substances which were thought to be acids in liquid ammonia were investigated qualitatively to deter- mine if a wave corresponding to the reduction of ammonium ion pairs could be observed. The determinations were made at a rotating platinum microelectrode using an electron e1ec~ trode as a reference electrode and sodium perchlorate as the supporting electrolyte. The same substances were observed at a conventional dropping mercury electrode using a mercury pool as the anode and a saturated solution of tetrabutyl- ammonium iodide as the supporting electrolyte. The results of this study are tabulated in Table VI. A §+ 62 TU ing the half—wave potential to more negative values for the reduction of acids in liquid ammonia. This is the reverse of the order observed by Laitinen and Kolthoff and implies that the reduction process in liquid ammonia is not the same as that which occurs in aqueous solution. Equation 16 repre- sents the alternative possibility, i.e., the reduction of ammonium ior pairs, or ammonium ions, to free ammonium. The division of the original wave into two more or less distinct waves, Figure 20, could be attributed to the simultaneous reduction of ion pairs at two different electrode surfaces. An exploratory study of the electrode characteristics Iof gold, silver, and nichrome was made. The ammonium ion pair reduction wave was not reproducible, although a deposit analogous to that formed with platinum was not observed with these electrode materials. A series of substances which were thought to be acids in liquid ammonia were investigated qualitatively to deter- mine if a wave corresponding to the reduction of ammonium iOn pairs could be observed. The determinations were made at a rotating platinum microelectrode using an electron elec- trode as a reference electrode and sodium perchlorate as the SUpporting electrolyte. The same substances were observed at a conventional dropping mercury electrode using a mercury P001 as the anode and a saturated solution of tetrabutyl- ammonium iodide as the supporting electrolyte. The results or this study are tabulated in Table VI. TABLE VI 65 QUALITATIVE OBSERVATIONS ON POTENTIAL ACIDS IN LIQUID AMMONIA Ammonium ion wave Ammonium ion wave Substance at R.P.E. at D.M.E. (-77°C.) {-56°C-) Urea No Very small Carbohydrazide No Yes (two waves present) S-Aminotetrazole Yes Yes Urazole Yes (but shifted Yes considerably) Guanazole Two reduction Two reduction waves, one is waves (one might ammonium ion be ammonium ion) Urazine Yes Yes Acetamide No Very small Hydrazidicarbamide No Yes l-Aminobiuret No Yes Thiocarbohydrazide Poorly defined Yes Diaminoguanidine hydrobromide Poorly defined Yes Guanizine hydrobromide Poorly defined Yes ErToluenesulfon- amide No Yes ' Thiourea No Yes Aniline No --- 64‘- Nearly all compounds investigated gave well defined reduction waves at a dropping mercury electrode. In general, the reduction waves at a platinum electrode were much more poorly defined, and some were drawn out to electron disso- lution. The compounds reduced at a dropping mercury elec— trode were Observed at -56°C. while those observed at a rotating platinum electrode were at —77°C. The temperature difference might be the explanation for the apparent lack of an ammonium ion wave at a rotating platinum electrode. If these compounds are weak acids, i.e., not completely ionized, it is conceivable that at the lower temperature the degree Of ionization is less than at higher temperatures. These compounds may still be acids, in that they give ammo— nium ions, but the method may not have been sufficiently sensitive to detect them. SUMMARY The voltammetric reduction wave which occurs at a ro— tating platinum microelectrode in liquid ammonia solutions of ammonium salts at -77°C. has been shown to result from the reduction of ion pairs containing the ammonium ion. Data based on the temperature coefficient of the diffusion current, the power dependence of the rate of rotation of the microelectrode, and the linearity of the plot of the limiting current versus the concentration Of ammonium salt indicate that the process is diffusion controlled. A dark deposit which occurs on the platinum microelec- trode when it is used as a cathode in liquid ammonia solutions containing ammonium salts has been identified as finely divided platinum. A mechanism for the formation of the dark deposit has been derived which is consistent with the known data. The nonreproducibility of a rotating platinum elec- trode which results from the formation of finely divided platinum precludes its use as an analytical method for de- termining ammonium ion pairs in solution. Preliminary experiments indicate that gold, silver, and nichrome microelectrodes behave in a manner similar to that of platinum electrodes, although no deposit could be Observed on the electrode surfaces. IM'I' 'r Iw‘ - . we: investigated qualitatively with a dropping mercury elec— trode and a rotating platinum electrode to determine whether these substances were acids, i.e., whether ammonium ion pairs _ were detectable . «1 —" fwagfé—Wafi __ PART TWO SPECTROPHOTOMETRY IN LIQUID AMMONIA HISTORICAL Several types of apparatus have been described for the determination of absorption spectra of solutions at low temr peratures (87, 88, 89, 90, 91); however, all of the absorption cells employed were constructed Of metal and were designed for use with solutions which could be handled easily at room temperature. The principle difficulty in low temperature absorption spectrosCOpy is to keep the cell windows free of condensed moisture. In general, this problem has been solved in the past by constructing absorption cells with double windows; the space between the windows is either evacuated or swept out continuously with a stream of dry air. The absorption spectra of both liquid and solid ammonia have been reported (92, 95, 94, 95, 96). Absorption spec- troscopy of liquid ammonia solutions is limited to the region between 240 mu and 1000 mm, because liquid ammonia exhibits a series of intense absorption bands beyond these limits. It is possible to determine absorption spectra at wavelengths as great as 2500 mp by using very thin absorption cells and compensating for the interfering ammonia bands (97). Semiquantitative absorption spectroscopy has been con- ducted at room temperature using liquid ammonia sclutions 68 contained in sealed glass or quartz tubes (98, 99, 100, 101), whereas unsilvered Dewar flasks have been used for solutions at -538C. (102, 105). Gibson and Argo (104, 105) constructed a Dewar flask containing four plane glass windows and deter- mined the absorption spectra of solutions of the alkali and alkaline earth metals in liquid ammonia. The apparatus was fragile and its construction difficult. Schattenstein and coworkers (106, 107, 108, 109) modified a polarimeter tube originally designed to investigate the optical properties of solutions in liquid ammonia at room temperature (110) to permit its use as an absorption cell. The polarimeter tube was modified further to permit low temperature absorption spectrosc0py. Double windows were introduced, and the cell was cooled by a massive copper bar which was attached to the body Of the cell and dipped into a cooling bath. The adap— tion of a conventional Beckman cell for use with liquid amp monia solutions at their boiling point has been described (97). Additional studies of absorption spectroscopy using liquid ammonia solutions have been reported without experi- mental details (111, 112, 113). There are a few reports in the literature concerning .' the behavior of acid—base indicators in liquid ammonia solu— tions. Franklin (114) has demonstrated the indicator prOp- erties of phenolphthalein. Liquid ammonia solutions of hydrazo and azo compounds change color upon the addition of a base. Solutions of potassium amide, mercuric nitride, or bismuth nitride become dark red upon the addition of either 69 hydrazobehzene or pfhydrazotoluene, whereas a solution of the hydrazo or azo compound alone, or in the presence of an ammonium salt, is yellow-brown in color (115). The color of the basic solution is attributed to the sodium salt of the hydrazo compound or to a complex ion formed through the azo group (116). White and Knight (117) obtained similar results upon treatment of hydrazobenzene with sodium metal. A brown color appears when a solution of hydrazobenzene or pehydrazotoluene is treated with potassium amide (115), sodium amide, or potassium hydroxide (118); apparently the reaction is reversible. Triphenylmethane may be used as an indicator to follow neutralization reactions in liquid am- monia solutions (114, 119). Using the sodium salts of tri- phenylmethane (red), fluorene (yellow), and indene (yellow), Corwin and Reinheimer (8) have determined the_relative acid- ity of carbohydrazide, semicarbazide, and urea in liquid am- monia. I Schattenstein (116, 120) has reported the colors exhib- ited by some common indicators, nitroanilines, and nitrophenols in acidic (ammonium nitrate) and basic (potassium amide) liquid ammonia solutions. Unfortunately the color of the neutral solution of the indicator has been reported in only a few cases. The absorption spectra of solutions of nitrophenols and nitroanilines have been reported (106, 107, 108, 116), and the behavior of g—nitroaniline is typical of the aniline derivatives. The spectra of a liquid ammonia solution and an aqueous potassium hydroxide solution of grnitroaniline 70 are 1mm. Addition of potassium amide to a liquid ammonia sclution of grnitroaniline causes a pronounced change in the absorption spectrum. Nitrophenols exhibit different absorp- tion spectra in liquid ammonia and in aqueous sodium hydroxide (107). Schattenstein (116) assumed that the nitrophenols were cOmpletely ionized in liquid ammonia, i.e., converted to the corresponding nitr0phenolate ion, and that the differ- ence in the absorption spectra was caused by the interaction of the nitro group and the solvent to form a complex ion or molecule. The reaction of a nitro compound with potassium amide is written - ' O ,0- R—N\ . 