ABSTRACT ACID-BASE EQUILIBRIA IN NONAQUEOUS SOLVENTS PART I: 1 , 1 , 5 , 5-TETRAMETHYLGUANIDINE PART II: ADIPONITRILE by Joseph Anthony Caruso Electrical conductances of tetrazole, nine S-sub- stituted tetrazoles, picric acid, tetrabutylammonium iodide and triisoamylfig-butylammonium tetraphenylborate were measured in 1,1,3,S-tetramethylguanidine (TMG) at 250. Overall dissociation constants of these compounds were de— termined from the conductance data and were found to be in the range of 10'3 to 10's. The values of the limiting equivalent conductances ranged from about 50 to 45. The in— ductive effect of the substituent groups in S-substituted tetrazoles is illustrated by a reasonable linearity of the Taft plot. The dielectric constant of TMG was found to be 11.00 :1: 0.02 at 25°. ‘ In addition, potentiometric studies using a hydrogen indicator electrode and a mercury-mercury (II) chloride reference electrode, were made on four 5-substituted tetra- zoles, perchloric acid, mrchlorobenzoic acid, and phenol. The overall dissociation constants ranged from 10’7 for phenol to approximately 10-3 for perchloric acid. The values Joseph Anthony Caruso obtained by the potentiometric method were in good agreement with those obtained from the electrical conductance measure- ments. The use of TMG as a medium for the titrations of weak acids has been also investigated. It has been found that the hydrogen electrode behaves reversibly in this solvent and can serve as an indicator electrode in the titration reactions. The titrant was a 0.1 fl_solution of tetrabutylammonium hydroxide in a 90v10% mixture of TMG and methanol. Hydrogen electrode, dipping into a TMG solution saturated with benzoic acid, served as the referenCe electrode. Potentiometric titrations of a number of weak acids gave results accurate to at least.i 0.5%. It was found that in most cases curcumin could be used as an end-point indicator with an accuracy com- parable to that of the potentiometric titration. Electrical conductances of five sodium and potassium salts and twelve quaternary ammonium salts in adiponitrile have been measured at 25°. The data were analyzed by the Fuoss-Onsager conductance equation using Kay's Fortran com- puter program for both nonassociated and associated electro- lytes. The dissociating nature of adiponitrile is reflected by fourteen of the salts showing no association and the other three having association constants of 28 or less. Limiting ionic equivalent conductances have been evaluated by the method of COplan and Fuoss using triisoamyl-grbutylammonium Joseph Anthony Caruso tetraphenylborate as a reference electrolyte. The dielectric constant of adiponitrile was found to be 52.45 at 250. ACID-BASE EQUILIBRIA IN NONAQUEOUS SOLVENTS PART I: 1,1,5,3-TETRAMETHYLGUANIDINE PART II: ADIPONITRILE BY Joseph Anthony Caruso A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1967 (497C /—«7 \:C ACKNOWLEDGMENTS The author wishes to extend his thanks to Professor Alexander I. Popov for his guidance, encouragement, and enthusiasm throughout this study. He also wishes to express his appreciation to Professor Paul G. Sears of the University of Kentucky for his comments and guidance. Thanks are extended to Professor R. M. Herbst and Mr. Thomas Wehman of this Laboratory for providing the 5—substituted tetrazoles. Thanks also go to the National Institutes of Health of the Department of Health, Education, and Welfare for partial support of this investigation. Special thanks go to Dr. Robert L. Kay Of the Mellon Institute for the use of his Fortran computer program in part of this study. Many thanks and appreciation go to the author's wife, Judy, for her patience, understanding, and encouragement throughout the years of graduate study. ii VITA Name: Joseph Anthony Caruso Born: April 15, 1940 Academic Career: Clinton High School Clinton, Michigan--1954-1958 Wayne State University Detroit, Michigan--1958-1960 Eastern Michigan University Ypsilanti, Michigan--1960-1962 Wayne State University Detroit, Michigan--1962-1964 Michigan State University East Lansing, Michigan--1964-1967 Degrees Held: B.A. Eastern Michigan University (1962) M.S. Wayne State University (1964) Positions Held: High school teacher at Cass Technical High School, Detroit, Michigan--1965-1964 iii TABLE OF CONTENTS Page PART I 1,1.5,5-TETRAMETHYLGUANIDINE INTRODUCTION 0 O O O O O O O O O O O O O O O O O O O l HISTORICAL I O O O O O O O O O 0 O O O O O O O O O O . 3 I. 1,1,5,3-Tetramethylguanidine . . . . . . . . 5 II. Tetrazole and the 5-Substituted Tetrazoles . 7 THEORETICAL O O O O O O O O O O O O O O O O O O O O O 9 I. Conductance Methods. . . . . . . . . . . . . 9 II. Potentiometric Methods . . . . . . . . . . . 13 EXPERIMENTAL . . . . . . . . . . . . . . . . . . . . 16 I. Reagents . . . . . . . . . . . . . . . . . . 16 II. Apparatus. . . . . . . . . . . . . . . . . . 19 III. Procedures . . . . . . . . . . . . . . . . . 25 RESULTS AND DISCUSSION . . . . . . . . . . . . . . . 50 I. Conductance Results. . . . . . . . . . . . . 50 II. Potentiometric Results . . . . . . . . . . . 49 III. Titration Results. . . . . . . . . . . . . . 61 CONCLUS IONS o o o o o o o o o o o o o o o o o o o o o 7 6 PART II ADIPONITRILE HISTORICAL INTRODUCTION. . . . . . . . . . . . . . . 78 THEORETICAL. . . . . . . . . . . . . . . . . . . . . 81 iv TABLE OF CONTENTS -- Continued Page EXPERIMENTAL. . . . . . . . . . . . . . . . . . . . 85 I. Reagents. . . . . . . . . . . . . . . . . . 85 II. Apparatus and Procedures. . . . . . . . . . 86 RESULTS AND DISCUSSION. . . . . . . . . . . . . . . 87 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . 102 'RECOMMENDATIONS FOR FUTURE STUDIES. . . . . . . . . 105 REFERENCES. . . . . . . . . . . . . . . . . . . . . 104 APPENDICES. . . . . . . . . . . . . . . . . . . . . 108 TABLE II. III. IV. VI. VII. VIII. XI. XII. XIII. XIV. LIST OF TABLES Physical constants for 1,1,5,3-tetramethyl- guanidine. . . . . . . . . . . . . . . . . . . Equivalent conductances in TMG at 250. . . . . Conductance results in TMG at 250. . . . . . . 6* constants for various tetrazoles. . . . . . Experimental data from potentiometric measure- ments in TMG O O O O O O O O I O O O O O O O 0 Results of potentiometric studies in TMG . . . Titration data for monoprotic acids in TMG . . Titration data for binary mixtures of acids in TMG I O O O O O O O O O O O O O O O O O O O C 0 Results of potentiometric and indicator titra- tions of weak acids in TMG . . . . . . . . . . Results of potentiometric titrations of binary mixtures of acids in TMG. . . . . . . . Conductances of salts in adiponitrile at 250 . Calculated parameters of the Fuoss-Onsager equation for salts in ADN using weighted data. Calculated parameters of the Fuoss-Onsager equation for salts in ADN using unweighted data 0 O O O O O 0 ~ 0 O I O O O O O O O O I O Averaged conductance parameters for adipo- nitrile solutions. . . . . . . . . . . . . . . Comparison of A0 values obtained from various conductance treatments . . . . . . . . . . . . Single ion limiting equivalent conductances in adiponitrile based on triisoamyl—gfbutyl- ammonium tetraphenylborate as reference. . . . vi Page 51 54 48 50 53 62 64 7O 74 88 91 94 95 96 100 LIST OF FIGURES FIGURE 1. Diagram of the cell used in potentiometric titrations. . . . . . . . . . . . . . . . . . 2. Diagram of the cell used in e.m.f. studies. . 3. Shedlovsky plots for A, 5-Bsz, B, 5-prleTz, and C, tetrazole in TMG . . . . . . . . . . . 4. Shedlovsky plots for A, 5-MeTz, B, S-Ef MeOPhTz, and C, picric acid in TMG. . . . . . 5. Shedlovsky plots for A, 5-PrTz, B, Bu4NI, and c, (_i_-Am)3BuNBPh4 in TMG. . . . . . . . . . . 6. Shedlovsky plots for A, 5-Eth, B, 5-PhTz, C, 5-prClPhTz, and D, 5-prN02PhTz in TMG . . . . 7. Relationship between log and 6* for some Sealiphatic substituted te azoles. . . . . . 8. E yg, log [(CHX)t -(1H+] for TMG solutions 10. 11. 12. 13. 14. o A, 5-PhTz, B, 5-Bsz, and C, mrchloro- benZOiC aCid. O O O O O O O O O O O O O O O O E gs, log [(CHX) - . +] for TMG solutions o¥x , HClO4, B, 5— -ClB T2, and C, 5-MeTz . . EHX gs, log (CHX)t for phenol solutions in TMG O O O O O O O O O O O O O O O O O O O O O Titration curves for A, phenol, B, grcresol, and C , E-Chloropheno l o o o o o o o o o o o o Titration curves for A, prchlorobenzoic acid, B, Etchlorobenzoic acid, C, gfchlorobenzoic acid, and D, 5-MeTz . . . . . . . . . . . . . Titration curves for binary mixtures of A, preresol and benzoic acid, B, phenol and mrchlorobenzoic acid, and C, phenol and benzoic acid. . . . . . . . . . . . .y. . . . A5 as a function of C for A, NaI, B, MesPhNI, D, BU4NI, and E, H6X4NI o o o o o o o o o o 0 vii Page 22 24 37 39 41 43 47 55 57 6O 66 68 73 99 LIST OF APPENDICES APPENDIX I. Computer Programs. . . . . . A. General Introduction. . B. Conductance Program . . C. E.M.F. Program. . . . . II. Derivation of the Equations for the Standard DeViationS Of A0 and Kim a o o o o o o o o 0 viii Page 109 109 112 117 119 INTRODUCTION The usefulness of nonaqueous solvents in the study of acid-base equilibria (particularly in the Bansted-Lowry sense) is clearly illustrated by the large number of ana- lytical techniques which utilize either pure nonaqueous solvents or their mixtures for a wide variety of titrations of substances which, for one reason or another, cannot be analyzed in aqueous solutions. With few exceptions, the development of the theory of acid—base equilibria in nonaqueous solvents, however, has not kept pace with the practical applications. Acidic sol- vents such as acetic acid and sulfuric acid have been studied very intensively and the nature of acid-base equi- libria in these solvents have been elucidated particularly by the classical investigations of Kolthoff and Bruckenstein in acetic acid solutions (1) and of GilleSpie and his co- workers (2) in sulfuric acid. On the other hand, acid-base equilibria in basic solvents seem to have been studied less completely, although of course, there are significant publi— cations on such solvents as pyridine (3-6), ethylenediamine (7-12), and ammonia (13-15). While 1,1,3,3-tetramethylguanidine (hereafter abbreviated as TMG) has been known for over seventy years (16) its appli- cation as a nonaqueous solvent has not been explored to any 1 significant extent. There are only two short reports in the literature which describe its use as a medium for the titration of weak acids (17). Valuable data on the solvent properties of TMG can also be found in an unpublished Ph.D. thesis of M. L. Anderson of this Laboratory (18). It seemed quite obvious that further study of the sol- vent properties of TMG would be a useful contribution to the field of nonaqueous solvents. Three objectives were defined: 1. The study of the dissociation and ionization equilibria of some typical electrolytes in TMG. 2. Identification of some useful electrode systems in the solvent. 3. Study of acid-base equilibria. Parallel with the general study of nonaqueous solvents, a comprehensive study of the chemistry of tetrazoles is being carried out in this laboratory. It is well known that 5-sub- stituted tetrazoles behave as weak acids, but their relative acidity constants have not been determined with sufficient accuracy; and therefore, the influence of the substituent groups on the acidity constants is not known. In part this is due to the insolubility of most of the 5-R-tetrazoles in water, in part to the inherent weakness of the acid properties. Since TMG, as a strongly basic solvent, should enhance con- siderably the acidic character of these tetrazoles, it was decided to include these compounds in the study of acid-base equilibria in TMG. HISTORICAL I. 1‘1,3,3-Tetramethylguanidine A.aPhysical Constants At room temperature TMG is a colorless liquid whose physical properties are given in Table I. The solvent has a rather wide liquid range. Its density is intermediate between water and ethylenediamine. The dielectric constant of 11.00 is within the useful range for an ionizing solvent and is quite comparable to those of ethylenediamine and pyridine, 12.9 and 12.3 respectively (12a). The specific conductance and viscosity are such that useful conductance measurements can be made. The high heat of vaporization, the Trouton constant, and the formation of "glass" at low temperatures indicate that the liquid must be highly associ- ated, very likely through hydrogen bonding. It should also be noted that the c=N infrared absorption band in TMG is shifted to lower energy than that generally found in guani- dines (19) which also indicates the possibility of hydrogen bonding. Most of the properties thus far mentioned are quite comparable to those for ethylenediamine. The differences of aqueous basicities for the two are quite marked, however, and are reflected by comparing the pr values of 0.4 for TMG (20) as opposed to 4.15 for ethylenediamine (21), 3 Table I. Physical constants for 1,1,3,3-tetramethylguanidine. Property Physical constant Reference Freezing point LA-70 to -80°C. 18 ("glass" formation) Boiling point 159.500. 