16 + NH2‘ .2 R—I'I-o + K“ (20) \O I NH 2 (a) where (a) represents an aromatic nitro compound or a nitro- phenolate ion (116). The complete conversion of nitrophenols to the corresponding nitrophenolate ions and the partial con— version of nitroanilines to the corresponding ammonium salts appears reasonable, since the existence of highly colored ammonium salts of a large number of nitrophenols and sub— stituted nitrophenols is well established (121, 122, 125, 124, 125). Highly colored sodium salts of various nitro— and substituted nitroanilines have been prepared (126), al- though the ammonium salts of these compounds have not been reported. '71 Solutions of aromatic nitro compounds in liquid ammonia are_intensely colored and conduct an electric current (5, 102, 127). When a solution of m—dinitrobenzene is electro- lyzed, nitrogen is evolved at the anode while at the cathode hydrogen is liberated and the nitro compound is partially reduced (128). The ionization of medinitrobenzene, and perhaps other nitro compounds, is believed to occur by the- formation of an ammonium salt, although there is no conclusive evidence for the structure of the anion (116, 128). Hydrazine or ethylenediamine solutions of m—dinitrobenzene exhibit similar properties. In view of these observations, aromatic nitro compounds could be used as indicators in liquid ammonia if the reaction to form the ammOnium salt is reversible. EXPERIMENTAL l_ Introduction In this investigation two low temperature cells were j? constructed for quantitative absorption spectrophotometric I measurements of liquid ammonia solutions (Figures 21 and 22). These cells are unique in that they utilize the "light pipe" prOperties of polymethyl methacrylate* plastics to transmit light between a spectrophotometer and a liquid am- monia solution. It is known that certain transparent materials such as glass, polymethyl methacrylate, or fused silica transmit light through bends in the medium as a result of internal reflection. Ordinary glass contains traces of impurities which absorb much of the light if the path of travel exceeds a few inches. Polymethyl methacrylate, on the other hand, ,, f is colorless and shows almost no absorption of the light passing through it. The absorption spectrum (129) of the plastic indicates a practical working range of 400 mu to 1000 mp in which no absorption bands occur. Polymethyl methacrylate becomes opaque to ultraviolet radiation below 280 mu, and absorption bands occur in the spectrum at 1.16 p, 1.40 p, and 1.72 u. hm; * Transparent polymethyl methacrylate is sold under the Erade name "Plexiglas" by the Rohm and Haas Company and as Lucite" by E. I. du Pont de Nemours and Company. Polyethylene 73 l shoulder liquid “33 Waste NH; solution removal .. I l, , I ‘3 Exhaust ;-- I I I I .‘ I I i l I I ' l l I I l <~1____Rubber .- , l I l | I stopper F : I ' II I I ‘1 ' I I I I; 1 I l I I I ' T I ,. /B:kelite clamp ' I -_ l I ‘g 5 1 2 x 2 1/2“ x 1" _ l ' l | \\ ' 1 O I l [13 I I I 500 m1 : I l l I AspElectrolytic I ' I beaker O . gjfr—T+ I I mann ' I bolts 1 l \ q I I \A l I I I I ' I O I ’ L I I ’ FIGURE 21 . LOW TEMPERATURE LIGHT ABSORPTION CELL Liquid NHa solution \‘I [To aapirator 'l‘o exhaust —r* ‘I To monochromator _ T0 photocell / 1/2" Plexigla a w r ADV-Ir! . . i I e—l"———> I~ 4” FIGURE 22. LOW TEMPERATURE LIGHT ABSORPTION CELL T 75 The light pipe prOperty of polymethyl methacrylate is dependent upon efficient internal reflection of light rays from the polished surface of the specimen. Light entering one end of a rod remains in the rod until it reaches the opposite end or until it strikes a point where the polished surface is scratched or broken. In general, total reflec- tion will occur at the boundary separating two media having different refractive indices when a ray of light in the medium of higher refractive index is directed toward the second medium at an angle of incidence greater than the critical angle. The critical angle is a function of the refractive indices of the two media (21) where g is the critical angle and 31 and 32 are the refrac- tive indices of the more dense and less dense media, respec— tively. From this expression it follows that the greater the difference between the refractive indices, the smaller the critical angle and hence the more probable the internal reflection of a ray of light in the plastic medium. The critical angles for light rays passing from the plastic to air, water, or Cellosolve are shown in Table VII where the data are calculated on the basis of 1.49 for the refractive index of Plexiglas brand of polymethyl methacrylate (130). Comparison of the critical angles listed in Table VII suggests 76 TABLE VII CRITICAL ANGLES AT THE INTERFACE BETWEEN PLEXIGLAS AND OTHER MEDIA -..____.__._nw-‘~ ,._' _ . Medium in contact Refractive sin c c with Plexiglas index Air 1.00 0.671 42°8' Water 1 . 33 O . 894 63°23 ' Ethyl Cellosolve l .41 (151) O . 946 7l°6 ' that Plexiglas in contact with air should be a more efficient light pipe than Plexiglas in contact with either water or Cellosolve; this is observed experimentally. It was observed that a rod of Plexiglas bent in the form of a right angle lost its light pipe property when immersed in either Cellosolve or water but retained this prOperty when covered with rubber tubing. Coating the Plexiglas rod with black enamel, aluminum paint, or opaque, plastic tape did not improve the light piping ability. The most efficient light pipe was obtained when a layer of air was in‘contact with the Plexiglas rod. Light Absorption Cells The first light absorption cell which was constructed is shown in Figure 21 and consisted of 1/2 inch diameter Plexiglas rods covered with aluminum foil, wrapped with Polyethylene tape, and held in position by a Bakelite clamp. The Plexiglas rods were bent to the desired shape after being Li‘softened in a mineral oil bath maintained at 130-140°C. The ends of the rods were polished by drilling a snug hole in a sheet of Plexiglas, pushing the rod through the sheet, and sanding and polishing the end of the rod flush with the sur— face of the sheet. Fine waterproof carborundum paper (No. 300)1umer water was used as the initial abrasive, and final polishing was done with a silk buffing wheel charged with precipitated calcium carbonate and lubricated with turpentine. The surfaces obtained by this polishing technique were not completely free of fine scratches but were satisfactory. Aluminum foil served to form an air space between the polyh ethylene tape and the Plexiglas rod and to reflect stray light back into the rod. Polyethylene shoulders were built up 1/2 inch from the ends of the light pipes to insure re— producible positioning of the cell in the spectrophotometer. The clamp which was used to hold the light pipe rods in position was constructed frOm a block of Bakelite and drilled longitudinally to accept the wrapped light pipe. The block was cut lengthwise to form the two halves of the clamp, and the halves were held together with Bakelite bolts. The Bake- lite clamp containing the light pipe was sealed into a large rubber stopper using Dow Corning room temperature vulcanizing silicone rubber; all joints in the Bakelite clamp were sealed similarly. In addition, the rubber stopper carried a gas exhaust tube and a solution inlet tube; the assembly was con, tained in a 500 ml. electrolytic beaker. 78 An absorption cell requiring a smaller volume of solu- tion than the cell illustrated in Figure 22 was constructed. I One-half inch diameter Plexiglas rods, bent to the shape” 1 shown in Figure 22, were sealed through the Plexiglas side pieces of the cell. The faces of the Plexiglas rods were ' ' ' polished before the cell was assembled. All seals were made with a cement consisting of a saturated solution of low molecular weight Plexiglas in ethylene dichloride and were allowed to age 24 hours before further handling. The cell walls were made from 1/4 inch Plexiglas sheet. To give added surface to the seal between the rod and the wall, a 1/4 inch l thick piece of Plexiglas sheet was cemented to the lower part of the cell wall prior to drilling the hole for the rod. The Plexiglas rods of the completely assembled cell were covered with aluminum foil and wrapped with polyethylene tape. To insure reproducible positioning of the cell in the spectro- photometer, shoulders of polyethylene tape were built up 1/2 inch from the ends of the light pipes. The absorption cell was closed with a rubber stepper carrying a solution inlet tube, a gas exhaust tube, and a tube which permitted removal of the cell contents with an aspirator. The absorption cells were constructed to‘have a light path of 0.5 to 1.0 cm.; the effective light path was obtained by determining the spectrum of a standard solution in the Plexiglas cells. The optical density at 510 mu of a 0003554 N solution of cobalt ammonium sulfate hexahydrate in r" a 1.000 cm. thick absorption cell is known to be 0.1742 (152), no The solution of cobalt ammonium sulfate hexahydrate was pre- pared according to the directions given by Mellon (132), and its absorption spectrum determined using the Plexiglas absorp- tion cells. The effective light path for each cell was cal- culated using the expression A )2 = é?