18 Density (25°) 0.9136 g. ml-l. 18 Dielectric constant (25?) 11.00 this study Specific conductance(25°) 3.54 x 10-sohm-lcm‘l. this study Viscosity (250) 1.40 cp. 18 Refractive index 1.4658 18 Heat of vaporization 11.2 kcal. mole'l 18 Trouton constant 25.9 cal. mole'ldeg‘l. 18 Aqueous pr 0.4 20 indicating TMG is a considerably stronger base than ethylene— diamine and therefore would probably be an even better leveling solvent toward protogenic species. B. Solubilities Anderson found that, in general, solubilities of inor- ganic salts in TMG parallel the order found in liquid ammonia. The influence of the lower dielectric constant of TMG is reflected in somewhat lower solubilities for most salts. Salts with large anions in conjunction with small cations show enhanced solubility as evidenced by the follow- ing orders cations: NH4+ a: 1.1+ > Na+ > K+ > Ca2+ > Sr2+ > Ba2+ anions: CNS- > 0104" > N03- > 1’ > Br- > C2H302- > Cl—> 5042 Organic compounds are reasonably soluble in TMG and complete miscibility was found with most common organic solvents. C. Chemical Properties Tetramethylguanidine undergoes slow hydrolysis at room temperature in the presence of atmospheric moisture forming 1,1-dimethylurea and dimethylamine. Anderson indicates that water may be removed from TMG by the addition of carbon dioxide to form the insoluble bicarbonate salt according to the following reaction NH H2N+H 003' (H3C)2N-C-N(CH3)2 + 002 + H20 -—9*(H3C)2N-C-N(CH3)2 He found that reactions of TMG with acids are vigorous and exothermic producing the species with a protonated imine nitrogen and localized charge on the central carbon atom, [(CH3)2N]2C+NH2. Chloride, bromide, acetate, and bicarbonate salts of the above cation were isolated. Attempts to prepare alkali metal guanidides of the type, + — M NC[N(CH3)2]2 , were unsuccessful. D. Metal Complexes In his study of metal complexes of TMG Anderson reports that a maximum of four molecules of tetramethylguanidine can coordinate with a transition metal ion such as cobalt (11). His study was not concerned with the coordination site, but Drago claims that complexation takes place through the imine nitrogen (22). E. Acid-Base Titrations Anderson performed both conductometric and indicator titrations in TMG using tetra-grbutylammonium hydroxide in methanol solution as the titrant. He found several acid- base indicators which exhibit color changes in TMG solutions with changes in the acid-base concentration. Titration of gfnitrophenol in TMG resulted in more than one conductometric end point supposedly because of hydroxyl ion addition to the aromatic ring. He claims excellent resolution of all three protons of citric acid. It would seem, however, that this observation would lead to the conclusion that TMG is a differentiating rather than leveling solvent toward acids. II. Tetrazole and The 5-Substituted Tetrazoles While it has been known for some time that tetrazole (I) and the 5—substituted tetrazoles (II) have definite acidic properties, the influence of structure factors upon the proton-donor ability of these compounds have not been thoroughly investigated. H-N - fi-H H-N - fi-R N N N N \\N/ \\N/ (I) (II) Dissociation constants of some water-soluble tetrazoles have been determined conductometrically by Oliveri-Mandala (23) who found that unsubstituted tetrazole had approximately the same acid strength (Ka = 1.54 x 10-5) as acetic acid. More recently, the acidic dissociation constants of a number of alkyl- and aryl—substituted tetrazoles have been determined potentiometrically by Herbst and co-workers (24). In the case of tetrazole, the Ka value of 1.62 x 10"5 agrees well with the value of Oliveri-Mandala. In a number of cases, however, the tetrazole derivatives were insoluble in water and water-alcohol mixtures of varying composition were used as"solution media. Since the change in the composition of the solvent should also change the liquid junction potential (aqueous SCE was used as the reference electrode), it is possible that the relative acid strengths of the tetrazoles may have been altered by this procedure. THEORETICAL 1. Conductance Methods Since tetramethylguanidine has a relatively low di- electric constant of 11.00 (see p. 26) it is to be expected that ionic equilibria in this solvent would be substantially influenced by ion-pairing. It has been shown by Kolthoff and Bruckenstein (1) that in such cases the overall dissoci- ation of a weak acid HX will proceed in two steps as shown below K. K +- .— Hx—J-‘b HX 43A H+ +x 1. *— ~.—- ' where HX represents the molecular form of the acid, H+X- the ion pair resulting from the ionization process, H+ the solvated proton, and X- the conjugate base of the acid Hx. The constants Ki and K represent the thermodynamic ioniza— d tion and dissociation constants respectively, I x :0 .K. "---—- I ész and aH+ ax- K = -—-—-——- 3. d QH x- These two relationships may be combined to give the overall dissociation constant, KHX 10 From the mass balance relationship we have ) = [H+] + [H+x’] + [rm] 5. (CHx t where (CHX)t is the total analytical concentration of the acid Hx and the terms in brackets represent the equilibrium concentrations of the respective species. If we assume that the activity coefficients of uncharged species equal unity, Expression 4 becomes + .- 4: fix [Hx] + [H+X-] KHX= and therefore from relationships 5 and 6 We have = gH+ ax- 7 KHx + ‘ (CHX)t - [H] or, assuming that fiH-F = fix- £2+ KHx = :1 8. + (cth-[H] Equation 8 may be rewritten as the mass action law = acacfa KHx 1 - y 9' where 7 represents the degree of dissociation, f the mean activity coefficient, and C, the total analytical concen- tration of the acid HX. 11 A. Application of the Ostwald Dilution Law to Conductance Studies It has been shown by Arrhennius that the degree of dissociation of a binary electrolyte can be obtained from the ratio of equivalent conductance at a given concentra- tion to the equivalent conductance at infinite dilution 7 = -—-— 10. Substituting this relationship into Equation 9 and assuming that f = 1, we obtain A20 KHX = AQ(Ao-A) 11. or, by rearrangement 2 KHX A0 = A20 + KHXAAO 12. Dividing Equation 12 by KHxAgA, we get 1 _ .1 K - ——Tz- + A0 . ~ 13. A plot of 1/A gs. CA yields an intercept of 1/A0 and a slope of 1/KHXA8. The values of Ab and KHx may then be calcu- lated. This equation gives approximate values of KHx for dilute solutions of weak electrolytes, however, in most cases it is unsatisfactory because it does not take into account interionic effects. B. The Shedlovsky Iteration Technique Following the lead taken by Fuoss and Kraus in 1933 and 1935 (25), Shedlovsky in 1938 proposed the following 12 conductance equation for weak electrolytes (26) A = 7 A0 — S-gg (VCYé where the Onsager slope, S, is given by S = dAo + B This parameter takes into account the relaxation and the electrophoretic effects, a and B respectively (27) which are given by a = 8.203 x 105 (DT) and 82.43 B = ‘fi n(DT) where D is the dielectric constant, n the viscosity, and T the absolute temperature. He defined a function, Sz, where 2- z = 5mg) A0 and S2 = 1 + z + fi-za + . . . Then a solution of Equation 14 was written as 52A 7- A0 Substitution in the mass action law, Equation 9, and re- arrangement yielded 14. 15. 16. 17. 18. 19. 20. 13 1 ’ 1 CAS f2 ’ ASz A0 KHX A0 As seen from Equation 21 a plot of 1/ASz s. CASzf2 yields — a a straight line with an intercept of 1/A0 and a slope of 1/KHXAS . The procedure in applying this technique is to assume a value for A0, solve for z and $2, and plot the appropriate functions. 'From the intercept a new value of A0 is obtained which is used to recalculate z and 82’ The process is repeated until consecutive A0 values agree to within an acceptable tolerance. It was shown by Fuoss and Shedlovsky (28) that the above procedure for the evalu- ation of A0 and the dissociation constant is more reliable than the older method of Fuoss and Kraus (25). Both the Ostwald and the Shedlovsky methods are best applied using the method of least squares and hence evalu- ation of A0 and KHx is easily handled on modern digital computers. A Fortran program listing which evaluates con- ductance data by both techniques is given in Appendix I. II. Potentiometric Methods Potentiometric studies of acids in TMG were carried out by means of a galvanic cell Ref. Electrode Hx(c ) (TMG) H2(1 atm.), Pt HX t The reference electrode consisted of a mercury—mercury (II) couple, which was composed of a mercury layer in contact with a saturated solution of mercury (II) chloride in TMG. 14 The e.m.f. generated by this cell is given by the equation EHX = 951' + 0.0592 log JH+ 22. where o' = 0 EH EH+,§H2 + El.j. + Eref. 25' It is possible to interpret the experimental results by assuming the ionization and dissociation equilibria as . . + . given on page 9. By assuming £H+ = [H ] Equation 8 becomes £2 + = 1 H H“ (c ) -£ + HX t H 24. from which, 3,; = (Kama), -£H+1)‘=* 25. Substituting Equation 25 into Equation 22 yields = 0' _ EHX EH + 0.0295 log KHX + 0.0296 log [(CHx)t fiHH 26. It is seen that a plot of EHX'—§' log [(CHx)t-‘ZH+] gives a straight line with slope of 0.0296 and intercept of 0' - - EH + 0.0296 log KHX' If KHX of an aCid is known from independent measurements, the value of E0. H (assuming that the liquid junction potential remains con- may be calculated stant). Essentially the same technique is then used in an iterative process to calculate KHx values for other sub- stances. As the first approximation we can write 15 I [(CHX)t -¢ZH+] = (CHX)t' The e.m.f. values are then plotted gs. log (CHX)t and a value of KHx obtained. From this value of KHx a first value of [ZH+ is calculated and EHx plotted gs, log [(CHX)t -t2h+] from which a new value of KHx is obtained. The process is repeated until the consecutive KHx values are within an acceptable tolerance. This method usually requires four or five iterative steps and is easily handled by a digital computer. A Fortran program listing for this procedure is given in Appendix I. In a similar potentiometric study using ethylenediamine as solvent, Bruckenstein and Mukherjee (12a), have postu- lated the following conjugate ion equilibrium x'+Hx ——'~ Hx; 27. _‘___ where éafi( For cases where the conjugate ion equilibrium is present a plot of E s. log(C ) yields two linear portions, one HX'—— HX t of slope 0.0296 representing Equilibria 1, and one of slope 0.0592 representing Equilibrium 27. At the point of inter— section of the two linear segments we have the relationship 1 - = f . 290 Kng (CHx)t where (CHX)t gives the concentration of the acid at the point of intersection. EXPERIMENTAL I. Reagents The solvent, 1,1,3,3-tetramethylguanidine was obtained from American Cyanamid and it was purified by vacuum dis- tillation from granulated barium oxide through a 70 cm. column packed with glass helices. The distillation was carried out at 36-380 under\/\0.1 mm. pressure. The system containing about 2 liters of TMG was first refluxed for ,several hours, then a first fraction of 100 ml. collected and discarded. Subsequent fractions of 500-700 ml. each were then collected for each experiment until approximately 100 ml. remained in the distilling flask. After use the solvent was redistilled. Solvent prepared in such manner exhibited specific conductances within the range of 4-10 x 10'eohms‘lcm'l. Gas chromatograms taken on an F & M Model 700 gas chromatograph equipped with a hydrogen flame detector, showed only one peak, while solvent purified at atmospheric pressure exhibited three peaks with the area ratios of about 2:2:96. Conductance water for potassium chloride solutions was prepared by passing distilled water through a mixed bed resin obtained from Crystalab Research Laboratories. The specific conductance of such water ranged from 5-7 x 10'7 ohms‘lcm’l. 16 17 Potassium chloride, Matheson Coleman and Bell "Reagent, A.C.S., Crystals" was fused in a platinum crucible, ground in an agate mortar, oven dried and stored. The preparation and purification of triisoamylfin- butylammonium, tetraphenylborate was carried out by a previously described technique (29). The melting point of the final product was 264-2650 instead of 274—2750 reported in the literature. The melting point, however, remained constant on several recrystallizations. It seems likely, therefore, that the literature value may be in error. Picric acid, Matheson, Coleman and Bell "Reagent Crystals," was recrystallized twice from ethanol and dried to constant weight ig_ygggg. Some of the 5-substituted tetrazoles were available as a result of previous work in this Laboratory (24), others were prepared according to the procedure of Finnegan §t_gl, (30). The compounds were purified as follows: 5-Ethyl(m.p. = 86.5 - 89.5°), and 5-_r_1-propyl(m.p. = 60 62O)tetrazoles were purified by triple sublimation. Since they were in such short supply, further purification was not attempted and consequently their purity may not be as high as would be desirable. 5—prNitrophenyl(m.p. = 226 - 227Od.), 5-prchlorophenyl» (m.p. = 260 - 261°d.), 5-prmethoxyphenyl(m.p. 239 — 2400), 5-phenyl(m.p. = 221 - 2220), 5-methyl(m.p. = 1480), 5- benzyl(m.p. = 124 - 1250), and 5-pfchlorobenzyl(m.p. = 18 162 - 163°) tetrazoles were all recrystallized twice. The respective tetrazole was added to 1,2-dichlorethane and the mixture brought to boiling. Just enough methanol was then added to dissolve the tetrazole. The solution was allowed to cool and the needle-like crystals filtered. The crystals were then dried in a vacuum desiccator for 24 hrs. The melting points, as given above, compare favorably with the literature values (24). Tetrazole was obtained from City Chemical Company and was purified by recrystallization from a 1:5 methanol- benzene mixture. The needle-like crystals were dried to constant weight ig_yaggg. The melting point of 1550 coin- cided with the literature value (31). Baker Analyzed Reagent mercury and perchloric acid, G. F. Smith sodium perchlorate, and Fisher Certified Re- agent mercury (II) chloride were used without further puri- fication. Matheson Co., Inc. prepurified hydrogen was passed through a flow meter to assure constant delivery to the hydrogen electrode half cell. It was then passed through a column of Ascarite and a column of Drierite before use. Tetra-nfbutylammonium hydroxide (TBAH) was obtained from Eastman Chemical Company as a 25% solution in methanol. Since preliminary results indicated that pure methanolic solutions could not be used as titrants, a solution of TBAH 19 in TMG-MeOH mixture was prepared by adding «213 ml. of the stock TBAH solution to 87 ml. of TMG. The solution was some— what unstable and showed a definite change in titer after standing for 24 hours. It was necessary, therefore, to standardize it at the onset of each series of titrations. Dahmen and van der Heijde (32) indicate that TBAH is unstable in pyridine as a consequence of the "Hofmann degradation." This may also be the case for the TBAH-TMG solutions. Curcumin (turmeric), 1,7-bis(4-hydroxy-3-methoxyphenyl)- 1,6-heptadiene-3,5-dione was obtained from Eastman (m.p. 179- 1810) and was not further purified. Indicator solution for the titrations was prepared at a concentration of approxi- mately 0.2 mg./ml. in TMG. Benzoic acid and the substituted benzoic acids were recrystallized from water-ethanol mixtures and dried to constant weight in vacuo. Phenol and prchlorophenol, obtained from Eastman Chemical Co., were purified by vacuum distillation in a micro distil- lation apparatus; gfcresol was purified by sublimation. II. Apparatus All melting points were taken on a Fisher-Johns melting point block for which the usual stem corrections were made. The conductance bridge used in this investigation was constructed in this Laboratory and has been described in a previous publication (33). The bridge was operated at a frequency of 2000 cycles/sec. 20 The cells were similar to those described by Daggett, Bair, and Kraus (34). The electrodes were platinized according to the technique of Jones and Bollinger (35). Potassium chloride solutions were made up by weight, and molar concentrations calculated, and the equivalent conductances calculated from the Lind, Zwolenik, and Fuoss equation (36). The constants of the four cells used in this investigation were calculated in the usual manner and are as follows: 0.2409.i 0.0001; 0.2320.i 0.0001; 0.1216 1.0.0002; and 0.4421.i 0.0004 cm‘l. The temperature of 25.00 1.0.03 was provided by a Sargent 8-84805 thermostatic bath assembly filled with light mineral oil. The e.m.f. readings were taken on a Beckman Expanded Scale pH Meter. The 0 to 200 mv. full scale was extended by recalibrating the 0 against the output of a Biddle-Gray Portable Potentiometer Model 605014. Readings were good to 1.0.2 mv. Potentiometric titrations were carried out in the concentration cell shown in Figure 1. Hydrogen electrode immersed in a saturated solution of benzoic acid in TMG ‘ served as the reference electrode. All titrations were performed using 10 ml. burets equipped with teflon stop— cocks. The cell used in the e.m.f. measurements is illustrated in Figure 2. The reference electrode consisted of a Figure 1. 21 Diagram of the cell used in potentiometric titrations. a: platinum electrode b: hydrogen bubbler c: outlet bubbler d: teflon stopcock e: fine porosity frit f: electrolyte chamber 9: buret h: 3 £9 30 22 ) D 9 TM) WW 1 1 3' h {A f ...... L e 3' / .) . e ..I.... _, u 3' F Ll) d 23 Figure 2. Diagram of the cell used in e.m.f. studies. 9 10/30 platinum electrode with mercury contact hydrogen outlet capillary gas dispersion tube; course frit hydrogen electrode half cell fine porosity frit teflon stopcock 5 14/20 reference electrode half cell filler hole teflon stopper platinum contact 9 19/20 electrolyte chamber :3 E HWU-P-D'LQ HOD-IOU!” 24 Figure 2 25 mercury-mercury (II) couple which was composed of a mercury layer in contact with a saturated solution of mercury (II) chloride in TMG. III. Procedures A. Conductance Measurements Freshly distilled solvent was weighed into a cell which had been previously steamed, rinsed with acetone and dried by a stream of dry nitrogen. The cells were then immersed into the thermostatic bath and allowed sufficient time to attain temperature equilibrium. Since the resistance read— ings for the pure solvent as well as for the solutions were generally above 30,000 ohms, the cell was shunted with a resistance of 30,000 ohms. The parallel resistance readings were then taken and converted to series cell resistances. The specific conductance of the solvent was then calculated. Stock solutions were prepared by weighing solvent into a flask containing previously weighed solute. The stock solu- tion was then added to the cell by means of a weight buret and the contents of the cell thoroughly mixed. After tempera- ture equilibration the contents of the cell were remixed in the bath and the resistance readings taken. An additional amount of the stock solution was then added to the cell and a new measurement was taken. In this manner it was possible to measure the conductance of a series of solutions of vary- ing concentration. 26 When solutions were prepared by the usual volumetric techniques rather than by weight, considerably more scatter was observed in the Shedlovsky plots. The dielectric constant of 11.00 i 0.02 for TMG was measured by a previously described technique (37). B. Potentiometric Measurements Solutions of various acids in TMG were prepared by the usual volumetric technique, but the manipulations were carried out in a dry box under a dry nitrogen atmosphere. It was found that mercury-mercury (II) electrode had a steady and reproducible potential when used in conjunction with a hydrogen electrode. A saturated solution of mercury (II) chloride was prepared by suspending 2.00 g. of dry salt in 100 ml. of solvent and stirring the mixture for two hours. The solutions appeared to be stable for at least 24 hours. After the solution had been aged for several days, however, a black deposit was formed on the bottom of the flask. In order to avoid a possible source of error fresh saturated solutions of mercury (II) chloride were prepared just prior to use. Attempts to prepare a calomel reference electrode in TMG were unsuccessful since addition of calomel to TMG instantly produced a black precipitate. The reference electrode half cell (shown in Figure 2) was filled toxrxl cm. from the bottom with mercury and a platinum contact inserted into the mercury. Saturated 27 mercury (II) chloride solution was then added to the refer- ence electrode compartment. Sixteen gage platinum wires of 1 to 1.5 inches in length were sealed into soft glass tubes and subsequently coated with platinum black by electrolysis in the previously described solution (p. 2%)) for 5 min. at 10 ma. The elec- trodes were then charged with hydrogen by cathodizing in a dilute sulfuric acid solution. As the measurements were taken electrodes were interchanged to compare their response. Fresh electrodes were used when readings became erratic or when readings did not agree to within 1.0.5 mv. between fresh and previously used electrodes. Immediately before use, the platinum electrodes were washed with distilled water, rinsed in acetone, and air dried. A gas dispersion tube was inserted into the hydrogen electrode half cell (Figure 2) and the half cell purged with hydrogen for 5 minutes. The reference electrode compartment was then filled with saturated mercury (II) solution. Finally, the hydrogen electrode compartment was filled with the solu- tion to be studied. The bridging compartment was also filled with the same solution to minimize errors due to diffusion. A current of hydrogen was allowed to stream through the solu- tion for at least 20 minutes. The readings were taken when changes in potential were about 2 mv. or less over a 20 to 30 minute recording interval. This behavior may be due to the hydrogen electrode coming slowly into equilibrium with 28 the solution. Even in aqueous solutions this electrode occasionally shows erratic behavior (38). It was found that when the system was thermostated in a constant temperature bath the accuracy of the measurements did not improve. Reproducible measurements could be obtained in a water thermostat only after 40 to 45 minutes. The reported e.m.f. values are the mean values of the best four readings and have average deviations of i.0.5 to i.1.0 mv. The hydrogen partial pressure correction to the observed e.m.f. was ignored since it would be less than experimental error. C. Titration Procedures Solutions were prepared by weighing an amount of acid to be titrated and diluting it with 25 to 50 ml. of TMG. This solution was then transferred to the cell for subsequent titration. The titrant was always standardized against benzoic acid. The hydrogen bubbling rate did not appear to have a sig— nificant influence on the potential readings and, therefore, the tank output regulated so as to maintain a slow passage of hydrogen through the solution throughout the titration. After the solutions were saturated with hydrogen (usually 15 to 30 min.) the titration was begun. The potential values were taken after the highest scale reading was reached (usually about one minute). Near the equivalence point the potentials were more unsteady and it took somewhat longer to reach the peak reading. After the equivalence point, the 29 readings were generally unsteady until a relatively large excess of titrant had been added. Again, the peak scale readings were taken. When curcumin indicator was used for the detection of the end-point, the titrations were carried out under nitrogen atmosphere because of the high affinity of the solvent for moisture and carbon dioxide. To insure that the color change corresponded to the potentiometric equivalence point, preliminary titrations were done potentiometrically with the indicator added to the cell. Initially, the solutions to be titrated had a red-violet color (3 or 4 drops of indicator solution per 50 ml. of solvent). The color changed to an intense blue upon addi- tion of a small amount of base and turned very sharply to yellow or gold at the equivalence point. Blank corrections were not made in as much as the experimental conditions, volume of solutions, and volume of indicator were kept the same during the standardization of the titrant solution and the titrations of the acids. Fresh indicator solution was prepared prior to each series of titrations since on stand- ing for long periods of time the indicator solution tended to decompose. RESULTS AND DISCUSSION I. Conductance Results Conductance data were obtained for tetrazole, nine 5- substituted tetrazoles, tetrabutylammonium iodide, triiso— amyl-grbutylammonium-tetraphenylborate and picric acid . solutions in TMG. These data