‘i%%§‘ x 1.000 (22) obtained from Beer's Law where g is the effective light path of the Plexiglas absorption cell, and (g) is the observed obs Optical density of the cobalt solution. Spectrophotometer A Beckman Model DU spectrophotometer was modified to I I I ‘ accept the absorption cells. The conventional cell compart- . ment was removed, and the photocell compartment was placed I a sufficient distance from the monochromator to accommodate the Plexiglas absorption cell, Figure 25. The absorption I cell contained in a Dewar flask of refrigerant was isolated I _ from stray radiation by enclosing it in a black cloth bag A attached by drawstrings to Bakelite flanges on the monochrom— ator and the photocell compartment, Figure 24. The mono- chromator, absorption cell, and photocell compartment were maintained in the same relative positions with respect to each other for all measurements. The contents of the absorp- tion cell were at atmospheric pressure but were protected by a drying tube containing calcium chloride and soda—lime. 8O Monochromator Photocell , “ Absorption cell compartment FIGURE 23. SPECTROPHOTOMETER Cloth sleeves with drawstrings Bakelite flange 8 \I\ ' : FYI I‘ . I T f | l : '3 I \\l I \L- t I D I Monochromator f Fhotocell g “" "‘\\ compartment 1 Bakelite ‘\ I flange \ Absorption cell E compartment made of black cloth FIGURE 24. DETAIL 0F ABSORPTION CELL COMPARTMENT ‘._Q 81 Bakelite adaptors were made which permitted the Plexiglas rods from the absorption cell to be inserted into the mono— chromator exit hole and the photocell compartment. The spectrOphotometer was equipped with a Beckman voltage stabi- lizer in place of the conventional storage battery which I requires frequent recharging. I ‘ The spectrophotometer was operated with a single cell, ‘ therefore the slit width to be used at each wavelength had to be determined with the cell filled with pure liquid am- monia. The cell was then cleaned and refilled with the I I solution under investigation, replaced in the spectrOphoto- meter, and the optical density of the solution determined at each wavelength using the predetermined value of the slit‘ width. The slit widths at various wavelengths were checked I two or three times per day and in general were found to agree within the reproducibility of a slit width dial setting. The success of this technique is illustrated by the fact that spectra of the same solutions determined at different times were in agreement to within the experimental error of the. instrument (* 1.0%). Dilution and Volumgtric Flasks Liquid ammonia solutions of known concentration were prepared using the apparatus illustrated in Figures 25 and 26. A volumetric flask, Figure 25, was constructed from a 'one liter Pyrex distilling flask. The neck of the flask was removed below the side arm, a short piece of 100 m1. Pyrex graduated cylinder was sealed to the bulb, and the L __4 12" FIGURE 25. To dilution flask Section of 100 m1 ‘knr“'graduated cylinder llllllll 1 liter round bottom ‘*:_’ flask VOLUMETRIC FLASK I85 ‘5— NHS and Ne Rubber sleeves Liquid removal / tube (a) To exhaust f “To aspirator \ Waste Nils solution re- moval tube T ‘4‘ Side tube a Section of 50 m1 rp graduated cylinder Gas inlet tube 10' Reference mark __r—7 l FIGURE 26. DILUTION FLASK -'-- 0 won-— 81+ neck of the flask was rescaled to the Pyrex graduated cylin- der. The volume of the flask at each graduation was deter- mined gravimetrically using distilled water; volumes could be estimated to i=0.05%. A soft rubber stepper carrying an 8 mm. glass tube was used to close the él‘ask; a gas inlet tube carrying a three-way stepcock passed through a rubber sleeve and into the flask. Ammonia could be condensed at a rapid rate when the end of the gas inlet tube was near the bottom of the flask. After the liquid level had reached the graduations on the neck and the solution had reached thermal equilibrium, the gas inlet tube was withdrawn and the volume of the solution determined. Prior to determining the volume, a stream of dry nitrogen was passed through the gas inlet tube to insure thorough mixing of the solution. The gas inlet tube was pushed back into the solution and used to remove the solu- tion by application of pressure. The volumetric flask was attached to the source of dry ammonia gas and the exhaust system with rubber tubing. A dilution flask, Figure 26, was constructed by sealing two 200 ml. round bottom flasks together with a reference mark between them. A short length of a 50 ml. Pyrex grad- uated cylinder was sealed to the neck of the upper flask, and a side tube was sealed at a 45° angle above the gradu- ations. The flask was closed with a soft rubber stepper carrying a T—tube; a gas or liquid inlet tube passed through the T—tube into the dilution flask. The other leg of the 85 T—tube served as the gas exhaust tube for the flask and was connected to the exhaust system with rubber tubing. A short length Of thin glass tubing also passed through the rubber stapper and was used to remove unwanted solution from the silution bulb with the aid of an aspirator. The gas inlet tube was introduced into the dilution flask to a greater or lesser extent by raising or lowering the flask. The volume of solution in the dilution flask was determined with the gas inlet and waste removal tubes withdrawn from the solution. The volume of the dilution flask at each graduation was deter- mined gravimetrically using distilled water. Thermostats The thermostats for the dilution flask, volumetric flask, and absorption cell consisted of Dewar flasks containing Cellosolve as the heat transfer medium and powdered Dry Ice as the refrigerant. A temperature of ~77°C. was insured by keeping an excess of Dry Ice in the Dewar flask. Temperatures were checked periodically with a toluene thermometer calibrated at the melting point of ice and the sublimation temperature or Dry Ice. Use of the Dilution Flask A weighed amount of the substance under investigation contained in a one cubic centimeter beaker was introduced into the dilution flask. In general, the weight of substance necessary to prepare a solution of the required concentration was sufficiently small to require the use of a microbalance; 86 ‘ Imights were determined by difference to $70.005 milligram. The dilution flask was attached to the ammonia line and im- mersed in a jDewar .flask containing the Dry Ice-~Cellosolve cooling mixture. With the gas inlet tube extending to the bottom, ammonia gas was passed into the dilution flask until sufficient liquid was condensed to bring the level to the graduations on the neck. The solution was allowed to equili- brate with the cooling bath for one hour, and the volume was measured. The gas inlet tube was introduced below the sur— face of the solution contained in the dilution flask, the absorption cell contained in a Dewar flask was attached to the liquid removal tube (a, Figure 26), and the liquid am- monia solution was forced from the dilution flask to the absorption cell with nitrogen pressure. The absorption cell was rinsed three times with the solution under investigation; unwanted solution was removed from the absorption.cell with the aid of an aspirator. During the filling operation the absorption cell was opened to the atmosphere through a calcium cthride and soda-lime drying tower. After the absorption cell was detached from the dilution flask, the spectrum of the solution was determined. To prepare a solution of lower concentration, the solu- tion remaining in the dilution flask above the reference mark between the two bulbs was removed with the aid of an aspirator. Sufficient ammonia was then condensed to bring the liquid level to the graduations on the neck of the flask. The solution was allowed to come to thermal equilibrium and the 87 total volume determined. A stream of dry nitrOgen was bub- bled through the liquid ammonia to mix the solution and hasten attainment of thermal equilibrium. Because the concentration of the original solution, the volume of the lower bulb of the dilution flask, and the new volume of the solution were all known, the concentration of the diluted solution could be calculated. A portion of the solution was removed to the absorption cell in the same manner as before and its spectrum determined. Dilution could be repeated as many times as necessary. The volume of the lower bulb was 210.1 ml. while the total volume of the flask ranged from 422.7 ml. to 452.5 ml. Thus, a solution could be diluted by. a factor of 1/2. Volumes could be estimated to $0.196. In experiments where two solutes were dissolved in liq- uid ammonia to form a series of solutions in which the con- centration of one component remained constant while the con- centration of the second varied, the volumetric flask (Figure 25) and the dilution flask (Figure 26) were used in conjunc— tion with each other. A solution of the solute to be kept at a constant concentration was prepared in the volumetric flask, and a weighed amount of the solute whose concentration was to be varied was introduced into the dilution flask. The volumetric flask, with its gas inlet tube below the sur- face of the solution, was attached to the dilution flask by means of the liquid removal tube. Liquid ammonia solution was forced from the volumetric flask to the dilution flask by nitrogen pressure. The volume of the solution in the ' -xflq~_‘ 88 dilution flask was determined.after agitation with a stream of dry nitrogen to insure complete solution of the solid and after thermal equilibrium had been attained. The volumetric flask was detached from the dilution flask, the absorption cell was rinsed and filled, and the spectrum of the solution was determined. A portion of the contents of the dilution flack was then diluted two-fold with liquid ammonia solution from.the volumetric flask, and.the spectrum was again recorded. The dilution flask, the volumetric flask, and the absorption cell were kept in Dewar flasks containing a Dry Ice-~Cellosolve cooling mixture during all operations. Volumes were measured by removing the flasks momentarily from their cooling baths. Indicator Studies The behavior of various substances as potential indi- cators in liquid ammonia was observed visually. Solid samples of the indicator were introduced into acidic (0.1 11 ammonium perchlorate), basic (0.1 E potassium amide), and neutral liquid ammonia solutions contained in test tubes cooled to -77°C. These solutions were dispensed by siphon tubes from 200 ml. round bottom flasks protected by magnesium perchlorate drying tubes and suspended in Dewar flasks containing a Dry Ice-«Cellosolve mixture. Approximately 0.1 E potassium amide solution was prepared by allowing the required amount of freshly cut potassium metal to react with liquid ammonia drawn from a siphon tank. Ammonia distilled from sodium metal was used as the neutral solution and for the preparation of 89 0.1 E ammonium perchlorate solution. The results of this study are summarized in Appendix 0. Absorption spectra of indicators which appeared promis- ing are given in Figures 52 to 60, Appendix D. Chemicals All ammonium salts, urea, thiourea, and acetamide were reagent grade chemicals, and their purity was established by Kjeldahl nitrogen (Table III). Samples of guanazole and urazole were recrystallized from water to a constant melting point and then analyzed. TABLE VIII SUMMARY OF ANALYSES Compound Calculated Found” % C % H 96 N 36 c 96 H % N Urazole 25 . 