are shown in Table II. It should be noted that the concentration range of these solu- tions is, perhaps, somewhat narrower than that usually found in similar studies. In general, the upper limit of concen- tration was determined by the Fuoss equation, C = 3.2 x max 10.171?3 (39), since at higher concentrations the simple laws of dilute solutions of electrolytes may no longer be obeyed. The lower limit was taken such that the specific conductance of the solvent would be less than 5% of the specific conduct— ance of the most dilute solution. Under these conditions, Ehe solvent correction was made by subtracting the specific conductance of the solvent from that of the respective solu- tion. The experimental data were evaluated according to the Fuoss-Shedlovsky method as previously described using a Fortran computer program run on the Control Data Corporation Model 3600 computer. The results including the respective standard deviations, are given in Table III, and the 30 31 Table II. Equivalent conductances in TMG at 250 (Superscripts designate series of determinations) 1040 A 104C A 1040 A 5-p-N02PhTz 5-preOPhTz 5—prClPhTz 0.4551 26.95a 0.6704 19.01a 0.6051 24.40a 1.297 25.52 1.618 14.66 1.517 20.11 1.751 21.66 2.427 12.78 2.809 17.05 2.401 20.04 5.599 11.55 5.547 15.90 5.166 18.87 4.152 10.54 0.8480 22.97 4.112 17.68 4.666 10.09 1.775 19.56 0.5510 27.75b 1.210 16.08b 5.051 16.64 1.165 25.89 2.569 12.89 3.841 15.51 1.757 22.07 5.557 11.59 2.585: 20.17 4.567 10.55 5.225 19.10 5.202 9.705 4.505 17.72 5.876 9.279 5-PhTz Tetrazole 5-MeTz 1.525 17.59a 1.705 16.75a 2.878 10.41a 2.455 15.02 5.559 15.15 5.014 “8.564 5.560 15.29 5.058 11.26 8.855 6.708 4.858 11.97 6.575 10.20 1.546 12.84 5.542 11.45 7.922 9.550 5.864 9.514 1.581 17.84b 9.451 8.915 4.961 8.419 2.126 15.67 2.089 15.71b 6.255 7.705 5.522 15.57 5.755 12.74 7.667 .7.122 4.487 12.28 5.885 10.72 9.140 6.657 5.572 11.55 7.655 9.707 9.382 8.986 11.21 8.588 continued Table II -- Continued m: 32 10‘0 A 1040 A 1040 A 5-Eth 5-PrTz 5-Bsz 1.799 11.45a 1.889 10.80a 1.251 15.71a 2.550 10.58 5.457 8.647 2.825 10.25 5.549 9.055 4.954 7.485 4.519 8.695 4.678 7.990 6.925 6.572 5.467 7.925 5.417 7.515 8.687 5.996 6.569 7.570 7.220 6.710 10.05 5.617 7.609 6.948 1.885 11.17b 1.944 10.75b 1.070 14.40b 2.414 10.19 5.505 8.597 2.520 10.97 5.759 8.655 5.715 7.098 5.580 9.524 5.108 7.648 7.400 6.417 4.274 8.705 5.704 7.528 9.075 5.912 5.557 7.986 7.255 6.669 10.60 5.565 6.186 7.558 5—3-0 113sz Picric Acid (_i_-Am) 3BuNBPh4 1.525 14.55a 0.7588 55.50a 0.5702 24.60a 5.008 11.69 1.720 50.64 0.6467 24.15 5.051 9.748 5.554 27.84 1.246 25.58 6.551 8.985 4.542 26.66 2.916 21.67 7.540 8.419 5.475 25.57 4.044 20.86 8.578 8.025 6.487 24.98 1.979 22.52 1.172 15.79b 0.4806 54.04b 0.5295 24.78b 2.178 15.05 1.188 51.96 0.5751 24.55 5.169 11.48 2.504 29.10 1.078 25.58 5.978 10.61 5.508 27.65 1.695 22.75 4.842 9.892 5.190 25.85 2.484 21.98 5.671 9.545 5.912 25.25 5.542 21.14 continued Table II -- Continued =-=====:— 1 10% A 104C A 1040 A Bu4NI 0.4566 22.97a 1.226 16.50 1.779 14.41 2.641 12.49 5.220 11.58 5.675 11.04 0.4259 25.58b 1.042 17.61 1.759 14.68 2.575 15.11 2.910 12.14 3.617 11.19 Tz = tetrazole; 32 = benzyl; Ph = phenyl; Bu irAm = isoamyl}, Me = methyl; Et = ethyl; Pr MeO = methoxy. g-butyl; srpropyl: 34 Table III. Conductance results in TMG at 250 ====: 1:: Substance Ao 6A0 KHx x 105 dKHx x 105 Tetrazole 45.5 1.2 2.94 0.16 5-MeTz 36.3 1.5 2.52 0.21 5-Eth 34.9 1.0 2.31 0.14 5-prTza 54.6 0.5 2.18 0.08 5-Bsz 36.0 0.5 2.45 0.07 5-p_-c leTza 52 . 6 --- 4 . 56 -- 5—PhTz 35.5 0.3 5.77 0.10 5-prMeOPhTz 35.1 0.4 3.89 0.10 SeprClPhTz 34.1 0.3 10.5 0.25 5fEfNOgPhTZ 33.0 0.5 18.9 0.72 Picric acid 38.2 0.2 55.8 1.2 (ifAm)3BuNBPh4 26.4 0.1 179.0 8.9 Bu4NI 42.7 0.9 2.48 0.11 aEvaluated by taking the mean of both data sets; all others were evaluated by combining both data sets. 35 Shedlovsky plots for the systems investigated are given in Figures 3-6. The plots, as taken from the computer print out, clearly reflect the linearity and reproducibility of the data. Bellobono and Favini, studied conductances of several electrolytes in ethylenediamine solutions (40) and reported that satisfactory values of A0 and KHx were obtained by the simple application of the Ostwald dilution law (Equation 13), as well as by the Fuoss and Kraus technique. Upon evaluation of their potassium iodide data with our computer program a rather surprising result was obtained, namely that over the concentration range they chose, the 1/A gg. cA_ plot was quite linear while the Shedlovsky plot was linear only for the most dilute solutions. Thus it appears as if better results were obtained by ignoring interionic effects and activity cor- rectionsl The Ostwald method was applied to the data in this in- vestigation but the plots were curved and the extrapolated values were much more uncertain than those obtained by the Fuoss-Shedlovsky treatment. As expected for a solvent with a dielectric constant of 11.00, all of the compounds studied are rather weak electro- lytes. The leveling effect of the basic solvent on acids is also evident from the relatively narrow range of the acid dissociation constants. For example, while the dissociation constants of picric acid and of tetrazole differ by a factor of 140,000 in aqueous solutions (41,23) (2.2 and 1.54 x 10’5, respectively), the factor is reduced to only 19.5 in TMG 36 Figure 3. Shedlovsky plots for A, 5-Bsz, B, 5—prCleTz, and C, tetrazole in TMG. 18.0 16.0 14.0 12.0 102 A52 10.0 8.0 6.0 4.0 2.0 37 0 Data Set a . Data Set b 1 l I 1.0 2.0 3.0 4.0 5.0 CASzf2 x 103 Figure 3 38 Figure 4. Shedlovsky plots for A, 5-MeTz. B, 5-prMeOPhTz, and C, picric acid in TMG. 39 18.0 '— 16.0 '- 14.0 "' 12.0 F' 10.01- Asz . ‘ 8.0 -- 6.0 L. 4.0 .— 2.0 ._ 0 Data Set a 0 Data Set b I l l l l l l 1.0 2.0 5.0 4.0 5.0 6.0 7.0 CASzf2 x 103 Figure 4 40 Figure 5. Shedlovsky plots for A, 5-PrTz, B, Bu4NI, and c, (i-Am)3BuNBPh4 in TMG. 18.0 16.0 14.0 12.0 102 AS 2 10.0 8.0 6.0 4.0 2.0 41. A . C 0 Data Set a 0 Data Set b l J 1 J I I 1.0 2.0 3.0 4.0 5.0 6.0 7.0 CASzf2 x 108 Figure 5 42 Figure 6. Shedlovsky plots for A, 5-Eth, B, 5-PhTz, C, Sep-ClPhTz, and D, 5-prN02PhTz in TMG. 43 14.0 )— 12.0 — 10.0.... 6.0— 4.0— 2.0.. 0 Data Set a ‘ Data Set b 1 I l J 2.0 5.0 4.0 5.0 CAszf2 4 103 Figure 6 42 Figure 6. Shedlovsky plots for A, 5-Eth, B, 5-PhTz, C, SeprClPhTz, and D, 5-27N02PhTz in TMG. 43 14.0 12.0 10.0 B 8.0... ' . 102 . .AS Z c 6.04—- ’ . , D 4.0—— . . ' ’r. 2.0.. 0 Data Set a . Data Set b I L 1 l J 1.0 2.0 5.0 4.0 5.0 CAszf2 x 103 Figure 6 44 solutions. In the case of tetrazole the overall acidity constant in TMG is greater than in water because of the basic nature of the solvent and therefore KEMG>> K?20 and this factor more than compensates for the ion-pair formation in TMG. On the other hand, picric acid is a strong acid in water and, therefore, Kgmqsc ngo but the overall constant is smaller in TMG than in water because of the low dielectric constant of the former solvent (KEMG<< K330). The overall acidity constant, however, still reflects the inductive effect of the substituent group on the acidity of the tetrazoles. Thus, for example, the acid strength varies in the order: HTz > 5-MeTz > S-Eth > 5-PrTz. With the phenyl derivatives the order is 5-prN02PhTz > 5—p7C1PhTz > 5-PhTz > 5-prMeOPhTz, and with benzyl derivatives, 5-27C1Bsz > 5-Bsz. The discrepancy between the ion—pair dissociation con— stants of triisoamyl-prbutylammonium tetraphenylborate and tetrabutylammonium iodide is puzzling, especially in view of the fact that both electrolytes exhibit normal behavior in adiponitrile solutions.1 It should be pointed out, however, that tetralkylammonium halides show appreciable association even in solvents of high dielectric constant such as aceto- nitrile (42) where the ion-pair dissociation constant for tetramethylammonium iodide, for example, is 3.62 x 10'2. The limiting conductance follows the usual trend of varying inversely with the size of the ions. In this respect 1See Part II of this work. 45 it is interesting to compare our results with those of Bellobono and Favini (40) since ethylenediamine has approxi- mately the same dielectric constant as TMG and both solvents are basic in nature. Their results indicate, for example, that the conductances of alkali metal halides in ethylene- diamine solutions, in general, increase with the size of the ions. Thus they obtain the following orders and LiBr NaBr 0 A0 < A KBr OCsBr < Ao > A Also the limiting conductances of the bromides are, in gen— eral, lower than those of the iodides. The limiting conductances of organic acids and their alkali metal salts showed little correlation with ionic size. An attempt was made to correlate the inductive effect of the substituent groups with the Taft d#.constant for the series of 5-aliphatic substituted tetrazoles. With tetrazole as a reference, 6* values (43) were plotted gs, log KHX' As seen from Figure 7, the result is a fairly reasonable linear plot which may be described by the equation , * * 0 * log KHX e p 6 + log KHX = 0.175 6 - 4.55 50. These data, also shown in Table IV, support the conclusion that the Taft 6* values provide a useful correlation for the estimation of acid strengths of weak acids, although as given 46 Figure 7. Relationship between log KTéx and 6* for some 5-aliphatic substituted te razoles. 47 6* -005 -005 -001 -007 Figure 7 -4.2 —- -4o4 — -4.8-— 48 I Table IV. 6* Constants for various tetrazoles Substance Log KHx 6* 5-MeTz -4.60 -0.490 S-Eth -4.64 -O.590 5-PrTz -4.66 -0.605 5-BZTZ -4.61 -O.275 Tetrazole -4.53 (log KHX) 0.000 aThe above 6* values are relative to tetrazole (containing the hydrogen substituent) with the reference value of 0.000. Taft gives the methyl substituent as the reference. To convert these values to those given by Taft (43), 0.490 is added to each value. bTaft gives median deviations for the 6* values of.i 0.02 to 1.0.04. 49 by Taft, the 6* values refer to the hydrolysis of esters in acidic or basic solutions. It has also been previously shown *- that log Kf is a linear function of the Taft 6 constant, where Kf is the formation constant of various halogen com- plexes (44). II. Potentiometric Results Overall dissociation constants of 5-MeTz, 5-Bsz, 5-PhTz, 5-prleTz, perchloric and mechlorobenzoic acids, and phenol were determined potentiometrically by the procedure outlined (Nigmh 26—28. Unfortunately, in a number of cases limited solubilities of acids in TMG precluded their study. For ex- ample, attempts have been made to study the dissociation of acetic acid, hydrochloric acid, and hydrobromic acid in TMG but the experiments could not be carried out due to the low solubility of these acids in TMG. The experimental data are given in Table V. The value for EH. was calculated from the KHx value for 5-Bsz obtained from the electrical conductance measurements. The e.m.f. data were fitted by the method of least squares to yield a straight line with a lepe of 0.0288 (1.0.0012) and an inter- cept of -0.8021 (i.0.0015), where the numbers in parenthesis represent the respective standard deviations. Recalling that intercept = E0. + 0.0296 log KHX’ the value of EH. was calcu- H I lated to be -0.6657 v. This value for EH was then used in conjunction with the data in Table V to calculate the overall acidity constants for the other systems. The results are given 50 Table V. Experimental data from potentiometric measurements in TMG. 1030 EHX(V.) 1030 EHx(v.) Phenola HClO4 422.5 -0.8490 142.9 -0.7829 283.3 -0.8622 36.69 -0.8083 194.3 -O.8779 24.09 —0.8035 189.7 -0.8763 19.3 —0.8156 106.8 -0.9066 5.04 -0.8357 105.3 -0.8965 3.56 -0.8411 36.11 -0.9315 2.51 -0.8404 31.16 -0.9278 1.17 -0.8575 10.6 -0.9467 3.00 -0.9590 5-prCleTz erhlorobenzoic Acid 12.7 -0.8485 23.61 -0.8547 7.81 -0.8575 16.07 —0.8615 4.72 -0.8619 9.47 -0.8710 2.82 -0.8679 5.84 -0.8815 2.19 —0.8719 3.40 -0.8808 1.88 -0.8794 1.43 -0.8936 0.916 -0.8854' continued 51 Table V -- Continued 103C EHx (v.) 103C EHx(v.) 5-M8TZ 5-PhTz 58.52 -0.8420 52.46 -0.8526 51.17 -0.8442 17.26 -0.8597 22.6 -0.8470 14.2 -0.8595 20.7 -0.8505 9.88 -0.8486 14.9 -0.8550 9.81 -0.8452 11.9 -0.8560 8.11 -0.8484 11.6 -0.8568 5.91 -0.8515 8.75 -0.8592 5.79 -0.8555 7.58 -0.8651 5.61 -0.8565 5.81 -0.8694 5.52 -0.8579 5.16 -0.8750 4.06 -0.8581 2.90 -0.8750 5.55 -0.8655 2.24 -0.8642 1.94 -0.8681 5-Bsz (cont.) 52.0 -0.8440 4.95 -0.8675 17.7 -0.8522 4.45 -0.8708 17.5 -0.8488 4.42 -0.8694 15.8 -0.8558 5.48 -0.8695 10.5 -0.8566 5.55 -0.8755 10.2 -0.8605 2.16 -0.8784 9.58 -0.8585 1.79 -0.8855 5.77 -0.8645 5.62 -0.8658 aThe last four data combinations listed were those used to evaluate pKHx for phenol. 