76 5 .00 41 . 58 25 . 86 5 . 06 41 . 52 Guanazole 24.24 5.09 70.68 24.26 5.09 70.59 Urazine 20.69 3.47 48.27 18.85 3.62 47.67 Carbo— 17-55 6.72 55-63 e Microanalyses were carried out by Spang Microanalytical Laboratory, Ann Arbor, Michigan. Carbohydrazide and urazine were recrystallized from water-~alc0hol and from water, respectively, until constant 9O melting points were obtained. The reason for the unsatis- factory analyses of these two compounds is not known. Reagent grade phenolphthalein (Mallinckrodt Chemical Company) was recrystallized once from alcohol. Chemicals were dried in M at 100°C. over phosphorus pentoxide and stored in a desiccator containing magnesium perchlorate. DISCUSSION Many compounds in liquid ammonia solutions change color in response to a change in hydrOgen ion concentration just as do indicators in water solutions. These color changes occur because the compounds are acids or bases and because the acid form has a different color form the base form. The hydrogen ion concentration at which the color change occurs depends 0n the acid or base strength of the compound. The acid strength of a compound in liquid ammonia is measured by the value of its ionization constant. The ionization and V dissociation constants of an acid may be obtained from an analysis of indicator data, yidg infpa. Experimental methods which detect the presence of ions, i.e., conductivity and electromotive force measurements, do not give direct estimates of the ionization constant of an acid, because these methods cannot distinguish between ion pairs and molecules. In liq- uid ammonia, a solvent in which ion association is appreci- able as a result of its low dielectric constant, conductivity data can give an overall equilibrium constant which compares the concentration of ions to the total concentration of ion pairs and molecules. Neither the ionization nor dissociation constant of a weak acid can be obtained from conductivity data, but these data may be treated to obtain the dissociation constant of a completely ionized substance (11). However, estimates of :— l. 92 I‘the ionization,constant obtained by conductivity methods are a good first approximation.t0 the order of acid strengths of weak acids. If the ionization constant for a weak acid as determined by conductivity methods, 31*, is defined by equa- tion 25, E? Mic] I = W <2” y then §i* can be expressed in terms of equations 10 and 11 as K.* = ___i__ . KB 0 (24) It has been shown (11) that the dissociation constants of completely ionized substances are of the same order of mag— nitude. As’a result, ED, which is dependent upon ion size, ’ is approximately constant for most substances, and therefore the actual values of the ionization constants of weak acids usually are in the same relative order as the values obtains t ed by conductometric or potentiometric methods. J The indicator behavior in liquid ammonia of thirty—nine E compounds was investigated qualitatively. These compounds ‘ are used as indicators in aqueous and nonaqueous solutions «- or have been suggested as potential indicators in liquid ammonia. The results of this study are summarized in Appen— dix C. It is apparent from these data that the majority of 95 compounds which have been used as indicators in aqueous so— lutions are not acid indicators in liquid ammonia but are basic indicators. In most instances the color of the indi- cator in aqueous base is the same as the color in liquid ammonia. This implies that the process which occurs in.b0th solutions is essentially the same; i.e., the indicator is converted to its basic form. Compounds which are weak acids in water are stronger acids in liquid ammonia because of the greater basicity of liquid ammonia relative to water. The conversion of unionized acid molecules to anions proceeds to a greater extent in.liquid.ammonia than in water. Indi- cators which are used in.aqueous solutions in their basic form remain in.the same form in.liquid ammonia. Addition of a strong base, such as potassium amide, to a liquid amr nmnia solution of an indicator brings about the complete conversion of the indicator to its basic form. Many indi- cators exhibit the same color in liquid ammonia solutions as they do in solutions of potassium.amide. In several cases, the addition of potassium.amide to liquid ammonia solutions causes the appearance of a color different from that in neu- tral liquid ammonia solutions. This behavior is noted espe- cially with aromatic azo and nitro compounds. Shatenshtein (116) attributes the color change of nitro compounds to com- plex formation (20). The reaction of the azo group with Potassium amide is formulated as Ar-N=N-Ar + K” + M2. at Ar-lf—N-Ar" + K”. (25) NH2 94 The choice of an indicator to determine acid strength in liquid ammonia is dependent on two factors. First, the compound must exhibit different colors in acid and neutral solutions, and secondly, at least one absorption maximum for the compound must lie within the visible region of the spec- trum. The latter condition is important, because Plexiglas absorbs appreciably in the near ultraviolet. Compounds which gave yellow solutions were excluded, because their absorption maxima occur in the near ultraviolet or in the shorter wave- length regions of the visible spectrum. With the cell illus- trated in Figure 22, spectra could be recorded to 585 mu employing slit widths of the order of 1.5 to 2.0 mm. in the lower wavelength region. Data were difficult to reproduce below about 420 mu. On the basis of preliminary studies, phenolphthalein, 2,4-dinitroaniline, and p-nitroacetanilide were selected for further investigation. Spectra of some of the indicators which were determined in the course of the I preliminary investigation are recorded in Appendix D. Liquid ammonia solutions of 2, 4-dinitroaniline exhibit absorption maxima at 585 mu and 555 mu, Figure 52, Appendix D. A study was made of the equilibria present in liquid ammonia solutions of 2, 4—dinitroaniline by observing the Optical density of neutral, acidic, and basic solutions of this indicator at 585 mu and 555 mp. Acidic or neutral solu- tions of 2, 4—dinitroaniline appear orange-red in color, and both absorption maxima are present. The absorption maximum at 555 mp is not present in strongly basic solutions of 95 2,4—dinitroaniline in liquid ammonia. The species giving rise to the absorption band at 585 mu obeys Beer's Law; i.e., a plot of concentration of 2,4-dinitr0aniline in potassium amide solutions of liquid ammonia versus the optical density is a straight line (Figure 27). The species giving rise to the absorption band at 555 mu apparently follows Beer's Law in neutral solution, whereas the species giving rise to the absorption maximum at 585 mp does not (Figure 28). The 0p— tical density at 585 mp. increases with increasing concentra- tion of potassium amide, whereas the optical density at 555 mu decreases (Figure 29). With increasing concentration of am- monium perchlorate, both absorption maxima decrease (Figure 50). An explanation consistent with the data available can be formulated in terms of the behavior of 2,4-dinitroaniline as either a monobasic or a dibasic acid. If 2,4-dinitro- aniline is assumed to be a dibasic acid, HZIn, equilibria 26 and 27 will be established in a liquid ammonia solution. 4. .— Haln + N35 4dr N34 + HIn (26) Elm” + NH3 :3: NH): + In: (27) Ion pair formation has been neglected for the purpose of discussion. In strongly basic solutions the doubly charged anion, In", is the predominating species, and this ion is assumed to give rise to the absorption band at 585 mu. The absorption band at 555 mu is assigned to the singly charged 96 1.5 _ .1-4 _ mm, = 0.01 p, 105 P 1.1 — 0.9 - 0.8 — 9|!!- 0.0 1 l L I n x L l I x J O 2 4 6 8 10 12 Concentration, 2,4-dinitroaniline x 10+5 y FIGURE 27 . OPTICAL DENSITY AT 585 mu VERSUS CONCENTRATION OF 2 , 4—DINITROANILINE IN STRONG BASE tans- 1047‘ 1.0—- 0.8—- 0.4L- 0.2- 0. 0 535 mp '3 585 mp [Ll I l l 1 1 l I I i I 2 4 6 8 10 12 Concentration, 2,4-dinitroaniline x 105 1_4_ FIGURE 28. OPTICAL DENSITY OF 2,4—DINITROANILINE AT 585 mp. AND 555 mp. IN LIQUID AMMONIA 97 98 man—HQ. awn—”Wade om no 53455on6 games as mmm g as mwm as. EHqquomaHante m so 352mg .2330 4mm gas w. m OH N NE .nogmnvnoofloo on 3 S 3 NH 2 n n e a WJJJJ’. . 06 do «.0 no N. 4 m n12 x as...” u enaaafieufifladd do as man 0 as mum m 99‘ fiaaoamommm 520% m0 szadezfluzOo mbmmfib .13 mmm a 13 mmm B4 EHHHEONBHZHle N m0 HaHmzmn QOHBAHO .Om Eme m N OH H #03me .noaponuncoaoo on m m p w n 1v n. m H o ,, a‘ _ _ _ _ d t _ _ J 0.0 , m 9.3 e 84. u onadenenflfinéd .. - we as man a as men e I |“ L F; anion, HIn-, and it is assumed that the molecular acid, Helm, does not absorb in the visible region of the spectrum. The behavior of 2,4-dinitroaniline as a monobasic acid may'be formulated in terms of equilibria 28 and 29. HIn + mi5 a NHL: + In“ (28) In- + NH- : InNH2= (29) Figures 27 through 50 may be explained in terms similar to those used for equilibria 26 and 27 if the assumption is made that the species In" and InNH2= give rise to the 555 mu and 585 mu absorption bands, respectively. Equation 29 rep- L resents a reaction similar to that proposed by Shatenshtein ,; (116) for the color formed in liquid ammonia solutions of ?