52 in Table VI. It is seen that there is good agreement between the potentiometric and conductometric methods. The behavior of all substances listed, except phenol, is characteristic of weakly acidic substances in the concentration range of V\0.002 to 0.03 M, The same behavior was found for the con- ductance measurements which were done at g_0.001 M, The potentiometric method has lead to pKHx values for systems which could not be readily studied conductometrically, i.e., phenol and Mrchlorobenzoic acid. In the case of tetrazoles the inductive nature of the substituent groups is reflected in their pKHx values. Perchloric acid, the strongest acid studied (pKHX of 3.11) does not differ greatly in acid strength from the rest of the substances with the exception of phenol. Even in the latter case the leveling effect of the solvent is clearly noted considering that aqueous phenol has a pKa of 10 while aqueous perchloric acid is completely dissociated. The pKHx value of perchloric acid also compares favorably with the value of 3.28 for picric acid as measured above. This is not surprising, however, since both are strong acids in aqueous solution and it would be expected that they exhibit similar acidic character in a strongly basic solvent such as TMG. The linearity of the EHx _s, log [(CHx)t - afifl plots is shown in Figures 8 and 9. Measure- ments at low concentrations (< 0.001 M) for hydrogen bromide solutions in TMG indicated that a pKHx value of \/~4 might be expected. Mukherjee found that hydrogen bromide had a pKHx of 3.28 in ethylenediamine (45). 53 .mCOHumw>mU pumpomum m>HuUmmmmH on» ucmmmummu mononucmumm Ga mumflfidzm nu «H.m Amaoo.ovmomo.o Rewoo.ovomme.ou «OHUm In em.e Ammoo.ovmmmo.o Amsoo.ovsmmm.ou Hocmrm in om.¢ Remoo.ovmomo.o Ameoo.ovmsom.ou cflom 0eouch000HroLm «m.¢ md.¢ Amaoo.ovmmmo.o Ammoo.ovamm>.ou uBnmlm em .4 mm .4 3.80 .9880 .o Ammoo .o 5 82. .o- wawmaoumum 00.4 om.w Amoco.ovowmo.o Amaoo.ovmdom.on nawznm am.¢ In Amaoo.ovmmmo.o Amaoo.ovamom.ou Amusmummwuvwaumlm A.Ucowwxm A.m.E.MWMm mmon A.>v ummuumusH mocmumnsm M 029 CH hpsum UHHumEOHucmuom HO muasmmm . H> OHQME 54 Figure 8. EHX gs. log[(CHx)t- U/H-t] for TMG solutions of A, 5~PhTz, B, 5-Bsz, and C, Mrchlorobenzoic acid. 55 ~0.750— -0.770_" —0. 830 -0.850 -0.870 -0.890 l l l 1.0 2.0 5.0 log [(CHX)t - an“ Figure 8 56 Figure 9. EHX'XE' log[(CHx)t - dhf] for TMG solu- tions of A, HClO4, B, S-B-ClBgTz, and C, S‘MeTZ. -0. 750 .770 .790 .810 .830 .850 .870 .890 57 J l l 1.00 2.0 5.0/"1 - iog[(cHx)t - 4g] Figure 9 58 The importance of the iterative process in evaluating the data may be illustrated by comparing the following data for perchloric acid. The original plot of EHx-§' log (CHX)t yielded a slope of 0.0349, an intercept of —0.7537v., and a pKHx value of 2.98, whereas in the final iterative step, for which EHx was plotted gs, log [(CHx)t-,£H+] a slope of 0.0305, an intercept of -0.7579 v., and a pKHx value of 3.11 were obtained. The pKHx value of phenol of 7.54 indicates that it be- haves as a stronger acid in TMG than in ethylenediamine for which the corresponding value is 8.23 (45). This behavior would be expected in as much as TMG is a considerably stronger base than ethylenediamine (aqueous pKa = 0.4 as Opposed to an aqueous pKa of 4.15 (21), respectively. The data illustrated in Figure 10 indicate that the conjugate ion, ng, may be one of the species present in the more concentrated phenol-TMG solutions. It would appear that the discussion given by Bruckenstein (12a) regarding phenolic ions of the HXE type would also be pertinent in this work, since he points out that ions of this type have been previously reported on the basis of photometric, potentio- metric, and conductometric information. The value for pKHx; was found from the data shown in Figure 10 to be 1.52 (KHx; = 34.2). 59 Figure 10. EHX gs. log (CI-Ix)t for phenol solutions in TMG. -0.82 -0.84 (volt) -0.86 -0.88 -0.90 -0.92 -0.94 -0.96 60 O O O O 1 l 1.0 2.0 - log(CHx)t ' Figure 10 3.0 61 III. Titration Results In the initial phases of this investigation an attempt was made to use methanolic solutions of tetrabutylammonium hydroxide as the titrant. The titration curves, however, were erratic and it was evident that methanol was undergoing a slow reaction with TMG. In order to minimize these ef- fects, titrations were performed with TBAH in a 90-10% mix— ture of TMG with methanol. The experimental data are listed in Tables VII and VIII, while the respective titration curves are shown in Figures 11-13. As expected, with weak acids, a sharp decrease in potential is observed in the initial stages of titration. 05:2 10) a sharp rise at the beginning Thus for phenol (pKaH2 of the titration is seen, while for Mrchlorobenzoic acid (pKaHaqt;.4) no noticeable inflection is observed at the start of the titration. A titration curve similar to that of phenol was observed for s—cresol. Likewise, in the case of the substituted benzoic acids, the titration curves are similar to that of Mrchlorobenzoic acid. While it is diffi- cult to compare directly acid strength in TMG to acid strength in water, it appears that the substituted benzoic acids titrate in TMG as strong acids do in water, while phenol and the substituted phenols yield titration curves similar to those of weak acids in aqueous solutions. Because of the relatively low dielectric constant of TMG, it would be expected that most of the electrolytes are Table VII. 62 Titration data for monoprotic acids in TMG.a ml. mv. ml. mv. ml. mv. Phenol sfcresol prchlorophenol 0.0 +2.0 0.0 $18.0 0.0 0.0 0.84 113 0.26 14.0 1.00 20.0 3.00 154 0.50 108 3.00 45.0 5.00 173 1.00 150 5.50 73.0 7.00 186 3.01 201 7.50 105 9.00 218 5.00 237 10.00 128 10.00 250 6.00 274 14.25 196 10.10 259 6.10 284 14.85 245 10.25 277 6.20 306 14.90 265 10.50 301 6.30 331 15.00 290 11.00 327 6.40 359 15.10 310 13.00 330 6.50 370 15.25 321 6.75 389 15.50 328 8.00 409 9.00 415 5-MeTz 0.0 +26.0 3.00 +22.0 7.00 +3.0 9.00 31.0 9.67 93.0 9.70 95.0 9.72 102 9.77 171 9.85 310 10.00 351 10.20 366 10.40 376 11.30 392 12.80 403 Continued 63 Table VII -- Continued w ml. mv. ml. mv. ml. mv. A srChlorobenzoic acid nghlorobenzoic acid pfchlorobenzoic acid 0.0 +31.0 0.0 +20.0 0.0 29.0 0.50 +20.0 1.00 2.0 1.00 44.0 1.00 +6.0 2.00 19.0 2.00 68.0 2.50 54.0 3.00 53.0 2.50 100. 2.75 82.0 3.15 67.0 2.62 127 2.86 203 3.34 128 2.65 139 2.89 271 3.36 147 2.70 206 2.91 312 3.39 254 2.73 295 2.95 359 3.42 319 2.75 335 3.05 396 3.46 363 2.80 385 3.25 429 3.51 379 2.90 398 4.00 455 3.58 392 3.00 406 5.00 459 4.00 412 3.25 425 4.50 421 3.80 430 5.00 425 4.50 435 aNo sign before data in the mv. column indicates a negative reading (-). 64 Table VIII. Titration data for binary mixtures of acids in TMG. a Phenol- Phenol- 97Cresol- benzoic acid Mrchlorobenzoic acid m-chlorobenzoic acid m1. mv. ml. mv. ml. mv. 0.0 +2.0 0.0 +9.0 0.0 +12.0 0.50 +1.0 0.80 15.0 0.50 4.0 1.00 14.0 1.75 69.0 1.50 50.0 1.50 31.0 1.85 82.0 1.85 87.0 2.50 84.0 1.95 96.0 1.95 112 2.66 100 2.05 112 2.05 135 2.75 113 2.25 138 2.15 158 3.00 140 3.00 177 2.25 180 3.75 179 4.50 221 2.50 189 4.25 195 6.00 272 3.00 212 6.00 254 6.20 289 4.50 252 6.25 271 6.30 301 5.20 294 6.45 296 6.40 332 5.30 320 6.55 322 6.50 376 5.40 360 6.60 343 6.60 396 5.50 395 6.70 379 6.80 419 5.60 415 6.80 401 7.25 435 5.80 428 7.50 435 8.00 444 6.00 435 9.50 448 9.00 447 7.00 446 8.00 448 aNo sign before data in the mv. column indicates a negative reading ( - ). 65 Figure 11. Titration curves for A, phenol, B, sfcresol, and C, prchlorophenol. Mv. -400 -300 -200 -100- 66 Volume of titrant Figure 11 67 Figure 12. Titration curves for A, prchlorobenzoic acid, B, Mrchlorobenzoic acid, C, sfchlorobenzoic acid, and D, 5-MeTz. 68 -400 .— -300 - Mv. -200 '- -100 -— Volume of titrant Figure 12 69 present in this solvent as ion-pairs. Conductance measure- ments (pp. 30-49) have shown that the overall dissociation constant, KHX' for picric acid is 5.6 x 10“ while the ion— pair dissociation constant for a strong electrolyte, tri- isoamyl-srbutylammonium tetraphenylborate was 1.8 x 10‘s. It is seen, therefore, that picric acid in TMG is essentially completely ionized, but, because of the low dielectric con- stant of the solvent, it is incompletely dissociated. On the basis of the potentiometric study, which supported the conclusions reached in the conductance study, similar be- havior is expected for the substituted benzoic acids. Thus, as would be expected, the titration curves are indicative of the ionization rather than of the dissociation process. The results of the titrations are shown in Table IX. It is seen that the results are quite acceptable and that the error is always less than 1%. Addition of 0.1% of water did not change significantly the results, but larger amounts produced increasing errors. The results were quite unreli— able when 1% or more of water was added. All titration curves were reproducible with starting potentials for identical solutions reproducible to within 10 mv. It was found that curcumin indicator exhibited a color change in the -170 to -250 mv. region. Acidic solutions were an intense blue color which turned very sharply to yellow at the equivalence point. In the titrations of secresol and 70 Table IX. Results of potentiometric and indicator titrations of weak acids in TMG. Meq. Meq. Recovery, Substance taken found phenola 0.659 0.656 99.5 srCresola 0.515 0.515 100 prChlorophenol 0.475 0.475 100 5-MeTz 1.215 1.212 99.75 0.7630 0.7650 100.3 eritrobenzoic acidb 0.660 0.660 100 0.414 0.412 99.4 McChlorobenzoic acid 0.6662 0.6667 100.1 prChlorobenzoic acid 0.6591 0.6585 99.91 0.9069 0.9055 99.85 97Chlorobenzoic acid 0.6853 0.6856 100.0 0.7798 0.7771 99.65 aPotentiometric titrations only. bIndicator titration only. 71 phenol, however, the equivalence points occurred below -250 mv. and consequently curcumin was unsuitable as an indicator for these species. In all other cases the equi- valence points occurred at higher potentials and, therefore, the indicator method gave the same end-point as the potentiometric titration. The indicator solution had sufficient stability to be useful over a twenty-four hour period. After this period it was discarded and fresh solution was prepared. An at- tempt was made to determine the indicator constants by the spectrophotometric technique introduced by Lagowski and co- workers (46). It was found, however, that the dilute indi— cator solutions in TMG were too unstable to yield a repro- ducible absorbance spectrum. Potentiometric titrations of organic acids with nitro groups, such as picric acid, were unsuccessful due to appar- ent reduction of the nitro group with hydrogen. The intense yellow color of picric acid obscured the indicator end- point but other nitro-acids, such as srnitrobenzoic acid, yielded clear and sharp end-points with curcumin. An attempt was made to titrate binary mixtures of acids. Figure 13 illustrates the titrations of mixtures. Although the titration curves clearly illustrated stepwise neutralization, Table X shows that only the total acid present could be determined with any degree of accuracy. The level- ing effect of TMG compresses the range of acid strengths and, 72 Titration curves for binary mixtures of A, sfcrebol and benzoic acid, B, phenol and grchlorobenzoic acid, and C, phenol and benzoic acid. Figure 13. -400 -300 Mv. -200 ‘ -100 73 Volume of titrant Figure 13 74 040.0 000.0 400000Am 004 004.0 400.0 004.0 004.0 0400 04000000004nous 400 000.0 000.0 400000 404 000.0 040.0 004.0 004.0 0400 0400000000400ns 400 000.0 000.0 40:0:0 004 404.0 004.0 040.0 000.0 0400 0400000 440 &.>40>oomu 0:500 cmxmu venom smxmu musuxwz 40009 40004 40009 .002 .00: .029 :4 00400 mo mmHSUxHE mumc4n mo 0:04004040 UAHumeowuomuom mo muasmmm .x 04406 75 for example, in the benzoic acid-phenol mixture, before all of the stronger acid, benzoic, is neutralized, the weaker acid, phenol, begins to react with the titrant. CONCLUSIONS The conductance and potentiometric studies have both shown conclusively that TMG is a suitable solvent for the study of acid-base equilibria even though it has a low dielectric constant of 11.00. The values of the overall dissociation constants, KHX' were in the range of 0010'3 to 10"7 with the strongest acids being perchloric and picric acid while the weakest acid was phenol. These also reflect the leveling effect TMG has on acidic substances in as much as the KHx values are very considerably com- pressed when compared to the same values for aqueous solu- tions. The inductive effect of the tetrazole.substituent groups is reflected in the KHx values for tetrazole and the 5-substituted tetrazoles. This would be expected since KHx is a function of the ionization constant Ki’ as well as the dissociation constant, Kd' The titration studies showed that the tetrazoles and substituted benzoic acids titrate in TMG as strong acids in water while phenol and the substituted phenols titrate in TMG as would weak acids in water. These results indicate that the former are essentially completely ionized to ion- pairs while the latter are only partially ionized. Analytical results, good to i 0.5%, were obtained. 