* potassium amide and aromatic nitro compounds, equation 20. Although sufficient data are not available to decide conclusively whether equilibrium 2? or 29 represents the second step in the ionization of 2,4-dinitroaniline, the suggestion that this compound is a dibasic acid in liquid ammonia solutions appears to be the more reasonable. Aniline,‘ the nitrogen analog of jphenol, would be expected to act as a dibasic acid in liquid ammonia. The ionization constants t” of phenol, g—nitrophenol, and 2,4—dinitr0phenol in water are 8 1.5 x 10’“), 6.8 x 10" , and 8.5 x 10"5 (155), respectively. Reasoning by analogy, the acid strength, i.e., ionization constant, of 2,4-dinitroaniline should be much greater than 4 101 that of aniline in liquid ammonia. Monosodium salts of a 'wnuety of substituted nitroanilines have been prepared (126), 1mm no salts which support the premise that aniline is a dibasic acid have been.reported. It is interesting to note that the sodium salt of N—ethyl-p—nitroaniline has been re- ported but that the salt of N,N—dimethyl-p—nitroaniline could not‘be isolated (126). Liquid ammonia solutions of penitroacetanilide are yellow-green, and the color intensifies as potassium amide is added to these solutions. A.solution 0f penitroacetanilide in 0.1 N ammonium perchlorate is colorless. The yellow-green solutions have absorption maxima at 450 mu, Figure 55, Ap- pendix D. The species which gives rise to the absorption band at 450 mu does not obey Beer's Law (Figure 51) in.neu— tral solutions. The deviation from Beer's Law can be explain- ed if penitroacetanilide is a monobasic acid, HIn, in liquid ammonia, equilibrium.50. HIn + NH5 as my," + In (30) It is assumed that the anion, Inf, gives rise to the absorp- tion band at 450 mm and that the molecule HIn does not absorb in.the visible region since liquid ammonia solutions of Ernitroacetanilide are colorless in acid and yellowegreen in base. prNitroacetanilide may be considered as either a sub- Stituted acetamide or as a substituted nitroaniline. In —...-_.r. bl» 0.0 l l Ji 102 0 1 2 5 ,4 Concentration, prnitroacetanilide x 10 FIGURE 51.» OPTICAL DENSITY OF p—NITROACETANILIDE AT 450 mp. IN LIQUID AMMONIA either case, the group attached to nitrogen, acetyl or ! prnitrophenyl, are electron withdrawing groups which make the hydrogen atom attached to the nitrogen more acidic than the correSponding hydrogen atom in the parent compounds. Green and Rowe (126) have isolated the sodium salt of N-ethyl— pynitroaniline. The absorption spectrum of phenolphthalein in liquid ammonia solution shows an absorption band at 575 mu, Figure 54, Appendix D. Dykhno and Shatenshtein (107) have observed an absorption band for phenolphthalein in liquid ammonia in this region also. Aqueous basic solutions of phenolphthalein show an absorption maximum at about 560 mp (154). The addi— tion of ammonium perchlorate causes the optical density of the solution at 575 mm to decrease, Figure 52, whereas the addition of potassium amide causes the optical density at 575 my to increase initially and then decrease rapidly to zero (Figure 55). The optical density at 575 mu of a liquid ammonia solution of phenolphthalein does not obey Beer's LaW, Figure 54. These data may be interpreted by assuming that phenolphthalein behaves as a dibasic acid in liquid ammonia, equilibria 51 and 52, and that the second ionization has not H 2In + NH as NH; + HIn‘ (51) 5 H111. + NH3 $ NHL: + In: (52) proceeded to an appreciable extent in neutral solution. on The basis of these assumptions, the anion, In=, and the un—- Phenolphthslein = 5.09 x 10‘5 y i 1 QIIIIJJLIII 02468101214161820 Concentration, mom, x 10+5 g FIGURE 52. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF AMMONIUM PERCHLORATE 104 105 Phenolphthalein= 5.07 x 10-5 M 0.0 | | 1 l J .2 r 0 2 4 6 8 10 12 14 16 18 1 Concentration, Mg 1: 10+} M ‘ FIGURE 55. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF POTASSIUM AMIDE I— l I I I I I I I I 0 ~ 1 2 5‘ 4 5‘ 6 Concentration, phenolphthalein x 1045 M FIGURE 34. OPTICAL DENSITY 0F PEENOLPHTHALEIN AT 575 mp. VERSUS CONCENTRATION OF PEENOLPHTHALEIN 106 107 ionized acid, 321n, do not absorb in the visible region of the spectrum, whereas the absorption.band at 575 mp is attri— buted to the species, HIn-. The addition of a strong base to a neutral solution containing phenolphthalein should cause the concentration of HInI to increase to a certain point, then the concentration of HIn_ should decrease because reac— tion 52 occurs (Figure 55). The addition of an acid to a neutral solution of phenolphthalein should cause the concen- tration of HIn- to decrease, Figure 52. The behavior of phenolphthalein in liquid ammonia is similar to its behavior in aqueous solution. The behavior of phenolphthalein as an indicator in aque— ous solutions is summarized (155, 156, 157) by the following equations. “Cage“ in, “@5ch H01 > Cg 0 O Lactone 2 Na+ I + 2 H 0 2 °C( 53°01) I?” \ H01 \ C NaOH —C-0- -C-0' 8 ll _ O J + H20 Carbinol Quinone 108 It is believed that the lactone and carbinol forms of the indicator are colorless, whereas the quinone structure is red (158). In all probability, the ionization constants for the removal of each of the phenolic hydrogen ions are essenp tially equal, and phenolphthalein may be considered as a di- basic acid. The red color is associated with removal of the first hydrogen ion, and further addition of base causes the red form to disappear. Using a colorimetric method, Rosen— stein (159) determined the first ionization constant for phenolphthalein to be 1.8 x 10"10 in aqueous solutions; this study was made assuming that phenolphthalein behaves as a monobasic acid when the color change colorless ——»red occurs. Assuming that phenolphthalein behaves as a dibasic acid in liquid ammonia and that equations 55 and 54 represent the NH + H In = NH4+HIn‘ (55) 5 2 NH4+HIn- e: N114+ + HIn‘ (34) equilibria involved in the color change, the ionization and dissociation constants were calculated using the method out- lined in Appendix E. The data used to construct the curve shown in Figure 54 were employed in these calculations. The ionization and dissociation constants, and the extinction coefficient at 575 mu for the red anion, were determined to be 0.21, 10.1 x 10'5, and 8.29 x 104, respectively, at ~77°C. The extinction coefficient of the red anion was determined 109 independently by completely converting a known concentration of phenolphthalein to the red anion with potassium amide. The experiments were conducted with sufficient potassium _ amide present to insure that the Optical density of the so- lution at 575 mu was the maximum (Figure 55). These data are summarized in Table IX. TABLE IX EXTINCTION COEFFICIENT OF PHENOLPHTHALEIN IN BASIC SOLUTION Concentration Optical density Concentration at KNHZ at 575 mu phenolphthalein ,575 mu (molarity) (molarity) x 10-4 1.45 x 10‘3 2.56 5.07 x 10‘5 7.70 1.66 x lo'4 2.58 5.07 x 10"5 7.75 4.01 x 10‘5 2.58 5.07 x 10'5 7.75 The effect of the addition of a strong acid, i.e., an ammonium salt, to a liquid ammonia solution of phenolphthalein can be deduced from equilibria 55 and 54. Figure 52 and Figures 55 through 40 illustrate the effect of adding various ammonium salts, urazine, and urazole on the Optical density 0f liquid ammonia solutions containing phenolphthalein. It was assumed that urazine and urazole were completely ionized in liquid ammonia because the data in Figures 59 and 40 are more comparable to the data for strong acids than for weak acids, Figures 45 and 44. Urazine and urazole exhibit acidic Properties in aqueous solutions. The ionization constant of WI 110 --.- -u_-__ Phenolphthalein : 2.60 x 10.5 fl PUP 0.5- calf- l 1 L 1— l L_ L g 4 J o 2 4 6 8 10 Concentration, M40104, x 10*“ 11 FIGURE 55. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF AMMONIUM PERCHLORATE M» 111 Phenolphthalein : 2.95 x 10"5 g 002?- OJ) 1 1 1 1L,44 41 1 1 1 J o 2 A 6 8 10 Concentration, NH4I x 10+4‘fl FIGURE 56. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF AMMONIUM IODIDE Hmenolphthalein: 2.88 x 10‘5 M 0.5 - I 1 I n l I l I I l o 2 4 6 8 1o Concentration, NH4Br 1: 104-4 E FIGURE 57. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF AMMONIUM BROMIDE 0.5- 0.1— FIGURE 1 l l l l 2 4 fhenolphthalein = 2.90 x 10r5 M 113 1 l 1 J__J 6 8 10 Concentration, NH401 x 10+4.M 58. OPTICAL DENSI VERSUS CONCENTRATI TY OF PHENOLPHTHALEIN AT 575 mp ON OF AMMONIUM CHLORIDE J .i . Phenolphthalein = 2.71 x 10"5 2:! 0.5 _ 0.5 - ' I 1 0.1 - 1 ‘ l l l l I I I I l J; o 2 II 6 8 10 Concentration, urazine x 10+“ M l l FIGURE 39. OPTICAL DENSITY OF PEENOLPHTHALEIN AT 575 mp. VERSUS CONCENTRATION OF URAZINE Phenolphthalein= 2.70 x 10"5 fl 0.1 — I I l I I I I I I I J 0 2 4 6 8 10 12 ,4 Concentration, urazole x 10 M FIGURE 40. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF URAZOLE III 11.! 012545678910 Concentration, acid x 1 M FIGURE 41. LOG DISSOCIATION CONSTANT OF ACID VERSUS CONCENTRATION OF ACID 116 F o Urazine 5' Ura 20 1e Log In 6'0 IllIIII 01334567891011 Concentration, acid x 10+)+ M FIGURE 42. LOG DISSOCIATION CONSTANT VERSUS CONCENTRATION OF ACID Phenolphthalein : 2.88 x 10'5 2'1 / _ 0.8 — Phenolphthalein 2.55 x 10"5 M CS — 0.4 — 0.2 — 0.0 I ' 1’4 o 1 2 5 +5! Concentration, thiourea x 10 FIGURE 45. OPTICAL DENSITY OF PHENOLPHTHAEEIN AT 575 mp VERSUS CONCENTRATION OF THIOURE , 2°!» _ Phenolphthalein: 2.94 x 10.5 M 1.0 — 008 '- 0.6 - 0.4 — 0.2 r I I 111________J———-———J 0 1 2 5 4 5 Concentration, Guanazole x 10 M EENOLPHTHALEIN AT 575 mp FIGURE 44. OPTICAL DENSITY OF P GUANAZOLE VERSUS CONCENTRATION OF 120 urazole in water has been reported as 1.6 x 10'6 (140). The pH of a saturated aqueous solution of urazine at 25°C. is 5.4 (141), and the ionization.constant can be estimated to be 4 x 10-6. Acids with ionization constants less than 4-x 10'6 in aqueous solution are known to form stable ammo- nium salts, and it would be expected that the ammonium salts of urazine and urazole would form when these compounds are dissolved in liquid ammonia. The data for urazine, urazole, and the ammonium salts were analyzed by the method outlined in-APPendix F to evaluate the dissociation constants of these comPOunds. Constant values for the dissociation constants were not obtained with this method. The dissociation constants decreased regularly with the total concentration of the acid, Eigures 41 and 42, and the decrease was more pronounced in the case of the ammonium salts than for urazine and urazole. The values for the dissociation constant at zero concentration 0f ammonium salt are summarized in Table X. TABLE X THE LIMITING VALUES OF KD FOR STRONG ACIDS Acid Limiting value of KD x 10+6 Ammonium chloride 8.71 Ammonium bromide 6-87 Ammonium iodide 4-75 Ammoflium perchlorate 4.96 Urazine 15.2 Urazole 15 . 