76 PART II ADIPONITRILE 77 HISTORICAL INTRODUCTION The use of mononitriles as nonaqueous solvents has been the subject of many investigations (47-56). Acetonitrile (47-53), benzonitrile (53-56), propionitrile (56), isobutyro- nitrile (52), and d-napthonitrile (53) have all been investi- gated, although, the greatest effort has been made with acetonitrile. As early as 1906 Walden studied the conducto- metric behavior of alkali metal and tetraalkylammonium salts in propionitrile, benzonitrile, and acetonitrile (56). Fuoss and Brown studied the behavior of tetrabutylammonium tetra- phenylborate, a large symmetrical electrolyte with cation and anion of approximately the same size, in acetonitrile and isobutyronitrile as a means of determining limiting ionic conductances (52). French and Muggleton investigated the behavior of picric acid in acetonitrile, benzonitrile, and o-napthonitrile (50). They proposed the formation of the triple ion, (Pi-H-Pi)-, to explain the conductance behavior over their chosen concentration range (Pi represents the picrate anion). Kay and co-workers found that tetraalkyl- ammonium halides had similar ion size parameters,sJof about 3.6 1.0.2 A0 and that only the tetramethylammonium halides showed appreciable association in acetonitrile (47). The latter results are in accord with the earlier findings of Popov and Humphrey (42). Kay et al., evaluated their 78 79 acetonitrile data by the latest Fuoss—Onsager treatment (57), while Harkness and Daggett (48), who investigated many of the same salts in acetonitrile at about the same time, evaluated AG by extrapolating the phoreograms and by Shedlovsky's iteration technique (26). The three treatments appear to yield comparable results foriAo while the results do not agree quite as well for the ion pair association constant, KA. For example, A0 values for tetra-srpropylammonium iodide by the Fuoss-Onsager, Phoreo- gram, and Shedlovsky methods were respectively, 172.9, 173.2, and 173.1. The KA values as determined by the Fuoss- Onsager and Shedlovsky treatments were respectively, 5 and 10.5. It should be pointed out, however, that in determin- ing small association constants as such, the errors are quite large. The use of nitriles as solvents in the study of acid- base equilibria has been limited with the exception of the studies of Coetzee ss_s;, (58). No equilibrium studies have been undertaken using dinitriles as solvents. The work presented here involves initial use of a dinitrile as an electrolytic solvent. As a prelude to studying acid-base equilibria in this solvent an electrical conductance study of sodium, potassium, and tetraalkylammonium salt solutions was initiated. Adiponitrile (abbreviated as ADN) presents an especially interesting case since it is a relatively polar solvent with 80 a high dielectric constant and an appreciable dipole moment. At the same time it has respectable donor properties toward Lewis acids such as transition metal ions and would prob- ably act as a bidentate ligand. Literature reports indicate that adiponitrile (1,4- dicyanobutane) has a density of 0.9579 g./1. (59), a vis- cosity of 0.0621 poise (sixfold greater than that of water) (59), and a dipole moment of 3.76 debyes (60). A dielectric constant of 32.45 was measured in this work (p. 269. It has a very broad liquid range (20 to uo3000) and may be purified by fractional freezing or fractional distillation. Most quaternary ammonium salts dissolve in adiponitrile whereas alkali metal salts are generally much less soluble even though some such as sodium perchlorate and sodium iodide form solvates. THEORETICAL The Onsager conductance equation (61) is given as follows .1. A = A0 "’ (GAO-F B)C2 1° where the terms have the same meanings as given in the previous section (p. 12). This equation is only a limit- ing law in as much as the higher terms have been neglected in the derivation. For dilute solutions of strong uni- univalent electrolytes, a plot of A gs, Cé (phoreogram) generally yields a straight line with slope S = vo-+ 8. By rearranging Equation 1 and solving for A0 (62) one can obtain the expression 5 A0 = A.+ QC 2. 1 - dc Shedlovsky has found that AD was not constant over any appreciable concentration range. Consequently he defined a new function, A0, by the following equation Aggie—L: - 5. 1-00 I If A0 is plotted gs, C, a straight line given by Equation 4 is obtained A0 = A0 + BC 4. 81 82 The value of.A$ at infinite dilution is the true limiting conductance, A0. It should be recalled that Equation 1 assumes that the degree of dissociation, 7, equals unity and assigns the decrease of,A with increasing concentration of the solutions to a decrease in ionic mobility arising from the interionic forces between the ions. The equation, however, only accounts for two interionic forces, the braking relaxation effect, a, and the electrophoretic effect, 8. In the modern conductance theory (57) two ad- ditional interionic forces are considered. The asymmetry in the atmosphere of a moving ion also produces a virtual osmotic force which slightly increases conductance, and also a correction must generally be made for the increase in static viscosity of the solution due to the presence of the ions. Two conductance equations then, result from the Fuoss-Onsager derivation (57). The first, for unassoci- ated electrolytes is A=Ao-SC§+EClogC+JC-FAOC 5. where, E, J, and F are given by the following relationships E=E1AO+E2 6. J = 0’le + 0’2 7. and F = 6.508x1021R3 8. 83 The constants, E1, E2, 63, and 6; are functions of funda- mental constants and are defined by Fuoss and Accascina (63). The parameter, R, is known as the "hydrodynamic radius" which Fuoss and Accascina describe as "the sphere around an ion, inside of which no other ion may penetrate." Equation 8 which defines F, the correction due to the in- crease of static viscosity of the solution with increasing concentration, is generally applied only when viscosity data for the individual solutions are unavailable. If viscosity data are available F may be calculated from these data (64). In the case of associated electrolytes Fuoss and Onsager have shown that the conductance equation takes the form A» = Ab - s(yc)é'+ E7C log 70 + ch - KAVC f2 - FADC 9. where KA is the association constant and f the mean activity coefficient. By ignoring the static viscosity correction, F, in dilute solutions, Equations 5 and 9 become A = A0 - sc§'+ EC 109 c + Jc' 10. and ’ A 0 A0 0 S(vC)% + Eyc log 7C + JyC - KAyC f2 11. The assumption that F is negligible would appear to be valid since in dilute solutions the static viscosity correction would be very small. 84 The application of Equations 10 and 11 to conductance data is aptly described by Fuoss and Accascina (65). Kay utilized the treatments in his least squares computer pro- gram, thereby making the modern conductance theories easily and readily applied.l 1Dr. R. L. Kay of the Mellon Institute, Pittsburg, Pa., kindly provided the Fortran program which was used in the final treatment of our data. EXPERIMENTAL I. Reagents Adiponitrile (hereafter referred to as ADN) was obtained from Eastman Chemical Co. and was subjected initially to successive fractional freezings until a constant freezing temperature of 2.150 was obtained. The solvent was then fractionally distilled from granulated barium oxide through a 24 in. Vigreaux column at 1 mm. pressure and 1230. The retained middle fractions had the following properties at 25°: specific conductance, 1-2 x 10‘8ohm‘1cm'1; dielectric constant at 1 megacycle, 32.45; viscosity, 0.0599 poise; density, 0.9585 g./m1. The procedures for the measurement of the dielectric constant, viscosity, and density have been previously described in detail (37). Comparison data for the specific conductance and dielectric constant are unavail— able. However, the values for the viscosity and density of ADN differ somewhat from the corresponding data of 0.0621 poise and 0.9579 g./ml. in the literature (59). The solvent was recovered for reuse by distillation. The synthesis and purification of triisoamyl-sfbutyl- ammonium iodide and triisoamyl-sfbutylammonium tetraphenyl- borate are described above (p. 17). Eastman Grade tetrabutyl- ammonium iodide, tetrahexylammonium iodide and tetrahexyl- ammonium bromide, as well as reagent grade potassium and 85 86 sodium salts, were used without further purification. The other seven quaternary ammonium salts were recrystallized from appropriate solvent systems. All salts were dried 42.22222 at 500 to constant weight prior to their use in the preparation of stock solutions. The subsequent con- firmation of additivity of ionic conductances indicated that the salts were generally pure. II. Apparatus and Procedures ‘The apparatus and procedures have been described above (p. 20). The additions of stock solutions to the conduct- ance cell were made under normal laboratory conditions since brief exposures of the non-hygroscopic solvent and solutions to the atmosphere caused no observable changes in resistances. RESULTS AND DISCUSSION The measured equivalent conductances of the solutions and the corresponding concentrations (in moles per liter) are summarized in Table XI. The data were all evaluated both as unassociated and associated electrolytes using Equations 10 and 11 respectively. The results report the individual species as associated or unassociated electrolytes based on the nature of the calculated degree of dissociations at various concentrations. If the degree of dissociation was greater than unity then the species was taken to be un- associated and the results reported in that manner. Because of the lack of information concerning the viscosities of solutions of salts in ADN, the normally small viscosity cor- rections associated with J were omitted. The viscosity cor- rection in each case has no effect on A0 or on the associa- tion constant and, if applied, leads to only slightly higher values for J and 3?. For each salt the upper concentration limit was below the concentration at which ',_K§_ = 0.2, where M is the Debye-Huckel parameter and s_is the ionic diameter. The conductance parameters obtained from least squares analysis of the data in Table XI using a CDC—3600 Computer are summarized in Table XII. Included also in Table XII are data for 6A; the standard deviation associated with the indi- vidual.A values. Calculations were made with unweighted values 87 88 Table XI. Conductances of salts in adiponitrile at 250 (Superscripts designate series of determinations) 1040 A 1040 A 1040 A NaI KI KSCN 2.461 12.07a 1.557 12.92a 2.558 15.56a 10.25 11.69 9.095 12-45 5.978 15.04 16.50 11.47 15.74 12.19 12.85 14.51 24.88 11.25 24.69 11.95 25.41 15.96 57.10 11.00 57.72 11.64 58.45 15.40 2.245 12.11b 4.441 12.68b 57.24 12.86 4.418 11.96 9.874 12.40 2.562 15.58b 8.944 11.74 17.15 12.14 5.675 15.05 14.95 11.55 27.72 11.85 12.05 14.56 25.58 11.51 41.78 11.57 22.95 14.01 55.56 11.05 56.96 15.48 55.56 12.94 NaClO4 NaBPh4 Et4NBr 4.562 12.55a 4.555 8.68a 4.855 12.44a 11.04 12.21 9.015 8.52 10.38 12.17 18.29 11.94 14.68 8.58 18.00 11.90 28.05 11.67 22.95 8.21 28.17 11.61 42.05 11.54 54.52 8.04 42.52 11.52 6.606 12.45b 5.116 8.64b 5.895 12.51b 12.96 12.14 9.506 8.50 9.272 12.22 21.29 11.86 15.50 8.55 16.45 11.95 55.58 11.55 25.81 8.18 25.61 11.68 50.58 11.19 55.44 8.02 59.18 11.58 continued Table XI -- Continued 1040 A .1040 A 1040 A MeaPhNBr MegPhNI Pr4NBr 2.778 12.58a 2.582 12.85a 1.921 11.55a 5.716 12.15 9.796 12.59 4.817 11.14 11.57 11.78 17.16 12.08 10.65 10.87 19.55 11.40 27.08 11.77 17.55 10.67 50.56 10.99 41.17 11.44 27.51 10.42 45.55 10.59 1.995 12.88b 41.57 10.18 2.401 12.45b 4.846 12.65 1.952 11.54b 5.202 12.19 9.695 12.57 5.501 11.11 11.65 11.76 17.19 12.08 10.26 10.90 19.29 11.40 26.40 11.78 17.67 10.67 50.79 10.98 40.54 11.46 26.94 10.44 46.66 10.56 41.24 10.19 Pr4NI Bu4NBr Bu4NI 2.181 11.67a 2.545 10.55a 2.688 ' 10.87a 5.026 11.49 4.851 10.58 5.208 10.72 9.957 11427 9.616 10.20 9.979 10.52 16.86 11.05 16.01 9.99 16.91 10.51 26.16 10.82 24.71 9.79 25.99 10.09 59.55 10.57 57.59 9.56 59.15 9.86 2.180 11.68b 2.560 10.55b 2.695 10.87b 4.980 11.50 4.869 10.59 5.085 10.75 9.756 11.28 9.745 10.19 10.05 10.52 16.45 11.07 16.55 9.98 16.69 10.52 25.62 10.85 25.54 9.77 25.52 10.15 58.80 10.58 58.50 9.55 58.67 9.88 continued 90 Table XI -— Continued 104C A 1040 A 1040 A Hex4NBr Hex4NI (i:Am)sBuNI 5.454 9.60a 5.467 9.85a 2.492 10.49a 6.978 9.44 9.872 9.66 6.160 10.50 12.44 9.26 15.86 9.49 10.14 10.15 19.69 9.08 25.00 9.29 16.84 9.95 29.21 8.90 56.95 9.09 25.84 9.75 45.57 8.69 5.019 9.86b 58.91 9.52 2.262 9.65b 9.257 9.68 2.978 10.47b 4.764 9.54 15.95 9.50 5.524 10.54 9.011 9.57 25.07 9.50 9.685 10.15 16.51 '9.18 57.75 9.09 17.60 9.92 24.50 9.02 27.01 9.71 57104 8.82 40.07 9.49 (ifAm)3BuNBPh4 MesPhN03SPh 4.061 7.149a 1.816 11.44a 7.542 7.025 5.125 11.12 10.81 6.929 10.00 10.84 16.88 6.789 17.20 10.51 25.91 6.654 27.10 10.17 57.77 6.480 40.88 9.79 5.410 7.185b 1.555 11.49b 7.262 7.041 5.259 11.15 10.622 6.940 9.481 “10.88 16.84 6.797. 