6 / A —_._ 121 , In the derivation (Appendix F) of the equations used to . calculate the dissociation constant of a strong acid, the ‘I dissociation constant was written in terms of the concentra- tions of the species present (equation 56). NHJX" a mg,” + X‘ (35) NH + x' - E 4”] (56) D ‘ [NH4+X'] The equilibrium constant for equation 55 should be written in terms of activity coefficients and concentrations. EH4? [Xj . KNH4+ z‘Xn c draft] “mgr 57) Substituting equation 56 into equation 57 and taking the lagarithm of both sides of the resulting equation gives 10g ° = log + logx + log 6 — log 6 . (58) According to the Debye—Hfickel theory (142), the activity coefficient of an ion is given by the relationship logK =- -A Vrfi‘ (59) 122 ”where A is a constant for a given solvent and temperature and In is the ionic strength of the solution. Kirkwood (145) 'has expressed the activity coefficient of an ion dipole as logIS = ~Bp (40) where Q is a constant dependent On the solvent and the size of the dipole. Assuming that equation 40 can be used to express the activity coefficient of an ion pair, equations 38: 39, and 40 may be combined to give log KD = log K5 + 2 A V p — By (41) As indicated by equation 41, the concentration constant, 10g KD’ is a function of the ionic strength. An attempt was made to fit the data in Figures 41 and 42 to equation 41, but constant values of K5, A, and B could not be obtained. The limiting value of ED for the ammonium salts are about two orders of magnitude less than the dissociation constants of Kraus and Bray (10). In addition, the order of the dissociation constants of ammonium chloride, ammonium bromide, and ammonium iodide is the reverse of that which would be expected from a OOnsideration of the relative sizes Of the halide ions. Neither of these apparent contradictions can be explained with the available data. An investigation was made of the ionization and disso- Ciation constants of several substances which were believed __ 125 Ito be weak acids in liquid ammonia. Only two of the sub~ stances studied, thiourea and guanazole, affected the color of a solution of phenolphthalein in liquid ammonia, Figures 45 and 44. Water, benzamide, acetamide, urea, aniline, and carbohydrazide were not sufficiently acidic to change the color of this indicator in liquid ammonia (Figures 45 through 50). The ionization and dissociation constants of thiourea and guanazole were determined by the method outlined in Appendix G; these calculations are summarized in Table XI. TABLE XI THE IONIZATION AND DISSOCIATION CONSTANTS OF THIOUREA AND GUANAZOLE Substance Ki KD Thiourea 4 x 10"5 11 x lo“5 Thiourea 5 x 10"3 8.0 x 10"5 Guanazole 5 x 10’5 9.6 x 10"5 Guanazole and thiourea exhibit no acidic prOperties in aque- ous solutions but are, on the contrary, weak bases (145, 146)} Using the method outlined in Appendix G, the ionization constant of a weak acid is determined from an equation con— taining an additive term (equation xxviii, Appendix G). As a result, the values for the ionization constants in Table XI cannot be determined to more than one significant figure. 124 s Anhydrous 0 Water = 7.7 x 10"2 g jiT I I l L J L I L J I 500 520 540 560 580 600 wavelength, my FIGURE 45. ABSORPTION SPECTRA OF PHENOLPHTHALEIN IN LIQUID AMMONIA Phenolphthalein = 5.10 x 10’5 A! 0 A W W ’ 0.6 — I Ooh '- I I 002 _ 0.0 l I L I I I I I o 1 2 5 4 5 6 7 8 Concentration, benzamide x 10’2‘M FIGURE 46. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 my VERSUS CONCENTRATION OF BENZAMIDE 126 Phenolphthalein: 2.69 x 10-5 3M f Concentration, acetamide x 10+ __ FIGURE 47. OPTICAL DENSITY OF PHENOLPHTHALEIN AT 575 mp. VERSUS CONCENTRATION OF ACETAMIDE Phenolphthalein = 2.68 x 10"5 fl FBHD OPTICAL DENSI 5’ 3 __’—-————-° l l_______L_._________L__________J 1 2 5 4 Concentration, urea x 10+} g TY OF PHENOLPHTHALEIN AT 575 mp VERSUS CONCENTRATION OF UREA 128 Phenolphthalein = 5.11 x 10-5 M FIGURE 49, l I I I I I I 2 4 6 8 10 12 14 e5M Concentration, aniline x 10 F PHENOLPHTHALEIN AT 575 mp OPTICAL DENSITY O N OF ANILINE VERSUS CONCENTRATIO FIGURE 50. l L O 2 4 6 Concentration, carbohydrazide x 10 I 8 I 10 L 12 Phenolphthalein: 2.94 x 10. M I 14 A OPTICAL DENSITY OF PHENCLPHTHALEIN AT 5 VERSUS CONCENTRATION OF CARBOHYDRAZIDE 129 75 In}: 150 erminess. of an indicator is determined by its ioniza- IttiOn constant and the ionization constant of the acid under ‘investigation in such a way that an indicator is most useful when its ionization constant and the ionization constant of the acid under investigation are Of the same order of mag- nitude. In view of this, it can.be seen that phenolphthalein, with an ionization constant of 0.21 in liquid ammonia, would not be a good indicator to use for an accurate determination of the ionization constant of thiourea or guanazole. On the basis of this investigation, the compounds studied exhibit the following relative order of acid strength. Ammonium salts Urazole )> Phenolphthalein ) Urazine Thiourea Water Guanazole :> Urea Benzamide Acetamide Aniline Carbohydrazide These data are in agreement with the observations Of Watt . and coworkers (55)- "— —-——-—- - -— SUMMARY A technique was developed to determine absorption spectra of liquid ammonia solutions at -77°C. The behavior of thirty- nine indicators has been studied visually, and nine of these were investigated spectrOphotometrically. Phenolphthalein, 2,4—dinitroaniline, and pynitroacetanilide were found to be useable in acid solutions in liquid ammonia. Two methods were developed to determine the ionization and dissociation constants of weak monobasic indicator acids in liquid ammonia. The ionization constant of phenolphthalein was found to be 0.211'Whereas the dissociation constant of the indicator in this solvent was observed to be 10.1 x 10’5. The dissociation constants of several ammonium salts, urazole, and urazine were determined using phenolphthalein as an indi- cator; in addition, values for the ionization and dissociation constants of guanazole and thiourea were obtained. Because water, urea, benzamide, acetamide, aniline, and carbohydrazide - were not sufficiently acidic to effect the color of phenol- phthalein in liquid ammonia, the ionization and dissociation constants of these substances could not be determined. APPENDIX A STUDY OF MEMBRANE MATERIALS Membrane materials were subjected to liquid ammonia solutions of sodium perchlorate and sodium metal, and the “electrical resistance of these membranes was determined by measuring the current flow between platinum electrodes a and b of the apparatus illustrated in Figure 51. Electrode b was immersed in a solution of sodium metal in liquid ammonia contained in a glass tube, one end of which was closed with a film of the membrane material. The film was held in position by rubber bands. Electrode g and the tube containing electrode 2 were placed in a Dewar flask con- taining a solution of sodium perchlorate in liquid ammonia. The potential applied across the electrodes and the current which flowed through the circuit were recorded by a Sargent Model XXI polarograph. The relative electrical resistance of various films was determined by using the same experimen— tal procedure for each film. Collodion membranes were completely soluble in anhydrous liquid ammonia, while Saran was attacked by solutions of SOdium in liquid ammonia within 24 hours giving a tarry, black residue. Polyethylene films and surgical rubber sheet- ing withstood chemical attack by liquid ammonia solutions of sodium metal and sodium perchlorate, but the high elec- trical resistance of these films precluded their use as semipermeable membranes. 135 It"? (’1 LII \, g1 Sodiun s olution / Membrane {- /‘\ Dewar flask .nr—f Sodium perchlorate / solution FIGURE 51 . APPARATUS TO TEST ELECTRICAL RESISTANCE OF MEMBRANE MATERIALS 154 Cellophane films, when placed in anhydrous liquid mmwnia,shrank fifty percent Of their length (measured par- aflel to the direction that the Cellophane leaves the roll) Within 24 hours. The shrinkage was greatest during the first 1mm hours of immersion. This shrinking process was accom- panied by an appreciable increase in film thickness. The Cellophane film was pliable while wet with liquid ammonia, but it became extremely brittle as the ammonia evaporated. The re was no apparent attack by liquid ammonia solution of sod' - lum metal or sodium perchlorate on Cellophane. The sres' lstance of Cellophane films was of the same order of mag- nit . . ude as.that of a medium glass frit substituted for the f. . 11m in the apparatus shown in Figure 51. Commercially available nonwaterproof CellOphane was not useabl ' - e directly as a membrane material, because it contains 1 . . 8 ycerol as a plasticizer. It was shown that glycerol in 11 ' - - . Quid ammonia is reducible at a platinum microelectrode and th . . at the reduction wave interferes with the interpretation of . . . " the ammonium ion pair reduction wave. waterproof Cello— Phan ' - ' e also introduced stray reduction waves which were caused Presumably by the coating material. Pieces of nonwaterproof Cellophane were extracted with distilled water in a Soxhlet apparatus for eight hours to and the extracted Cellophan To form a diaphragm, remove the glycerol, e was stored s used. blotted as dry as pos- r the appropriate I - . . 1n distilled water until it wa a Piece of extracted Cellophane was Slble with absorbent tissue, stretched ove 155 openings, and held in position with rubber bands. After the diaphragm had been constructed and installed in the electrol- ysis cell, the cell was filled with a liquid ammonia solution of sodium metal and allowed to remain for 5—4 hours; this treatment insured the removal of water and trace amounts of i reducible substances which might not have been removed. ‘ ,,,,,,, APPENDIX B THE RELATIONSHIP BETWEEN THE ANALYTICAL CONCENTRATION OF AMMONIUM SALT AND THE CONCENTRATIONS OF AMMONIUM IONS OR ION PAIRS Equilibria i and ii are established when an ammonium salt, NH4X, and a sodium salt, NaX, are dissolved in liquid ammonia, and the concentrations of all the species must adjust 17° SatiSfy equations iii and iv. Concentrations have been N34+X— a: NH; + X'- (i) N3+X- #3 Na+ + X— (ii) + KD = EHE+J.Efj (iii) [3%, X] K. .__ mini (1.) D [Na+X'j substituted for activities, since very little is known con- cerning activity coefficients in liquid ammonia solutions under the conditions employed in this investigation. , Let a and p represent the initial concentrations of the ammonium salt and the sodium salt, respectively. Also, let g and X be the equilibrium concentration of ammonium ions and SOdium ions, respectively. The equilibrium concentra- tions of all species may be expressed in terms of a, p, g, and I, 137 EN-Hqfi = X fifiaf] - y [NH4+Xj = a — x (v) [kani] = b — y [X‘] X+y EQuations vi and vii are obtained by substituting the ex— Pressions v into equations iii and iv. (vi) x X + D a - x x + (vii) In the Case where-b is very much larger than a, equations Vi and vii may be solved readily. It is assumed that x is negligible when compared to 1, although ED and ED. are of the same Order of magnitude. Equations vi and vii become KD = _EEZ£ZZ_ (viii) (a - X) 2 Kv=..l————. - (ix) D (b - y) Assuming 1 is negligible when compared to 2, equation 1X may be rewritten as 1;; (X) Solving equation x for y, substituting the results into equation viii, and rearranging the expression, equation xi is obtained. K a . x _ D (xi) I KD + KDb Equation v has defined x as the concentration of ammonium a . ' ' + - ions in solution. The concentration of the ion pair, NH4 X , is obtained from equations v and xi. EWH*x':| = (a-x)=a-————-—I§2—:—'— (xii) ‘ 4 KD +‘V7%;fi; Equation xii may be rearranged to l Kv'b (xiii) +- — ——'—'-—-_ EquLX] ‘ a K13” KD'b Thus, the ammonium ion, ammonium ion pair, and the tOtal e linear functions of the ana— ammonium ion concentration ar . . I lytical concentration of the ammonium salt, Since 39 v —D’ t for a given combination of ammonium salt and b are constan and supporting electrolyte. )- to .an. .. APPENDIX C THE COLORS OF VARIOUS INDICATORS IN LIQUID AMMONIA AND AQUEOUS SOLUTIONS L .Hoaoo poaowb pnoflmqwnp m dmpflnfinxo poHOH> thpcs mo dospsaom owes ad .m .dOflPSHom canon as noonm dam mdoapdaom ofldwom dam awnpdos as Boaaoh dogwommm noonw opflnowamfi mo mHMptho on» .mmoasoaoo ohms machSHom on» flmfioflpad .H .Hopmoaqu omhp afloamnpnmsouadm so nwmawnpnm Amv .obfipmem906 ahflpoaahqonmasa ABV .eoaats I w .emaoae I > .eoa I m .anaa I am a a o camhsm I m .owqmno I 0 .soon I w .mmoanoaoo I o .dsonfi I Hm asap I m sense I 4 o.mno.m e m , w.aum.o >Im w e nmuo 0 mass poaoae assets . r m.mum.n m a w o.mIo.N d o m m m Amav can HomoHo o.mHIe.HH o m o.mua.o mum w o o o anav steam opasomams mum > sum as _ o.mIo.o . one s o o o Aav poaoae stem 0 omtm eaoa mass mH.o Hmnpsmz soaoemz ma.o J uncapsdom macapsaom HOpMOanH owadm mm msoosU< HH HOHQU manoaad dflswflq Ga soaoo mZOHBDROmw mDOnHDd< Rand. dunno; .QHDGHH an QNOBdoHnE/HH MDOHmdb MO MNQHOD HMS o NHQZHMMd .mdfifiomaoo cud Adv m.auo.w m s ous m m Amav mean Hoses» seem o.uuo.c a a sum sum sum Aav ewes enammom m.aum.m s o m s s Hoqosaonpazum o.mue.¢ w m m s a nav eon assets m.mum.m m w w m m Amsv magnum Homage scum o.muo.s m s o m m m eon canmnaaa e.eua.m w m m o o Aav omqmno assets o.muo.m m m m m m Aav eon omqoo m.¢uo.m m w nmum m m Amsv asap HoqanSosm m.mrm H o m M M Asv onosqoponwosfiaslm m.mu¢.a w m s w w Aav oo oqaaomeona m.muo.m m s m.mum.H w m mum mum m Amav mean Hogans ommm eao< mass ma.o stepson eoaeemz ma.o mGOHPSHOm waneduhzuow .HOPwOHdHHH mqum mm mucosvd a“ HOHOU manoass Uwswwq as soaoo n.9200 O NHQZfimmd m uuu u u m m m oflfimahqonaosfifin III I I o o o oddnmabqonmwn llu. l u. I «~le Mlfim CC Podofirowd III I I m o o 95 onmnposnmbsonmfisa eauma o m. m o w nuances oammm eaums m a cum cum oum Ase Boasts nopsaao oéauméa m. w m m m 93 a mango mHuOH m m cum . m m as? assets mauoa m s m cum 0 23 m eofims £9334 oéflumé m m such oum oum 0:3 333 o.oaum.w m o o s E .3 $3 naoamnpsfioqonm w.mum.w m o e e > £3 mamamfinflomenoum m.mum.a mm M w m o cantata o.wum.m a m m w w e8 H8302 team 33. NE 36 attests eoaoemz mic . . HomeoHUqH muoflfipflom mqoflpnflom owsmm Mm 35384 as Hedoo cadences UHDWHH sun .HOHOO firm—“ZOO O NHQZHEEH. 143 .noonw op cownmno Hoaoo on» owes me sowpaddm on» moms momqmsounsonn op cowqmno onfinmsdhnahnoflmoansIm mo Hoaoo coulomnmso Heavens one .oSHp snap on deflpdaom noosm can donate dfiom we soapflodm qufldqmpm some soosw op downwno odwnmndhnahdonmonpflslm Ho soapsaom canon .609 one .dflmww Boaaoh ass» 0» soup dam haflsmsomsop Ecosw and» on sowpfiaom Boaaoh can oomswo soapsHom oedaow amp ou camp mmooxo Ho soapflddd .soaaoh IlunoosmIoSanulquon.Il.ooHImmdeo “momsmno soaoo mqwsoaaom on» psossodnfi osflnwsdhnahnoamospHQIm mo afloapdaom oadwo4 .m u o s w mama oeaaaqapoomonpaZLm W III I I H @009 GIN o odflafldmpoomospHZIm a uuu u u m m o mqaaaqeonpagaaue.m l uuu u u w w w onaaaneonpazum uuu u u m w s mqaaaqtoneazum uuu u u m w s mqaaanwonpazum uuu u u a sum sue emanatessasqosaonpanaaue.m III I I m MIC Hlo monfiumadhflahsonmoanZLm uuu u u o c o oHoeeH u_ team sacs mass ma.o statute eoaoemz ma.o _ mdoapSHom mnOHpsHom .HOpMOfiddH odem mm m500fid4 QH Hoaoo dflnoaa¢ dflflwwg nH Hoaoo QIHHOO O NHQzummm—ufl APPENDIX D THE VISIBLE ABSORPTION SPECTRA OF SEVERAL INDICATORS IN LIQUID AMMONIA SOLUTIONS AT —77°C. 145 b: 0.019 n ma, _5 Indicator = 5.75 x 10 y, n = Neutral solution J. I Indicator = 1.02 x 10 M I I I i I I u u I I .___|___.|___I——-|-———l 580 420 460 500 54° 58° Wavelength, In}! 52. ABSORPTION SPECTRA or 2,4-DINITROANILINE 0.02 gs mug ;/‘/ Indicator : 2.26 x 10.4 M m Indicator: 5.65 x 10.4 g 1 I L 400 420 440 460 480 500 520 u Wavelength, mp J FIGURE 55. ABSORPTION SPECTRA OF p—NITROACETANILIDE 1 | 500 FIGURE 54. ABSORPTIO I I I l I l I l l 520 540 560 580 600 Wavelength, mp N SPECTRUM OF PHENOLPHTHALEIN 148 OINKNH // ‘— 2 Indicator = 4.x 10"5 g “‘t————-O.IN Ammo,L Indicator = 1 x 10.4 y I l I I I I I l 550 590 650 670 Have length, my FIGURE 55. ABSORPTION SPECTRA or TROPEOLINE OO 149 Indicator = l x 10.4 M a = 0.1 g mom, b= 0.1 :1 m2 590 650 670 Wavelength, mp FIGURE 56. ABSORPTION SPECTRA OF METHYL VIOLET Indicator = 1 x 10'4 M h a = °-1 N macho,b b = 0.1 g KNHE n : Neutral solution 150 FIGURE 57. Wavelength, my ABSORPTION SPECTRA OF THYMOL BLUE I1]. .u‘fiifl J‘lluuuulul lqudiu 0.8 - “lb 0.6 - 0.2 - 440 FIGURE 58. A Concentration unknown O'OL I I I I I I I u I 480 520 560 600 640 Ma ve length, my ABSORPTION SPECTRUM OF Q—NITROACETANILIDE “lb 152 Indicator : 1 x 104M 401} — a = 0'1 N NH‘OIO‘ h: 001 E KN'H2 a I I I us I 570 610 650 ’50 490 550 Wavelength, my FIGURE 59. ABSORPTION SPECTRA OF BROM CRESOL PURPLE Indicator: 1 x 10‘4 H a: 001 I! NH‘OIO‘ b: 0.1 y my,a 42° 460 500 540 580 620 Ila ve length, mp FIGURE 60. ABSORPTION SPECTRA OF METHYL ORANGE APPENDIX E SPECTROPHOTOMETRIC DETERMINATION OF THE EQUILIBRIUM AND DISSOCIATION CONSTANTS OF A WEAK INDICATOR ACID When a weak monobasic acid, HIn, is introduced into liquid ammonia solution, equilibria i and ii are established. HIn + NH5 ee- NH4+In- (1) NH +In_ :2 NH + + In- (ii) Equation 1 represents the ionization of the acid, whereas eQuation ii describes the equilibrium which exists between iOnS and ion pairs. If the concentration of indicator is sufficiently small, the equilibrium constants for equations 1 and ii may be written in terms of the molar concentrations of the species involved. AEIE:EE:1 ' (iii) 1" [HIE] an [In'] A.) D = W4+Inj ' . d The activity of ammonia is assumed to be unity, and 51 an ED are defin n constants. id, ed as the ionization and dissociatio ' c Let a represent the analytical concentration of the a . . . 'ts HIn, X the total equilibrium concentration of aCld in i 155 ionized form, and y the equilibrium concentration of ammonium ions. The equilibrium concentrations of all species can be represented in terms of these definitions (equations v). [Eli = a - x 1 [111E4+In-:l = X " y u (v) [NW] = y [In’] =y Equations iii and iv may be rewritten in terms of the defi- nitions in equations v. ’ K. = X _ y (vi) 1 a - x I | 2 y (vii) X ‘ y Assume that there is a wavelength, x , where the anion, ‘ In-, absorbs, but the molecular species, HIn, does not absorb. Beer's Law may be written as A — sch (viii) y of the solution at a given ‘ c is the molar Wavelength, e is the extinction coefficient, _ and JD is the length of where A is the Optical densit concentration of absorbing species, ' ' ' d that the light path through the solution. If it is assume 156 the anion, In‘, and the ion pair, NH4+In', have the same absorption spectra, i.e., extinction coefficients of the two species are the same, the concentration of absorbing species at wavelength )\ is given by c = [l1H4+In":I + [In-:I . (ix) Equation ix may be rewritten in terms of the definitions given in equations v as c = x (X) Equation xi is Obtained by substituting equation x into equation viii and solving for x. A ' x __ __ (X1) Equations vi and vii may be rearranged to equations x11 and xiii. (x — y) = Ki (a — X) (xii) y = VKiKD (a - x)”z (xiii) Eliminating y from equations xii and x111 gives 1 yé , x - (a — x)/2 b/KiKD + Ki (a — x) J . (x1v) 157 Equation xv is obtained by substituting equation xi into equation xiv and dividing through by g. VK. A A )6 €aD = (l- Eat)?