16.85 10.54 25.56 6.644 26.62 10.20 57.58 6.490 40.48 9.82 Ph ? phenyl; Me = methyl; Et sfbutyl; Hex = sfhexyl; srAm ethyl; Pr = sfpropyl; Bu = isoamyl. 91 003:40coo 0.004 0.00 44.0w 0 4.040.m 40.0440.44 000.0 Q 0.004 0.00 04.4w 0 4.040.m 40.0400.44 000.0 0 4m24nm 0.004 0.40 00.0m 0 4.040.N 40.040N.m4 000.0 Q 0.004 0.40 00.0w 0 4-040.N 40.040m.m4 000.0 0 4220002 0.NON 0.00 04.00 040m 0.04N.0 40.0400.N4 «00.0 Q 0.004 0.00 04.0w 440m 0.040.4 N0.0400.N4 000.0 0 umznmmmz 0.004 0.00 0N.0N 0 4.040.m 000.0400.m4 N00.0 Q 0.004 0.00 0N.0N 0 4.040.m 000.0400.M4 000.0 m 4m240m 0.004 0.00 00.4w 0 4.040.m 40.0404.0 000.0 Q 0.004 0.00 N0.4N 0 N.04N.0 40.0404.0 400.0 m 40mmmz 0.N04 0.00 00.0m 0 4.040.N 40.0404.m4 000.0 Q 0.004 0.00 00.0N 0 4.040.N 40.0404.m4 000.0 0 404002 0.004 0.404 40.0N N404 N.040.N 40.0400.04 N00.0 Q 0.44m 0.404 00.0N .044N 0.044.m .mo.0400.m4. 000.0 0 200% N.mm4 0.40 00.0m 0 00.040.m 000.040N.M4 400.0 Q 4.404 0.40 04.00 0. 4.040.m 40.040N.m4 000.0 0 HM 0.004 0.00 40.4w 0 4.040.0 40.04N0.N4 000.0 Q 0.404 0.00 40.0w 0 - 4.040.m 40.Qflmm.m4 000.0 m 402 00 m 0 <4 am 0< . 020 0.004 0.00 00.00 0004 0.000.0 40.0040.44 000.0 A 0.004 0.00 04.00 0004 0.000.0 00.0000.44 000.0 0 00000200002 0.004 0.00 00.00 0 4.000.0 000.00000.0 000.0 a .I 0.004 0.00 00.00 0 4.000.0 000.00000.0. 000.0 m «ammzsmmhsdu4v 0.004 0.00 00.00 0 4.004.0 40.0040.04 000.0 a .I 0.004 0.00 00.00 0 4.000.0 40.0040.04 000.0 0 H2500050u40 0.004 0.00 00.00 0 4.000.0 40.0000.04 000.0 0 0.004 0.00 00.00 0 4.000.0 40.0000.04 000.0 m H20xmm 0.404 0.00 00.00 0 0.000.0 00.0000.04 000.0 a 0.004 0.00 .00.00 0 4.000.0 40.0000.04 000.0 m 0020xmm 0.004 0.00 00.00 0 4.000.0 40.0000.44 000.0 a 0.004 0.00 00.00 0 4.004.0 40.0000.44 000.0 0 H2050 0.004 0.00 00.00 0 4.000.0 40.0000.04 000.0 a 0.404 0.00 00.00 0 4.000.0 40.0000.04 000.0 0 002050 0.004 0.00 00.00 0 4.000.0 40.0000.04 000.0 a 0.004 0.00 00.00 0 4.000.0 40.0000.04 000.0 0 H2000 00 0 0 00 cm. 0 < < 0 00.0.80 04mm ©0DGHOGOU II HHx 04Q0B 95 of A and values of A.weighted by the concentration, C. The weighted data yielded a considerably better fit to the theoretical equations, as evidenced by the smaller values of 6A, therefore the final results are reported on that basis. For comparison sake, the same parameters as reported in Table XII are given in Table XIII using uni weighted data for six of the systems studied. The detailed results given in Table XII are summarized in Table XIV where the results of the two series of measurements on each salt have been averaged by weighting each parameter inverse- ly by its standard deviation. The constants a, E, El, and E2 for ADN at 250 have values of 0.8620, 14.01, 7.479, and 17.81, respectively. The A0 values listed in Table XII consistently are 0.0140.02 unit higher than those in Table XIII as calculated using unweighted data. The A0 values of Table XII are about 0.05 unit larger than the corresponding values obtained from preliminary Shedlovsky plots of A5 gs, C. The A0 values as obtained by the two different methods as well as by the Shedlovsky iteration technique (26) are listed in Table XV. The percentage differences between the Fuoss—Onsager and the two other methods are also included. The average percentage difference between the Fuoss-Onsager and the A; gs, C method is 0.55% for the twelve salts considered, while the average difference is only 0.50% between the Fuoss-Onsager and the Shedlovsky iteration technique. These observations then 94 .Umflammm coauomnuoo muflmoomfl> 02m m.a¢fi m.mn «m.om o N.owo.m noo.owm>m.h moo.o n .l m.0¢a m.mm wm.om o «.0wm.¢ oo.Owa>m.> moo.o m «smmzsmofis¢uflv m.wnd m.mm >m.mm o N.0Hm.¢ «0.0Hmm.oa «Ho.o A ¢.o>a 0.0m mm.mm o H.o“¢.¢ Ho.oao¢.oa moo.o m Hz.xmm $.mnd m.mw m¢.mm o a.onm.w Ho.owmm.oa moo.o n . N.m>a m.mm m¢.mm o H.0Hm.¢ H0.0Hmm.oa mfio.o m umZ¢sm o.>>a >.mm oa.¢m o a.owo.¢ H0.0HO>.aH moo.o Q m.m>a m.mm mo.¢m o H.0Ho.¢ Ho.owmw.aa oao.o m um2¢um m.¢ma e.ms «H.mm «Hmm m.OWs.m Ho.ofimm.ma oao.o n m.mma >.m> #H.mm mMNN m.OHw.m No.0HHm.NH mao.o m umznmmmz m.mma m.m> om.wm o H.owa.¢ do.owam.ma «Ho.o n N.mma >.mh m>.¢m o N.OHO.¢ No.0Hom.NH mao.o m Hmz . d .I on m m M on o < < .0 mounumm 3mm .mumo counmflmBGS moan: zed cw wuamm Mom coaumsqo HomMmCOImmosm map mo mumumsmumm UmumHsUHmo .HHHX magma Table XIV. Averaged Conductance parameters for adiponitrile solutions. Salt Ao 1° .KA NaI 12.52 5.9 0 KI 15.26 5.6 O KSCN 15.91 5.1 20 NaClO4 15.16 2.9 0 NaBPh4 9.16 5.2 0 Et4NBr 15.06 5.5 0 MesPhNBr 12.95 4.2 28 MesPhNI 15.27 2.7 0 Pr4NBr 11.71 5.9 0 Pr4NI 12.08 4.0 0 Bu4NBr 10.94 4.2 0 Bu4NI 11.50 4.2 0 Hex4NBr 10.06 4.6 0 Hex4NI 10.40 4.4 O (jg-Am aBuNI 10. 91 4.1 o (ifAm)3BuNBPh4 7.58 4.9 o MegPhN03SPh 11.80 2.8 14 96 .w50323000 203000003 hxm>03omnm may 0020000000 0 “020800000 0 .m m< may mucmmm0mmu m “020800000 Hmmmmcolmmosm may mucmmmummu <0 00.0 30.0 30.33 00.33 00.33 00000220002 00 .0 00 .0 00 . 0 00 . 0 00 . 0 00002000 2.0.00 00.0 00.0 00.3 00.03 30.3 020.00 15700 00.0 00.0 00.03 00.03 00.03 0020202 00.0 00.0 00.33 00.33 00.33 32050 00.0 00.0 00.03 00.03 00.03 002050 00.0 00.0 00.03 00.03 00.03 02000 00.0 00.0 00.33 00.33 30.33 002000 00.0 00.0 00.03 00.03 00.03 022000: 00.0 30.3 00.03 00.03 00.03 00200002 00.0 00.0 00.03 00.03 30.03 2002 00.0 00.0 00.03 00.03 00.03 002 o 0:0 0 0 0:0 0 .o 0 0 03mm .0030 0 .0000 0 o< o< o< M .0020800000 00200056200 050300> mg cm>wm mm 00530> o< mo somHHMQEou .>x 03909 97 point out that although the modern conductance theory is considerably more complex in both derivation and application than the earlier methods, the refinements are relatively small. This observance is in accord with findings of Harkness and Daggett in their acetonitrile study 148). Figure 14 illustrates the A6 5. C plots obtained by least squares analysis. Calculation of the conductance differences at infinite dilution between corresponding bromides and io- dides and between corresponding sodium and triisoamylfinr butylammonium salts indicates an uncertainty inl\o values of 0.05 units or about 0.5%. This apparent level of accuracy is quite satisfactory in comparison to the results for most other nonaqueous systems and reflects the general consistency of the overall results. Single ion limiting conductances were obtained on the basis of the assumption of Coplan and Fuoss (29) that the limit— ing conductance of the triisoamylagrbutylammonium ion is equal to that of the tetraphenylborate ion in all solvents. That is _ _ =.1 7“°(_i_-Am)313uN+ "' M(139m) 2 A°(i_-Am)3BuNB?h4 12. From the4Ao values for salts with a common ion, limiting equi— valent ionic conductances of fourteen ions in ADN have been calculated; the results are summarized in Table XVI. These data will reproduce the experimentally determinedHAo value for each of the salts within 0.01 unit. For example the.Ao value for MesPhNI as obtained from Table XIV is 15.27, whereas the 98 Figure 14. A; as a function of C for A, NaI, B, MesPhNI, D, Bu4NI, and E, Hex4NI. 14.0 15.0 12.0 11.0 10.0 99 Cx104 Figure 14 h— M + 30 _ln__A _a_o—I——o—.—————o—o———-O—t ’9‘.— B ++ G” + W +1) Jln__E f 3 —-£—— + 0 Series a . Series b l l l l l 6.0 12.0 18.0 24.0 50.0 56.0 42.0 100 Table XVI. Single ion limiting equivalent conductances in adiponitrile based on triisoamyl-gfbutylam- monium tetraphenylborate as reference elec- trolyte. + -I- Ion lo Ion Ag + — Et4N 6.29 SCN 9.79 + — MeaPhN 6.15 C104 7.77 + - K 6.12 I 7.15 + .— Na 5.58 Br 6.77 + — Pr4N 4.94 PhSOa 5.65 + .— Bu4N 4.17 BPh4 5.79 . + + HEX4N 5.28 101 value obtained from adding the ionic conductances of MeaPhN+ and I- as given in Table XVI is 15.28. The potas- sium and sodium ions have limiting conductances between those of the trimethylphenylammonium and tetra-grpropyl- ammonium ions: all other ionic conductances occur in the expected sequences. CONCLUSIONS The above results indicate that adiponitrile is a good dissociating solvent, since only three of the seventeen salts studied show any ion-pair association in the concen- tration range ofv‘10'4 to 5 x 10"8 g, The relatively high viscosity is reflected in the low values obtained for the limiting conductance (e.g., A0 value for Bu4NI is 11.50 as compared with 164.6 for the same salt in acetonitrile (47) and 101.72 in methanol (66)). On the other hand it is inter- esting to note that although dielectric constants of aceto- nitrile and methanol are very close to that of adiponitrile (56.02 and 52.65 as opposed to 52.45 at 250 respectively). The latter seems to have a greater dissociating power, since, in general, it has been shown that tetraalkylammonium salts are slightly associated both in acetonitrile (47) and methanol (66). Despite its high viscosity, therefore, adiponitrile should be a very useful solvent for the study of inorganic reactions. 102 RECOMMENDATIONS FOR FUTURE STUDIES Additional research which might be performed on 1,1,5,5-tetramethylguanidine could include: 1. 5. Determining A0 and values for a series of tetraalkylammonium sa 3 and in conjunction with this the determination of limiting ionic con- ductances. This could in turn reflect on the nature of solvation in TMG. Development of a more suitable proton sensitive electrode in TMG to be used in conjunction with a reference electrode of known behavior such as aqueous SCE. Formation of the lyate ion, TMG-, and as a result determining the autoprotolysis constant, KS. Spectrophotometric study of acid-base indicators in TMG alone or in conjunction with electrochemical studies. Polarography in TMG. In as much as adiponitrile is the first of the dinitriles to be studied, some of the following might be attempted: 1. 5. Conductance studies of a series of dinitriles such as malononitrile, glutaronitrile, and succinonitrile to determine A0 values and limiting ionic conductances. Potentiometric studies in ADN using some of the electrode systems already characterized for aceto- nitrile. Acid-base equilibrium studies by electrochemical or spectroscopic techniques. 105 1. 11. 12. 15. 14. REFERENCES (a) I. M. Kolthoff and S. Bruckenstein, J. Am. Chem. Soc., 18, 1 (1956). (b) I. M. Kolthoff and S. Bruckenstein, ibid., 18, 2974 (1956). R. J. Gillespie and E. A. Robinson in T. C. Waddington, Ed., Non-Aqueous Solvent Systems, Academic Press, New York, N. Y., 1965, Chapter 4. P. Walden, L. F. Audrieth and E. J. Birr, Z. Physik. Chem., A 160, 557 (1952). . W. A. Luder and C. A. Kraus, J. Am. Chem. Soc., 69, 2481 (1947). D. S. Burgess and C. A. Kraus, ibid., 70, 706 (1948). R. Gopal and M. M. Hussain, J. Indian Chem. Soc., 49, 981 (1965). C. A., 69, 11429h. M. L. Moss, J. S. Elliot, and R. T. Hall, Anal. Chem., g). 784 (1948). M. Katz and R. A. Glenn, ibid., 24, 1157 (1952). A. J. Martin, ibid., 29, 79 (1957). B. B. Hibbard and F. C. Schmidt, J. Am. Chem. Soc., 11, 225 (1955). J. Peacock, F. C. Schmidt, R. E. Davis, W. B. Schaap, ibid., 11, 5829 (1955). (a) L. M. Mukherjee and S. Bruckenstein, J. Phys. Chem., §_6_. 2228 (1962). (b) L. M. Mukherjee, S. Bruckenstein, and F. A. K. Badawi, ibid., 69, 2557 (1965). V. A. Pleskov and A. Monosson, Z. Physik. Chem., 56, 176 (1951). p G. W. Watt, J. L. Hall, and G. R. Choppin, J. Phys. Chem., .51. 567 (1955). 104 15. 16. 17. 18. 19. .20. 21. 22. 25. 24. 25. 26. 27. 28. 29. 50. 