é [Kiu— Gal) +—l$_ (xv) a Let E , the apparent extinction coefficient, be defined by equation xvi . ‘ _ ._A_ (xvi) € _ all Substituting equation xvi into equation xv gives - a A 5 % TI KiKD < '1) ._. xv1 —E— = (l - -€-') Ki (1 " e > + a , which may be expanded to - 'VK.K — — e l D . . o ‘2’: Ki (1 _ ‘2') + (l — E )% T . (XVI-ll) . t 0 ' . i . b EQuation xix may be obtained by d1V1d1ng equation “111 y VKiKD and rearranging- K (1 ’ got __i_=——T— 8. K1) (xix) mlmu 158 If € , the extinction coefficient for the anion In—, is known, equation xix may be used to evaluate the ionization and dissociation constants from experimental data. Equation xix is of the familiar form for a straight line Y = mX + b, (xx) . é . Where i is associated with the quantity (1 - e: )jé/ayza E Wlth (1 + Ki) / I/ KiKD , g with E/e , and p_ with VKi/KD' . The experimental data necessary to use equation XiX are the 0P- A i tical densities, A, of liquid ammonia solutions containing known analytical concentrations, 33, of the indicator and, 16 a l + Ki/ VEDKi Hin. The quantity 5 can be calculated from its definition, I . - it ‘ equation xvi. A plot of the quantity (1 - 5/5 ) / | versus E/e will give a straight line with slope and intercept —VK,/KD . The equilibrium and dissociation i constants may be evaluated from the slope and the intercept If the extinction coefficient, € , is unknown, a different . . - . ' 0... method must be used to determine the GQUlllbrlum and (1185 . . . ' xxi ciation constants for the weak aCld indicator. Equation may be obtained by squaring equation Xix and multiplylng through by g . 2 E2 (1 + Ki) _ 2a§ 11:51 + Kia €2KDKi D KD (xxi) I—‘ I mlmu of the plot. I 159 The right side of equation xxi may be rearranged to give ‘ K.a é(l + K.) ]2 E 1 [ 1 . 1 _ __ = _ 1 (xx1i) 6 KD L 6 Ki or e K ‘(1 + K.) 2 (1 - ‘2') J- : i—n—i— - l o (XXIII) Kia 1 By definition, let 1 + Ki X1 = T K1) x2 = —KI— (xxiv) KD - deare Where £1, £2, and g5 are constants Since Ki, ED. an __ . - - ' x ' made for constants. The definitions in equations xXiv are ... ' ms of convenience.~ Equation xx111 may be expressed 1n ter equations xxiv. I; (xxv) a II X 2 (éxl’l)2 a —X5 160 Expanding equation xxv and solving for 952, equation xxvi is obtained. x2 = a5 x1 - 2a€xl + 6x5 + a (mi) Equation xxvi must be satisfied for any solution of the in- dicator acid. The constants x1, 3; , and :55 may be evaluated by expressing the experimental data, a_6'2, 2&5 , I I and a. for three different solutions in terms Of equation xxvi, and then solving the three resulting simultaneous equations for Elu £2, and x5. After evaluating x1, x2, and x5, the defini— tions in equations xxiv may be used to determine the values Of the ionization and dissociation constants and the extinc- tion coefficient. The data can be checked using this value of 6 and equation xix. APPENDIX F THE DETERMINATION OF THE DISSOCIATION CONSTANT OF A STRONG ACID The equilibria which occur in liquid ammonia solutions containing a strong acid, i.e., an ammonium salt, and a mono- basic indicator are expressed by equations 1, ii, and iii. HIn + NH5 Se NH4+In- (i) NH4+In- Se NHL,+ + In. (ii) + " .. + 1(’ (iii) NHAL X .. NH4 + The equilibrium constants for equations i, ii, and iii are given by equations iv, v, and vi. respectively. Emmi] (iv) Ki ‘ [En] BlHqfl [ID-II (v) KD ENH4+Inj [M4fl [Xi] (Vi) = —---;:-:" t [NH4 x] h-u.. he acid tio for to of 77W , fig—”———fi 162 The ionization and dissociation constants of the indicator acid and the dissociation constant of the ammonium salt are defined as $1, ED, and Eb', respectively. In dilute solu- tions, molar concentrations of the species may be substituted for their activities, and the activity of ammonia is assumed to be unity. Let a represent the analytical concentration of the indicator, b the analytical concentration of the am- ‘monium salt, g the total equilibrium concentration of indi- cator in its ionized form, 1 the equilibrium concentration of indicator as the free anion, and g the equilibrium con- centration of the ammonium salt anion, X'. The eQUilibrium concentrations of all the species in solution can be eXPrGSS‘ ed in terms of these definitions (equations vii). m = a - x finf] = Y + -— EH4] _ y + Z (vii) [Xi] = Z [NH4+Xj = b - z 5314+]:n-j = X — y . ' of e ua- Equations iv, v, and vi may be rewritten in terms q tions vii. x - y (viii) 165 KB = (y + Z)(Y) (ix) X ‘ y + z z b — 2 Equation viii may be rearranged to give equation xi. y = x — Ki(a — x) (Xi) Combining equations viii and ix and rearranging the results gives (y + z) y = KDKi (a — x) . (xii) The definitions in equations xiii.are made for convenience, (xiii) and equations xi and xii may be expressed in terms of these definitions to give Y = x — Ki (a - x) (xiv) (XV) Z = KDKi (8.“X)o 164 If the ionization and dissociation constants of the in— dicator have been determined previously, values for X and Q may be calculated from equations xiv and xv, because a and x are experimental values (see equations viii through Xi: APPendiX E). The quantities on the right side of equa- nitions in equa— tion x may be expressed in terms of the defi tions xiii. £I>_’_TY__L§I_% (m, Z ——————(y+z)y-y=§-Y (xvii) Y 3 SubStituting equations xvi and xvii into equation x gives 2. [a _ Y] ____Y____.._Y—-—--— (X'Viii) L a (:11 I ated f: l . . . . . T!- Z a 1 . mentally determinable. s of Y and Z for any analytical concentration of Value ' ’on indicator, a, and the optical denSity, A, of the soluti - . . o E and- ' may be readily obtained from equations xiv and xv xp ’ ' see ing equations xiv and xv and substituting A/EQ' for g ( equation xi, Appendix E) gives 165 A (l + Ki) El. - aKi (xix) z = aKiKD — e, (xx) Nomographs, Figures 61 and 62, were constructed to deter- mine values of I and g for any value of a and the correspond- ing value of A from equations xix and xx using phenolphthalein as an indicator. The ionization and dissociation constants for phenolphthalein were determined by the method outlined in Appendix Em m+OH an Hopwnfiddfl Ho noapmnpdooqoo HMHPHQH rm _ _ _ . \|L <.. _ ................... _. ... _ ......... . ..... 1!... AW 0 o 0 AW 1 2 z./ 1..” 5 m G 0 M 0 N o l p .>_.>>>->>p->->>p>r-p— ....... ->---— m _ _ _ 0 O 0.. nTu. o n 0 2 1 F s s A 9.. s a 4 2 .>».. n — .—...>.-p >— .h.-p—.-r-..p.>—pprp—..-.— I»....-_.-p-—-».-_...-—o.. ._u ......pIrI-LLLLL 1 . . . _ 4 4 . _ . . . _ . . _ . . . . o 0 o o 1 0 EH33 3038 .4 167 9.. A s a 2 I... s s . . O . n-V - a )L O _ h - nw . o - .0 p AW r b q.. . .e.... .. ...-<44. 4. .. < . a a u q ... I. 4.1. .u .. ......u q ......... a .1 ‘— n o n O 1 2 m G O M O N N 2+3 N . 2 . .> . p.» . . -. ... . _ 6 7 . . . . a . _ . . _ O 8 6 I... 2 0 m 1 G I F m+OH N soapmapnoosoo HopwofiosH 3m _->>>>>_-.....-...-.—-..-p...p-p. ..... —- ............. ->.-—._-. n - . .— ...... . .... ...— .|‘ _ _ . . _ m m m a n n 5 h. z} 2 1 O APPENDIX G DETERMINATION OF THE IONIZATION AND DISSOCIATION CONSTANTS OF WEAK ACIDS When a weak acid, HR, is dissolved in a liquid ammonia solution containing an indicator, HIn, the following equilib- ria are established. HIn + m5 2 NH4+In— (i) NH4+In— an- NH4+ + In- (ii) RH + mi5 a» NHJR‘ (iii) ‘ NH4+R" a» N114+ + R“ (iv) The equilibrium constants for equations i through iv are . expressed by equations v through viii, respectively. ‘ + .— ETH4 In] (v) i— [HInJ i @7sz [If] (vi) ! K = -—-""’"':"" D [$114+an +— K. Efil (vii) ' 3 RH l 169 K, as [3-] D ‘ W (viii) It is assumed that the concentrations of indicator and acid are sufficiently small so that the concentrations of the species may be substituted for activities; the activity of ammonia is assumed to be unity. The ionization and disso— ciation constants of the indicator are defined as Ei and ED, respectively, and are determined as outlined in Appendix F, whereas Ei' and ED. represent the ionization and dissociation constants of the weak acid. Let a and 2 represent the analytical concentrations of the indicator and the weak acid. Also, let x represent the total equilibrium concentration of the ionized indicator, 2 the total equilibrium concentration of ionized acid, 1 the equilibrium concentration of indicator anion, and q the equi- librium concentration of the weak acid anion. The equilibrium concentrations of all species present in the solution may be expressed in terms of these variables. [Eli] = a — x [3H] = b-p [Rt—l = q [in-j = 3’ (ix) Emfl = q+¥ ETi4+Rf1 = p - q [fiH4+In:] a X ' y 170 The equilibrium constants, equations v through viii, may be expressed in terms of the definitions ix. K' = x - y (x) KD = (q + 7) 3' (xi) X ’ y (xii) KD' = q (q + y) (xiii) EQuation x may be rearranged to give y = x — Ki(a — x) . (XiV) Combining equations x and xi and rearranging the results gives (q + y) y = KDKiCa - x) . (XV) Definitions xvi and xvii are made for convenience, Y = y (3071) Z = (q + y) y (xvii) a (Jun... 3-... 171 and equations xiv and xv may be rewritten in terms of these definitions to give Y = x - Ki(a — x) (xviii) and Z = KDKi (a - x) . (xiX) Equations xviii and xix are the same as equations xiv and xv of Appendix F and may be treated in a similar manner. The terms in equations xii and xiii involving 1 and 9 may be expressed in terms of Y and g. z, (q+y) —————(q+y)y =—f— (’0‘) Y £z_:_sl_z _ y = _ Y (xxi) 7 RUN Equations xii and xiii may be combined to give q (q +1) , (xxii) KIK.I ' xxi and xxii may be rewritten in terms of equations xx and . ' , i%)(% _ Y} (xxiii) KD Ki ‘ (b — p) T 172 If it is assumed that RH is a weak acid and that the concentration of acid which exists as ionized species is negligible when compared to the total concentration of acid, the product KD'Ki' can be evaluated.from equation xxiii, since 1 and Q are expressed in terms of experimentally deter— mined quantities (equations xviii and xix). A second expres- sion involving ED. and Ei' must be obtained before ED. or E1. can be evaluated. Equation xiii can be solved for p to give q