105 J. L. Hawes and R. L. Kay, J. Phys. Chem., _9, 2420 (1965). A. Berg, Compt. Rend., 1 6, 887 (1895). (a) T. R. Williams and J. Custer, Talanta, 9, 175 (1962). (b) T. R. Williams and M. Lautenschleger, ibid., 19, 804 (1965). M. L. Anderson, Ph. D. Thesis, Michigan State Univer- sity, East Lansing, Michigan, 1965. H. M. Randall, R. G. Fowler, N. Fuson, and J. R. Dangle, Infrared Determination of Organic Substances, D. van Nostrand Co., Inc., New York, 1949. S. J. Angyal and W. K. Warburton, J. Chem. Soc., 2492 (1951). M. L. Mukherjee, Ph. D. Thesis, University of Minnesota, Minneapolis, Minnesota, 1961, p. 4. R. Longhi and R. S. Drago, Inorg. Chem., 4, (1965). E. Oliveri-Mandala, Gazz. Chim. Ital., 44, II, 175 (1914). (a) T. S. Mihina and R. M. Herbst, J. Org. Chem., 15, 1082 (1950). (b) R. M. Herbst and K. R. Wilson, ibid., 22, 1142 (1957). (a) R. M. Fuoss and C. A. Kraus, J. Am. Chem. Soc., 55, 476 (1955). (b) R. M. Fuoss, ibid., _1, 488 (1955). T. Shedlovsky, J. Franklin Inst., 225, 759 (1958). D. A. MacInnes,, The Principles of Electrochemistry, Reinhold Publishing Co., New York, N. Y., 1959, Chapter 18. R. M. Fuoss and T. Shedlovsky, J. Am. Chem. Soc., 11, 1496 (1949). M. A. Coplan and R. M. Fuoss, J. Phys. Chem., 68, 1181 (1964). W. G. Finnegan, R. A. Henry, and R. Lofquist, J. Am. Chem. Soc., 89, 5908 (1958). 51. 52. 55. 54. 55. 56. 57. 58. 59. 40. 41. 42. 45. 44. 45. 46. 47. 48. 49. 106 F. R. Benson, Chem. Rev., 4;, 5 (1947). H. B. van der Heijde and E. A. M. F. Dahmen, Anal. Chim. Acta.,1§. 581 (1957). H. B. Thompson and M. T. Rogers, Rev. Sci. Instr., 51, 1079 (1956). H. M. Daggett, E. J. Bair, and C. A. Kraus, J. Am. Chem. Soc., 15J 799 (1951). G. Jones and D. M. Bollinger, ibid., 7 280 (1955). _' J. E. Lind, J. J. Zwolenik, and R. M. Fuoss, ibid., §1. 1557 (1959). J. W. Vaughn and P. G. Sears, J. Phys. Chem., 5;, 185 (1958). G. J. Janz and D. J. G. Ives, Reference Electrodes, _Academic Press Inc., New York, N. Y., 1961, Chapter 2. R. M. Fuoss, J. Am. Chem. Soc., 51, 2604 (1955). I. R. Bellobono and G. Favini, Ann. Chim. (Rome), .§§. 52 (1966). D. J. G. Ives and P. G. N. Musley, J. Chem. Soc., 757 (1966). A. I. Popov and N. E. Skelly, J. Am. Chem. Soc., 15, 5509 (1954). R. W. Taft, in M. S. Newman, Ed., Steric Effects in Organic Chemistry, John Wiley and Sons, Inc., New York, N. Y., 1956, Chapter 15. W. B. Person, W. C. Golton, and A. I. Popov, J. Am. Chem. Soc., 55, 891 (1965). M. L. Mukherjee, loc. cit., p. 71. R. E. Cuthrell, E. C. Fohn, and J. J. Lagowski, Inorg. Chem., 5, 111 (1966). D. F. Evans, C. Zawoyski, and R. L. Kay, J. Phys. Chem., £2. 5878 (1965). A. C. Harkness and H. M. Daggett, Jr., Can. J. Chem., éé, 1215 (1965). J. F. Coetzee and G. P. Cunningham, J. Am. Chem. Soc., ,él. 2529 (1965). 50. 51. 52. 55. 54. 55. 56. 57. 58. 59. 60. 61. 62. 65. 64. 65. 66. 67. 107 C. M. French and D. F. Muggleton, J. Chem. Soc., 2151 (1957). P. Walden and E. J. Birr, Z. Physik. Chem., 144A, 269 (1929). A. M. Brown and R. M. Fuoss, J. Phys. Chem., _4, 1541 (1960). C. M. French and I. G. Roe, Trans. Faraday Soc., 55, 514 (1955). G. J. Janz, A. E. Marcinkowsky and I. Ahmad, J. Elec- trochem. Soc., 112, 104 (1965). A. R. Martin, J. Chem. Soc., 550 (1950). P. Walden, Z. Physik. Chem., §g, 129 (1926); 55, 685 (1906). R. M. Fuoss and L. Onsager, J. Phys. Chem., 1, 668 (1957). J. F. Coetzee and G. R. Padmanabhan, ibid., 66, 1708 (1962). '“' A. L. Woodman, W. J. Murbach, and M. H. Kaufman, ibid., g4. 658 (1960). H. B. Thompson and S. L. Hanson, ibid., 1005 (1961). L. Onsager, Physik. Z., 21, 588 (1926). T. Shedlovsky, J. Am. Chem. Soc., 55, 1405 (1952). R. M. Fuoss and F. Accascina, Electrolytic Conductance, Interscience Publishers, Inc., New York, N. Y., 1959, p. 195. R. M. Fuoss, J. Am. Chem. Soc., 5;, 2659 (1959). R. M. Fuoss and F. Accascina, loc. cit., Chapters XV and XVII. R. L. Kay, C. Zawoyski, and D. F. Evans, J. Phys. Chem., 62. 4209 (1965). F. Daniels, J. W. Williams, P. Bender, R. A. Alberty and C. D. Cornwell, Experimental Physical Chemistry, McGraw- Hill Book Co., Inc., New York, N. Y., 1962, Chapter 18. APPENDICE S 108 APPENDIX I COMPUTER PROGRAMS A. General Introduction The numerical calculations given in this thesis were performed on a Control Data 5600 digital computer with the programs written in Fortran. Since this system is widely used and compatible with most modern computers, Fortran programs are listed below for evaluating both conductance and potentiometric data. For the conductance program the following data are read in: ID, which is the identification; ETA, which is the viscosity in poise; DIELEC, which is the dielectric constant; TEMP, which is the absolute temperature; ZERO, which is a first assumption to A0; IAM, which is an integer controlling the input with respect to accepting literature or laboratory data; N, the number of data sets read in; IAC, an integer which controls the extent to which the program is executed; RHO, which is the density in g./ml.; KONST, the cell constant; LSOLV, the specific conductance of the solvent; M2, the molecular weight of the solute; SOLV, which is the original weight of the solvent; RATIOl which is the g. solute/g. stock solution; RATIO2, which is the g. solvent/g. stock solution; R, which is the resistance 109 110 in ohms; WTSS, the weight of stock solution; IJ, which is END OF D always placed in column 21 of the last data card; LAMBDA, the equivalent conductance; and C, the molar concen- tration. It should be pointed out, however, that not all {of the above are read in for one data set. The read in [data are governed by the input of laboratory or literature data. Examination of the comment, C, and the READ state- ments will clarify this matter. The output consists of printing the values above plus A0 values as obtained by three methods, the overall acidity constants KS and KF as obtained by the Fuoss-Shedlovsky and by the Fuoss-Kraus methods, respectively, and the value of KHx obtained by the Ostwald dilution technique; X, which is the notation for CAssz ; Y, the symbol for 1/Asz; and YCALC,T,DEVIATION, which are parameters evaluated in the statistical section of the program concerned with the rejection of points. The other output data are clearly labeled and should be familiar to the conductance experimenter and are consistent with the notation used in the text above. The statistical routine is only incorporated with the Fuoss-Shedlovsky treatment. For the e.m.f. program the following data are read in: L, which is always the integer 1; Q, the value of E§.: ID, the identification; E, the e.m.f. value in volts; C, which is the molar concentration corresponding to a given E value; and IJ, which is END OF D always placed in column 21 of the 111 last data card. The output consists of printing the above plus K, the value for KHX; LOG K, which is -pKHx; ACTIVITY which is aH+; ARG, which is [(C -(1H+]; and LOG ARG, HX)t which is loglo of ARG. The other output parameters are clearly labeled such that there should be no ambiguity when referring to the text. 112 002200200 002.000 02020 20.00*u000002*20.02030*u3o0a02*203\.0.00*u 2002200020 a20>3 000 .02*20.0.00*u.2.2020.03.030*u>0o00*20.0.030*n00202*203\0022200 0 3u0 0 000022.300022.>0o0.02.>0000.00202.002020 203000822200 3 000002.300002.>000.02.>0o00.00202 .002.30202 000 000.00023 .00.2200 00 20000022200 300 020.2.200.300 0202 .20002000020 02020 0200 200200 020>000200 000 02 0002202200 00 2220020 000 2000 .3 u 000 00 .0000000200 02020020 00 2220020 020 2020 22200 00 020 00 0020 000 200 3 u 220 .2020 020 200 on 200 20.00*u<000 02200200 2000020*203\.0.00*u 003 002 02000200 200002o*203\.0.00*u 02000200 002002 00000*203\Va222o0 000 00.30.2.000 02020 AA0220*000000V00200*2000\00.00n00 20.3**A0200*000000vv\00000.0u30 20.3**20220*000000Vv\00000.3u< 20.00*u 020023 200200020.0.00*u .00200 0020000000020.0.00*n 0000oom0>0203\00022o0 000 0200.000000.200.000 02020 20.03000002200 000 o200.0220.000000.200.000 0002 000012 00 02000.00.00000 2020.200.3030022200 0 00.0 02020 20200022200 0 20.0 0202 03 -200 00020 000 0000 200002.200022.2000>00.200000 .200000202.200000200.200002020.20000002.2000>0o002.2000 0000033 .“0002.200020000.1000200200.20000.20002.20000 200020200 02.02. 00202.>0o00.20000.2.2.2002<0 0202 0009 >000020 2020020 0. Emumoum 00200026200 .m 0000 115 000030000 .OMWN ¢Qm2<fl mH OMMN madem<> Mme 0 92¢ ¢0m2<fl mo¢w mom M QZ¢ N mmmeHm EUHEZ mOOA Zmem 30.0303 .00.000v00 203.000*n 0003 Am*NOH\.¢.mm*H BOAm HEHmm OMEN ¢Qm2¢q 20mm OMMN ¢Qm20000u00020000v*.0003u00v000200 033 Abv0\ 00202u20020000 AA0000000030*m2v\200000002*000*.0003u00v0 >000+ 0000003*000000ufinv>00003 0000003*300002u000000003 0.3u0 033 00 003 03 00 000 3+0u0 03 03.00300 00 02000.00.00V00 00.030.¢.m30.203v002000 00 0000003.0000.00 02020 000.03000002200 0 00.0000002.0022.0 0000 03 .02 2*2N3\\*0000 00020 00 20020*200002000 00 00 02020 00.00*n 2000200*203 0002200 000 114 000000000 003.m3m*um&*Xw\VB0zmom m 2.0 02000 AAm**0200\0**00200*30*000v-202\.3vv\.3u2 AOH.mHh* H mM*Nm\v B00v00 000>00.0000.00000002.0002.00002000 . 0*.0afibv0u000>00 000000002u0002v0000n00v0 0+0002*2u00000002 0.3n0330 00 003.0300.2030002000 000 “\3 *200000>00 0 00002 2*203\V002000 000 000 02020 . AOH.¢HW*NH 02 00 .000 .000*203\.03.030*u 0200 000200 00 .000 .000*203\V002200 000 2000.0000.000 02020 AAN**ZV\AN**MmV*AN**mv*w+A¢**ZV\AN**000000 00 02 020 02000200 00002 020 00000 00 2 116 m* 020 02200\A0*2200u222000u0 020\0000u0 022200022000-02200*022000u0000 02200*22000u00*022000n020 2H0 0002*A0V2+ 22200u22200 0002.100 2+02200u02200 . 0002+2200u2200 02200+ 0002*00V2u02200 0002+2200u2200 2.3u0 30000 0.0u02200 0.0flMEDm 0.0n22200 0 002200 o.on2200 00002.00002 200020200 00.0.2.2.200000020 0200000000 020 3N OH. 06 3a2u2 3u2n0 20n2 03+0V000200u200000200 03t000n0000 0.0u0 300 00 0H0 203.030*u 02000 00000000*203\v002000 0002.300 02020 03 00 00 00.033 .00200 .0000 0002000020.0.000n 0200 000200 0002000*203\V002000 330 m0.0.HH> BZHmm Qm\m0flm0 mo\.3uo EU :Hm .OHN BZHmm 30m 3mm 3mm N3m Am.N3m*fl BmWUMMBZH QA 117 UmDGHuCOU 300.00003.00.0V00 0n020 02200\0002200u22200vu2 020\0000n0 222200022000:02200*022000u0000 A2200*22000102*022000"020 0n: 22200+000202002n22200 02200+000200002u02200 0002+2200u2200 02200+2002¢0002n02200 0002+2200u2200 0.3u0300 00 0.0u02200 0.0u2200 0.0u22200 0.0u02200 0.0u2200 000.0\0000000000u0002 0000u0002 0.3u0 000 00 00.030* n 0*203\V002000 0.0 02000 003 00 00 0 3+0u0 30.0000 00 02000.00.00v00 “00.03000002200 00.2000.00V0.0 0002 "0 000002 00 02000.00.00000 “000.200.3030002200 00.002020 0000.0.00.30V002200 00.0.0.3 0002 20000000000 0000 00002.00002.000V020 .000000.00000.00000.00000 200020200 32.2.020.2 0002 0020 0000020 2020000 8000000 .m.z.m .U 3ON COM COM mm 3N 0.0 3 303 118 020 000 00 00 «"0 20. 000. 20. m. 00. 20. m. 00. 20. 0. 000. 20. 00. N00. 2000002000 0 0000. 2000. 0002. 000000. 00000. 0 02000 00 mom.m\020000000000n2002 20000u0000u000000 .m\2212200 0*2* .0 + m**20000000u20000 0.0n0 mm 00 A\*.0200 00000 0 020 000 000 000 000>0000*200\\0002000 0 0 02000 20u0 20.000*n 0 000 00 .>00 .00m*200\0002000 00 00000.0002000 2000 + m**0mv00000*220:0200\m¢m¢.0u2000m N**HHOO.OHNOM A\.OH.¢HM*H BmNQMHBZH ho .>MQ .Q9m*xOH\.OH.¢HM*H Md 0000 00 .>00 .00m*xm.00.000*u 0 000200 0 00 .>00 .00m*x00\0002000 000 00.0m.m.000 02000 0000000000u00 Am**x200umx200*200\mx2sm*mmummm 2000000000u0m A020\m**x2000umx2amv\mmnm0m 200000000um 02.0u200\000000nmm 00000:A20\m**02000u00200n0 A20\m**x200|mx2000\00**220\0200*x200u0220000u00000 zu20 Am. mh*fl M 004*Kmd OH. mHh*l M*Nm m Ofim*fl9mm0mmEZH*Nm m. OHh*I mmOAm*xOH\\v demom h 2200. 0. 020. 2. 0 02000 A\\*020000 200000000 302*200\\\\0002000 m0 00 02000 00000.\20u0200u2200 000 00u2 000 000.00002*0000. .00.0000000 2210200000u0000 Ammmmo.\20-02000**.00u00 000 000 00 00 Ammmmo.\00102000**.00n0 000 APPENDIX II Derivation of the Equations for the Standard Deviations of Ag and £11K If the probable error is known for two independent variables x,y from which the function u is calculated, the probable error in u may be computed according to the technique illustrated by Daniels §£_§l. (67). That is —)2 P2 .+ (QB-)2 p; Iir 1. Pu = [(8x y X By x where Pu, Px, and Py represent the probable errors associ- ated with u, x, and y. Since . _ Pi ‘51 “ 0.6745 2' where di represents the standard deviation of any variable, i, Equation 1 may be written in terms of the standard devi— ations an, 6x, and dy associated with u, x, and y, respec— tively. X _ iv du [(SX: 6? + (g—uy): 6; 1 5. For the case where u is a function of only one vari- able, x, Equation 3 reduces to 119 120 du = %2_ 6x 4. x Since A0 = 1/b and the standard deviation, 6b, of the intercept, b, is known from least squares analysis,Equation 4 may be solved for the standard deviation, 6A0 associated with A0. d0=§§9 db 5. Differentiating A0 with respect to b yields dAo=-g§ s. or in statistical terms db 6A0 = .1; 32' 7. For calculating the standard deviation of KHX' dKHX’ where KHX = b2/m and 60, the standard deviation of the slope, m, and db are known Equation 5 becomes _ 3K . 2 5K 2 -§ 6Krm— [ ( Hx). . 62 + ( Hx) . 62 ] 8. 8m b m ob m b The following equation results after taking the indicated derivatives __ b4 2 .4132 2 é' dlfim=IinT5m+de 1 9- which may also be written as g 613m=i¢fi§dm2+fi§36b21§ 10. lffli‘rnm m": 082 70 llllfllllN/IJIIIIUH "Imi‘fiiifluflfll: