T HE U NI VE R SI TY O F MI C HI GA N COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Chemistry Technical Report No. 1 THE CONDUCTANCE OF SOME HIGH VALENCE TYPE ELECTROLYTES CalVin J. ~~lada Go'rdon At ns~r OAProject 03637 under contract with: U. S. ARMY RESEARCH OFFICE (DURHAM) CONTRACT NO. DA 20-018-ORD-22375 PROJECT-~NO. 235-5C DURHAM., NORTH CAROLINA.administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARDOR February 1961

In the interpretation of ultrasonic velocity and absorption measurements in equilibrium chemical systems it is desirable to know other thermodynamic parameters of the systems as accurately as possible. Our work on ultrasonic measurements in solutions of electrolytes demands that We know the association constants of these electrolytes in the solvent systems of interest as well as any other parameters obtainable. Therefore, Mr. liallada kindly consented to measure these association constants by preci sion conductance techniques and apply the extended Fuoss-Onsager theory to the results. This resulted in the following technical report. We would like to acknowledge support for the conductance work from the National Science Foundation and the Horace Rackham School of Graduate Studies. Dr. Gor'don Atkinson, Project Supervisor Dr. Daisaku Tabuchi Mr. Robert L. Jones Mr. Calvin J. Hallada Ann Arbor, Michigan February, 1961

TABLE-OF CONTENTS.Page ACKNOWLEDGEMENTS.. i LIST OF TABLES..i LIST OF FIGURES....vi LIST OF APPENDICES...vii INTRODUCTION...1 STATEMENT OF THE PROBLEM..0 00.. 00 8 EXPERIMENTAL...10 Preparation of Acids and Salts..0 00010 m-Benzenedisulfonic Acid and m-Benzenedisulfonate Salts. 10 1,5, 6-Naphthalenetrisulfonic Acid and l.,3,6-Naphthalenetrisulfonate Salts.1 Analyses of Acids and Salts.1 Preparation of Solvents...- — o14.Water.. —-. oooo14.Methanol..00- 0*l. b14 Conductance Measurements..0015 General Equipment..o o15 Cells.. 15 Preparation of Solutions..16 RESULTS.... a..1 8 Treaatmrint..of Raw: Data *..1 8 Apt~I ~li -.AtJ, io-,-ncofT)Data 1toJnheory..15

Page

LIST OF TABLES Table Page I. Equivalent Conductance, Concentration Data m-Benzenedisulfonic Acid and m-Benzenedisulfonate Salts in'Water.25;II. Equivalent Conductance, Concentration Data l,3j,6-Naphthalenetrisulfonic Acid and l.,3,6-Naphthalenetrisulfonate Salts in Water. 27 III. Equivalent Conductance., Concentration-Data Copper Sulfate and Manganese Sulfate in Water. 29 IV. Equivalent Conductance, Concentration Data Manganese m-Benzenedisulfonate in MethanolWater.15.0& 00f 0 6 0 3 V. Equivalent Conductance., Concentration Data Manganese Sulfate in Methanol-Water.152 VI. The Crossover Parameters.42 VII. Experimental Parameters rn-Benz enedi sulfonic Acid, rn-Benz enedisul fonate Salts and Copper Sulfate in Water.43~ VIII. Experimental Parameters l,35,6-Naphthalenetrisulfonic Acid and l,5.,6-Naphthalenetrisulfonate Salts in Water. 45 IX. Experimental Parameters

LIST OF FIGURES Figure Page I. -Phoreograms of m-Benzenedisulfonic Acid and Sulfuric Acid..00 *...la 15)] 3 2. Phoreograms of Sodium m-Benzenedisulfonate, Potassium m-Benzenedisulfonate and Sodium Sulfate... *.0. 0..0.. I Is. 0 355 15. Fuoss'Plots of Sodium m-Benzenedisulfonate and Potassium m-Benzenedisulfonate.... Is 157 4-. -Phoreograms of Copper m-Benzenedisulfonate and Copper Sulfate..0I 00I l aI.... 158 5. Fuoss Plots of Copper m-Benzenedisulfonate and ~Copper Sulfate.... 6 000 159 6.Fuoss Plots of Sodium,15,6,-Naphthalenetrisulfonate and Potassium l.,3,6-Naphthalenetrisulfonate 0000 9 0ID 0 *0 l @' ID. 4-6 7. Phoreogram of Lanthanum l,35,6-Naphthalenetrisulfonate..***4-7 8. Fuoss Plot of Lanthanum l,35,6-Naphthalenetrisulf onate...... - e l ID....0.. 4-8 9. Phoreograms of Manganese m-Benzenedisulfonate and Mangan e se Sulf a t e.......0..0....09 5 2 10. Fuoss:Plot of Manganese m-Benzenedisulfonate..515 11. Phore~ograms of Manganese m-Benzenedisulfonate in Methanol-Water Systems..... 55 12. The Association Constants of Manganese m-IBenzenedisulfonate and Manganese Sulfate as a Function of Dielectric Constant.... 60

LIST OF APPENDICES Appendix Page I. Definition of Terms in the Limiting-Law and Extended Law Equations for'Unassociated Electrolytes.67 II. Viscosity and Dielectric Data for -.Me'thanol-Water Systems. *0a 9*0 71 III. Calculated Values for the Conductance,Equation Terms of the Systems Studied... 72

INTRODUCTION In electrolyte solutions, the interactions usually incorporated into theoretical models and experimental interpretations are of three categories: long range ionLion, short range ion-ion, and short range ion-solvent. The first type has been extensively studied and is described by the Debye-Hfckel theory (1) set forth in 1923. For unassociated 1:1 electrolytes in dilute solutions, this theory and experimental data are in excellent agreement. Differences however, between measured activity coefficients and those calculated from the Debye-HiUckel theory for some strong electrolytes led N. Bjerrum in 1926 to propose a model for short range ion-ion interaction (2). Since his proposal, many other attempts have been made to describe ion-ion association (3,4,5); however, none of these theories has been entirely satisfactory. To help clarify ion-ion association and, at the same time, extend the validity of long range ion-ion interaction beyond the Debye-Hackel theory, short range ion-solvent interaction must be considered.

2 An interesting approach to the study of ionsolvent interaction was made in 1953 and 1954 by J. Bjerrum and C. K. Jorgensen (6,7) when they applied the J. Bjerrum method of treating step-wise complexation (8) to the aquo-ion formation of several first row transition metal ions in solution. Their objective was to determine the successive formation constants, kl through kN, involved in the presumed selective solvation of the cation by water over an organic solvent (methanol). The method employs ultraviolet and visible spectral shifts obtained when the solvent composition is changed at constant ion concentration. The major objections to their work are: (1) they assumed a value for N (the maximum number of waters coordinated by the cation), although this is unnecessary if the treatment is valid and a sufficiently extensive range of solvent mixtures is used, (2) they disregarded any anion-solvent interaction and any ion-ion association; the latter, even while the bulk dielectric constant of the solvent (and thus the coulombic force) was continuously being varied (9). Following J. Bjerrum and C. K. Jorgensen, this investigator, employing spectral shifts, attempted to determine rather than assume N. Again, first row transition metal ions were used, but now in a salt with a very large anion: p-toluenesulfonate (to be abbreviated PTS-) as opposed to the previously used C1

and NOs3 anions. The thought was that a larger anion, with its consequent smaller charge density, would possibly relegate ion-ion association and anion-solvent interaction to such minor roles that they could be ignored. If treatment of the spectral data from such salts in mixed solvents proved a valid method of determining N, then the same treatment could be used on data from other physical measurements (such as nuclear magnetic resonance and vapor pressure) so that N could be found by several independent methods. However, this work did not give the sought-after indication of an abrupt completion of a step-wise aquation process, even when the experiments were carried out over the entire range of solvent mixtures from pure water to pure methanol, at constant ion concentration. That no N was reached can be explained in two ways: either the cation exhibited no selectivity towards water over the organic solvent or, ion-ion association was still taking place in the changing dielectric media to such an extent that it could not be ignored. From electrostatic considerations, the fact that water has a larger dipole than methanol would lead to the belief that the cation should show a greater selectivity towards water over methanol. It is apparent then, that one must return to the problem of ion-ion association before any conclusions are to be drawn about the interaction of ion and solvent from the mixed

solvent method. Association constants have been determined in an attempt to clarify the problem of ion association. However, except for those electrolytes known to be completely unassociated (such as KC1) and those highly associated (such as the covalently bonded carboxylic acids), the meaning of these association constants has been vague. This ambiguity has arisen from the fact that for a given electrolyte, widely divergent values for its association constant have been obtained. Not only from varying physical measurements are there found different values for an association constant of a particular electrolyte, but even from one technique can such a result occur. In 1938, Owen and Gurry (10) demonstrated that from conductance measurements on CuS04 and ZnS04, several association constants for each salt could be found simply by varying the technique of curve fitting. As late as 1957, Prue and his associates (11,12) showed that spectrophotometric data on CuS04 could be so manipulated that the dissociation constant for this electrolyte could be given any value from 8.0 x 10-3 to 3.5 x 10-3 from the same set of experimental results. Differences for the association constant of a given electrolyte obtained from varying experimental techniques may be attributed to the inherent differences in the techniques themselves. However, when such

5 differences occur even by the use of a single technique, the problem is much more acute. Taking a unique attitude, Guggenheim (13) in 1957, went so far as to question whether an electrolyte like CuS04 was even associated at all. Others have instead tried to fit experimental data on associated electrolytes to the numerous theories by the method of simply adding empirical terms to the theoretical equations to accommodate the behavior of each electrolyte, thus making every electrolyte a separate case, practically unrelated to any other electrolyte (14). It is this investigator's feeling that the farreaching dilemma existent in the study of ion association must be due to a lack of a suitable baseline. That is, one must know unambiguously, either theoretically or experimentally, how a given associated electrolyte would behave if it were not associated. Only then can an association constant have some meaning. Without the use of any unreasonable parameters, the Onsager-Fuoss conductance theory (15,16,17) agrees with conductance data for the entire range of 1:1 electrolytes, from the completely unassociated, through the weakly associated, to the highly associated. This theory, which is an extension of the Onsager limiting law (18), describes the behavior of unassociated and of pair-wise associated electrolytes by the following equations for equivalent conductance:

6 Unassociated: = A~ - S c1/2 + E c log c + J c Associated: A A= a(JAo -S (ca)l/2 + E ca log ca + J ca) where J_ = equivalent conductance, ohm-1 cm2 equivalent1 A~ = equivalent conductance at infinite dilution, ohm-lcm2 equivalent-1 S = the Onsaager limiting law slope; a function of JA~, temperature, dielectric constant and viscosity of the solvent, the valence type of the solute, and universal constants c = molarity; ca = molarity of the ions E = a constant defined by the same variables as S; it is a term resulting from the mathematical extension of the Onsager limiting law J = a constant defined by the same variables as S and E, and also the closest distance of approach Q of the ions, a; it results from both mathematical extensions of the Onsager limiting law and the inclusion of the size parameter (1-a) = the fraction of ions pair-wise associated. (For a more complete definition of terms, see Appendix I) Although the mathematical treatment employed in reaching the final equations from the assumed model is very complex, the agreement of the theory with data on 1:1 electrolytes is excellent. This fact leads to the belief that the theory might also apply to higher valence type

7 electrolytes, even if in more dilute solutions (so that the mathematical approximations are not exceeded)

STATEMENT OF THE PROBLEM Because of the success of the Onsager-Fuoss theory on 1:1 electrolytes, conductance measurements were proposed to study the association of higher valence type electrolytes. The determined association constants for these species would then have some consistency since the Onsager-Fuoss model would describe how associated ions would behave if they were unassociated. Most electrolyte solution theories are more valid for symmetrical electrolytes because of the form of the distribution function used in their derivations. Therefore, this type of electrolyte was chosen for the association studies. Although there has not been found any symmetrical unassociated electrolyte of higher charge type than 1:1, the ideal complement to the determination of association constants for these electrolytes would be the discovery of a completely unassociated higher charged electrolyte. Such a fortunate discovery would lead the way for the use of different physical measurements (on the unassociated electrolyte) to test the validity of other theories beyond. the simple case of the 11. It was felt that the best possibility for obtaining

9 an electrolyte which might be unassociated in water would be to select a salt containing the large anion of a strong acid. Because m-benzenedisulfonic acid (to be abbreviated H2BDS) is a well-known strong acid, and because the charge on the m-benzenedisulfonate ion (BDS-) is spread over a large framework, CuBDS was prepared. If the comparison of the conductance data of a salt such as CuBDS (in water) to its limiting law indicated that it might be unassociated, an attempt to fit its data to the extended theory equation could be made. Furthermore, the study of the conductance of this electrolyte could be carried to mixed solvents where higher association would be forced. It would then be possible to determine whether the Onsager-Fuoss theory could handle the transition smoothly. In conjunction with this, the conductance of another salt, like CuS04, could be studied to see if it and CuBDS showed consistent behavior in the mixed solvents. Also, if the BDS salt was found to be unassociated, it would be interesting to see if an unassociated 3:3 sulfonate salt could be found.

EXPERIMENTAL Preparation of Acids and Salts m-Benzenedisulfonic Acid and m-Benzenedisulfonate Salts Two methods of purification were used on the crude commercial H2BDS (Matheson, Coleman and Bell, Norwood, Ohio, Item T-1164) which contains a large H2S04 impurity. In the first method, Ca(OH)2 was neutralized with the acid (H2BDS) to form the soluble salt CaBDS and thus remove the large S04- impurity. Since the CaBDS was very difficultly recrystallized, it was converted to K2BDS by use of K2C03. The K2BDS was recrystallized twice from water. Part of this purified K2BDS was reconverted to H2BDS by passing it through a column containing cation exchange resin in the acid form. The cation exchange resin used throughout the experimental work was Dowex 50. Next, a portion of this acid was used to prepare CuBDS and Na2BDS by reaction with CuC03 and NaOH respectively. The final salts (K2BDS, CuBDS and Na2BDS) were recrystallized twice from conductivity water and dried over CaCl2 at room temperature. The second method adopted was much less tedious. The crude H2BDS was reacted with Ba(OH)2 to remove the S04 impurity. The resulting BaBDS was recrystallized and then 10

11 converted to the acid using a cation exchange resin. 1,3,6-Naphthalenetrisulfonic Acid and 1,3,6-Naphthalenetrisulfonate Salts Sodium 1,3,6-naphthalenetrisulfonate (Na3NTS) is available commercially (Aldrich Chemical Co., Milwaukee 10, Wisconsin) and, like the crude H2BDS, contains S04 as its major impurity. In this case, the Na+ salt was converted to the acid by ion exchange. The acid was then reacted with La203. The resulting LaNTS, with La2(S04)3 impurity, was recrystallized twice from hot water. The much lower solubility of La2(S04)3 (over LaNTS) and its retrograde temperature dependence allowed a good separation. This LaNTS was used, in part, to prepare the acid, Na+ and K+ salts by ion exchange. These salts were recrystallized from conductivity water and dried over CaC12 at room temperature. Analyses of Acids and Salts None of the purified BDS and NTS salts and acids showed any traces of S04 when tested with Ba(NO3)2. A check of the isomer purity of the m-benzenedisulfonate anion was made by converting a sample of the anhydrous K+ salt to the sulfonyl chloride by use of PC15. The product obtained was recrystallized from petroleum ether. Since the para isomer has a sulfonyl chloride which is much less soluble than either the ortho or meta isomer, its presence could be noted during recrystallization. The product obtained was free of this para isomer. The melting

12 point of the sulfonyl chloride was found to be 62~C; the literature value of the meta product is 63~C and that of the ortho is 1320C (19). Analyses for total cation content in the salts were performed by quantitative conversion to the acids (H2BDS and H3NTS) by ion exchange technique and subsequent titrations of the acids with standard NaOH, using a Beckman GS pH meter. Both H2BDS and H3NTS are strong acids giving single endpoints. A check of the accuracy of the method, using analytical grade KC1, showed no systematic errors. The precision of the total cation measurements was + 0.1 %. To ensure that the total cation was Cu++ in CuBDS, K+ in K2BDS, Mn++ in MnBDS, and La+++ in LaNTS, separate determinations of these ions were performed. Copper was determined by electrodeposition, while the K+ content of the K2BDS salt was found by using the sodium tetraphenyl boron technique. The pyrophosphate method was employed in the Mn++ determination. Lanthanum was analyzed by precipitation as the oxalate and ignition to the oxide. For all the salts but CuBDS, water of hydration was determined by the Karl Fischer method, using a Pt-W electrode pair and a potentiometer for endpoint detection (20). Because the Cu++ ion reacts with the Karl Fischer reagent, its water of hydration was determined by heating the hydrated salt to 1400C. The weight loss agreed with the reported (21) change from a six hydrate to a one hydrate. Both acids were extremely difficult to obtain in a

13 good weighing form by recrystallization; they were therefore, not analyzed from solid samples. In the actual conductance work, concentrated solutions were used to make up stock solutions which were then analyzed for acid strength. The Na+ and K+ salts of NTS are hygroscopic and difficulty was again encountered in attempting any weighing of the solid forms. Therefore, as with the acid, the stock solutions used were analyzed: first by ion exchange to the acid, followed by titration with standard NaOH. The copper, potassium, manganese and lanthanum analyses agreed with their respective total cation determinations within two parts per thousand. The precision of the Karl Fischer analyses was less than 2% in all cases. Total content was based on the fact that each salt or acid contained the proper anion (BDS= or NTS ). The error in total content ranged from as low as 0.2% to a maximum of 0.5% for each substance, the magnitude of the error being dependent on the precision of the Karl Fischer analysis for the particular substance. Both the MnSO4 and the CuS04 were Baker and Adamson reagent grade, recrystallized twice from conductivity water and dried at 1100C to their monohydrates. The weighing forms of the salts (on which analyses were possible) were, upon drying over CaCl2 at room temperature: Na2BDS'4H20, K2BDS'H20, CuBDSE6H20, MnBDS'3-1/2H20, LaNTS 5-1/2H20.

14 Preparation of Solvents Water The conductivity water was prepared by redistilling distilled water from permanganate (block-tin condenser). This gave water with a specific conductance from 1.0 x 10 -6 -l -1 to 1.5 x 10 ohm cm. The water was then passed through a Barnstead Bantam demineralizing column which gave water with a final specific conductance of about 0.7 x 10O6 -1 -l ohm cm at 25~C. Methanol The starting methanol was Baker analyzed reagent whose main impurities are about 0.1% H20 and lesser amounts of aldehydes and ketones. The test for aldehydes and ketones outlined by Hartley and Raikes (22) using Hg(CN)2 in strong base, which is reportedly sensitive to 0.002% ketones and 0.004% aldehydes, was employed on the solvent. The test proved negative for the Baker reagent. The H20 was eliminated by refluxing over Mg for an hour and fractionating, the center cut of about 60-70% being taken. At first, the methanol thus obtained was stored over molecular sieves. However, the conductance of the methanol was considerably higher than could be tolerated for a conductance solvent. When the methanol was not stored over molecular sieves, the measured conductance was suitable for a conductance solvent. Therefore, the purified methanol was not stored over molecular sieves. The physical properties of the purified solvent as compared with

15 literature values were: Experimental Literature (23) Boiling Point 64.5 - 64.70C at 743mm 64.70C at 760mm Density 0.7876 g/ml 0.7872 g/ml Conductance Measurements General Equipment The bridge arrangement for the resistance measurements consisted of a General Radio 1301A variable frequency oscillator, a Leeds and Northrup Jones Bridge, a Fisher TR-1 battery-powered preamplifier and a DuMont 304H oscilloscope for null detection. A large (approximately 18 gallon) fish tank filled with transformer oil served as the constant temperature bath. The thermoregulator used was a differential range type made by the Precision Scientific Company. This thermoregulator was connected through a thyratron relay to a heating lamp outside the bath. Cooling was accomplished by several turns of copper wire through which tap water was run. By these means, the bath gave a constant temperature of 25.000 ~ 0.0050C. The bridge and bath were placed on a large copper sheet to obtain adequate grounding. The oscillator, bridge and preamplifier were set up as specified by Dike (24). Cells Two flask type cells were used for the conductance measurements, that is, erlenmeyer flasks with the electrodes contained in a side arm. The electrodes were made of smooth

platinum and were so spaced to give cell constants of about -1 0.10 and 0.25 cm. These two cells were calibrated with KC1 solutions using the Fuoss equation for KC1 (25): A = 149.93 - 94.65 c1/2 + 58.74 c log c + 198.4 c where c is the molar concentration of KC1. The cell constants were determined as functions of the measured specific conductance (26) and were: Cell 1: k = (0.26390 - 0.45 Lm) cm 1 Cell 2: k = (0.08808 - 0.04 Lm) cm where Lm is the measured specific conductance. Preparation of Solutions The solutions whose resistances were measured were made up in the conductance cell by a weight dilution method. Conductivity water was weighed into the cell and allowed to come to equilibrium (indicated by a constant resistance reading). Four to seven successive weighed amounts of stock solution were added, each time allowing the solution to equilibrate. The resistance was measured at 1000, 2000, 4000 and 10,000 cycles/sec, and a plot of resistance versus 1/ 2 (f = frequency in cycles/sec) extrapolated to infinite frequency (27) gave the resistance at infinite frequency, Roo. The weight dilution method has the advantage that resistance measurements at several concentrations can be made in a relatively short period of time. Also, the correction for solvent conductance is for that specific

17 batch of solvent on that day and not just the average correction for several batches. This is especially significant in the very dilute solutions where the solvent contributes a considerable part of the measured resistance. Each stock solution was run in both cells at least once; at least two different stock solutions were used for each electrolyte-solvent system. When possible, the stock solutions were made up by weight: when the solute had a definite weighing form or, in the case of the mixed solvent work, when the solute could be dried to not higher than a one hydrate. The latter corresponds to only about 0.001% change in the percentage of water in the solvent used, so that no correction would then be necessary for the percentage of water in the mixed solvent. Those materials (H2BDS, H3NTS, Na3NTS and K3NTS in water, and MnBDS in mixed solvent) whose stock solutions could not be made up by weight, were analyzed for concentration by titration with standard NaOH; the salt solutions were first converted to the acid by the ion exchange technique. The density of each stock solution and each mixed solvent was measured in a pycnometer, giving results to ~ 5 x 10-5 g/ml at 250~Co

RESULTS Treatment of Raw Data The measured resistances and solution concentrations are treated to obtain sets of equivalent conductance, concentration (A, c) data. In using the weight dilution technique, it is assumed that the volume of the solution is simply.the sum of the volume of the solvent used and the volume of the stock solution addedV =V + v solution solvent stock solution (1) The concentration (in moles/l) of the stock solution is obtained: in the case of the salts with known weighing form, by use of molality and density; for the other, by titration of the acid form with standard NaOH. The weights of solvent and stock solution introduced into the conductance cell, along with their densities, readily give the volumes of these solutions. Thus, the concentration of the solution whose resistance is measured is calculated: c =mCstock(moles/1) X Vstock(ml). (2) Csolution(moles/l) Vsolution(ml) As successive weighed amounts of stock solution are added to the cell, the resistance of each of a series of 18

19 solutions can be measured. It is evident then, that the weight dilution method greatly facilitates obtaining an entire set of resistances and concentrations. As mentioned previously (see page 16), the resistances measured are extrapolated to give the resistance at infinite frequency, Ro. Since the specific conductance L, is given by: L ell (3) Roo where kcell is the cell constant, a simple calculation converts the resistances of the solvent and the solution to their specific conductances. Then, the specific conductance of the solute is: Lsolute - Lsolution solvent~ (4) The equivalent conductance of the solute is calculated from Lsolute and the normality of the solution (N): J- -1000 solute solute (5) When there are no other effects which could change the values of L or c, a set of A, c data is thus found, However, solutes containing one or more substances which hydrolyze, force a reconsideration of Lsolute and csolution~ The A c data needed must apply to the solute existing as such, that is, exclusive of any hydrolysis products. Comparison of the conductances of H2BDS and H3NTS with the Onsager-Fuoss extended law indicates these acids are completely dissociated in water. Therefore, for the

20 BDS- and NTS ions, hydrolysis need not be considered. But hydrolysis must be considered for the Cu++ Mn++, La++and S04 ions, and the C02 absorbed from the air. The Cu*, Mn+~ and La++ hydrolysis constants were obtained by measuring the pH of solutions of their salts (CuBDS, MnBDS, LaNTS). The solutions on which pH measurements were made, corresponded to the solutions used in resistance measurements, that is, a series of solutions of a given salt were made up by the weight dilution method and the pH of each solution was read with a Beckman GS pH meter. The [H+] of the solvent is assumed to be due entirely to the C02-H20 equilibrium. Since the amount of stock solution used in all cases is small (dilute solutions), no [H+] contribution from a C02-H20 equilibrium is designated to the stock solution. It is also assumed that the C02 content of the solvent does not change during the addition of the solute. This last assumption was checked by following the conductance of the solvent for a day while periodically opening the cell cap. The change in conductance was negligible. The hydrolysis constants thus found (Cu++ = 1.5 x 10-8, Mn++ 2.5 x 1011 La+++ - 1.2 x 109) were in good agreement with the literature (28,29,30). The hydrolysis constant used for S04 was 8.3 x 10 11 (31) and the dissociation constant used for H2C03 was 4.3 x 10-7 (32). An outline of a typidaL~calculation using CuBDS will indicate the method for correcting Csolution and Lsolute.

21 The concentration of the solution, given in equation (2) must be corrected for the moles of solute hydrolyzed, that is, the amount of CuOH+ present must be subtracted. The interdependent equilibria involved in the dissociation of H2C03 and the hydrolysis of Cu++, along with the conditions: [HC03-] + [H2C03] = total hydrolyzed C02 (6) and [HC03-] + [CuOH+] = [H+] solution (7) must be simultaneously satisfied in the determination of the amount of CuOH+ present. The technique of obtaining this correction was to pick values for [H+]solution to be used in the dissociation expression for H2C03 and the hydrolysis expression for Cu++ until the final conditions, given by equations (6) and (7) were satisfied. This is a very tedious, but valid process of calculation which not only gives [CuOH+] needed for correction to csolution, but also [H+] and [HC03 ] needed for the corrections to Lsolute' The specific conductances of the ions H+ and HCO3 and whatever residual species are present, make up the measured Lsolvent: Lsolvent = LH+ + LHC03- + Lresidual (8) where Lresidual is the specific conductance of any impurities other than C02 in the solvent, plus the specific conductance of the solvent itself. But when solute is added to the solvent, the specific

22 conductances of the CuOH+ present and an amount of BDS equal to the amount of Cu++ ions removed by hydrolysis, as well as the specific conductances of Lresidual and of the changed concentrations of HC03- and H+ (as found in the Csolution correction), now totally constitute the specific conductances to be accounted for in calculating Lsolute. Equation (4) now must be changed to read: Lsolute Lsolution - Ls (9) where Ls LH+ + LHC03- + Lresidual + LCuH+ + LBDS= (10) The evaluation of L5 involves the calculations of L for each ion and Lresidual For each of the ions: 7 N. L.. ion ion 1000 or, since the corrections are so small: O~ N L ~ ion ion 10011) where A is the equivalent ionic conductance and?A is the limiting equivalent ionic conductance. To obtain Lresidual' the resistance of the solvent is measured and Lsolvent calculated. The [H+] in the solvent is determined by pH measurements before each run. Since the [H+] is assumed to be due solely to the C02-H20 equilibrium, [HI+] = [HC03 ], and LH C0 can be found:

LH2CO = LH+ + LHCO0+[H+] + 0H03-[HC03-] H2C03 1000 ( H*+ AHC3) [H+] H2C03 1000 LHCO -/H~2CO3 EH (12) LH2aC 3 -1000 Rearranging equation (8): Lresidual = Lsolvent LH2C03 (13) and the value for Lresidual is obtained. Thus, having the corrected Lsolute and the corrected csolution, the equivalent conductance of the solute may now be calculated. One finally obtains a set of A, c data for the CuBDS present as such, exclusive of hydrolysis products0 The corrections for hydrolysis, although tedious, were indeed necessary: for CuBDS, the correction to Ai ranged from 0.8% at 10-4 M to 0.2% at 5 x 10-3 M, and for LaNTS, from 0.1% at 5 x 10-5 M to 0.06% at 2 x 10-3 Mo Although the corrections for LaNTS are near the limit of the over-all precision of the A. results for this substance (0.1%), the corrections were made. However, the S04 and Mn++ hydrolysis corrections to A- are <0.03% at the lowest concentrations. This is well below the over-all reproducibility of the measurements on these substances, and

24 therefore no hydrolysis corrections were warranted for these ions. For H2BDS and H3NTS, no solvent corrections were made since the major conducting species in the solvent are from the dissociation of H2C03; this dissociation is suppressed by the addition of strong acid. It may be noted here that in all solutions, whether hydrolysis corrections were applied or not, data for which Ls >3 Lsolution were dropped for all calculations. This is a rather arbitrary cut-off point, but those solutions in which Lo>3% Lsolution were also the least concentrated solutions, the precision of whose t data is quite poor. Tables showing the sets of t, c data for H2BDS and the BDS= salts (Table I), H3NTS and the NTS salts (Table II), MnSO4 and CuS04 (Table III) in water are now presented, followed by the mixed solventJA., c data for MnBDS (Table IV) and MnSO4 (Table V).

TABLE I Equivalent Conductance, Concentration Data m-Benzenedisulfonic Acid and m-Benzenedisulfonate Salts in Water H2BDS 104c (moles/liter) 0o 746 408.5 2.438 405.6 5.372 402.1 12.007 397.7 18.576 394.8 25.890 392.1 37?558 388.6 Na2BDS K2BDS 104c 10 c J (moles/liter) (moles/liter) 1.3672 106,90 0.7512 131o 33 3.6213 105o 25 1.5726 130.25 5.4140 104.27 2.4585 129.53 7.2115 103.o 27 4.3921 128.12 10.304 102.52 8.2340 126.32 14.455 101.36 12.881 124.68 18.072 100.39 20. 344 122.69 23. 788 99. 36 31o 483 120 54 32.127 98.03 46.236 118o 39 46.720 96 10 59,180 116o 68

26 TABLE I (continued) CuBDS MnBDS 104oc 104c A\ (moles/liter) (moles/liter) 0.9035 109.57 1.6202 107.02 1.4132 108.73 3. 0881 104.39 1.8535 107.74 4.5834 102.71 4.6921 103.40 7.2762 100.12 5.6935 102.05 8.7987 99.03 7.2820 100.61 15.667 95.04 13.158 97.15 17.335 94.35 17.489 95.63 30.710 89.82 21.650 92.99 50.255a 85.66 26.781 91.80 31. 177 90.31 43. 553a 87.75 54. 560a 85.89 66.830a 84.09 aFor completeness of data, these points are included. However, the validity of applying theoretical calculations to them is questionable since, at these concentrations, a>)0.2 (see Appendix I).

27 TABLE II Equivalent Conductance, Concentration Data 1,3,6-Naphthalenetrisulfonic Acid and 1,35, 6-Naphthalenetrisulfonate Salts in Water H3NTS LaNTS 104c J\_ 104c A. (moles/liter) (moles/liter) 0.928 413.6 0.5202 118o39 4.263 405.8.o0450 109 70 5.283 403.6 1.8211 101.23 9.151 398.9 3.5221 90.65 10.528 397.1 5.0143 84.90 17.069 392.0 6.7760 80. 30 24.722a 386 8 l0.453 73.61 28.064a 385.4 14.037a 69.65 21o 088a 64.40 32.455a 59.65 aFor completeness of data, these points are included. However, the validity of applying theoretical calculations t8 them is questionable since, at these concentrations, Ka>0.2 (see Appendix I).

28 TABLE II (continued) Na3NTS K3NTS 104c 104c (moles/liter) (moles/liter) 1.0199 116.63 1.0574 139.96 1.7592 115.38 5.2771 134.39 4.4823 112.13 9.4206 131.27 5.8743 110.97 15.021 128.19 9.4072 108.54 24.905a 124.36 11.449 107.45 34.682a 121.63 18.365 104.51 40.437a 120.36 23.983a 102.69 a 27.905a 101.53 31.847a 100.62 aFor completeness of data, these points are included. However, the validity of applying theoretical calculations ts them is questionable since, at these concentrations, 1%a>0.2 (see Appendix I).

29 TABLE III Equivalent Conductance, Concentration Data Copper Sulfate and Manganese Sulfate in Water CuS04 MnSO04 104c 104c (moles/liter) (moles/liter) 4.0000a 117.52 2.0134 122.84 9.0000a 108.55 2.6134 121.39 16.000a 100.74 3.2881 119.89 25.000a 94.07 3. 9939 118.01 36.000a'b 88.35 5.0626 115.98 1.7554 123.73 7.6176 111.81 2.5373 119.43 8.9728 109.94 4.8951 115.59 13.945 104.54 12.618 103.84 19.570 100.00 22.449 95.65 23.732 97.14 28.273 92.70 28.230 94.56 31.411 93.02 aValues from Owen and Gurry (10). For completeness of data, these points are included. However, the validity of applying theoretical calculations to them is questionable since, at these concentrations, /Ka>0.2 (see Appendix I).

30 TABLE IV Equivalent Conductance, Concentration Data Manganese m-Benzenedisulfonate in Methanol-Water 100% Methanol 80% Methanol (weight %) (weight %) 104c 104c (moles/liter) (moles/liter) 2.4312 27.89 1.8569 56.49 7.3039 19.95 2.4658 53.89 9.1328 18.36 3.1599 51.55 131.162 16.09 4.9331 47.21 17.249a 14.62 7.8202 42.63 23.867a 13.08 15.397 36.33 19.477a 34.30 22.646a 33.03 60% Methanol 40% Methanol (weight %) (weight %) 104c J 104c (moles/liter) (moles/liter) 1.4611 55.78 1.6284 55.73 5.4190 48.27 5.9389 51.04 7.4454 46.95 13.119 47.07 12.403 42.74 17.769 45.39 18.031 40.15 22.640 44.00 23.729a 38.27 27.530a 42.88 28.084a 37.13 j 32.809a 41.87 39I. 418a 40.80 aFor completeness of data, these points are included. However, the validity-of applying theoretical calculatigns to them is questionable since, at these concentrations, )a>0O.2 (see Appendix I).

31 TABLE IV (continued) 30% Methanol (weight %) 4 4 10 c (moles/liter) 2.0449 58.48 5.0302 55.71 9.1027 53.14 14.352 50.89 18.989 49.40 24.685a 47.95 20% Methanol 10% Methanol (weight %) (weight %) 104c Jv 104c A (moles/liter) (moles/liter) 1.2249 67.96 1.7387 82.85 2.9912 65.58 4.5360 79.45 6.7493 62.52 10.182 75.51 10.498 60.53 16.903 72.55 14.879 58.75 21.694 70.94 20.221 57.04 25.843a 69.81 24.799a 55.91 29.480a 68.89 aFor completeness of data, these points are included. However, the validity of applying theoretical calculations to them is questionable since, at these concentrations, )a>0.2 (see Appendix I).

32 TABLE V Equivalent Conductance, Concentration Data Manganese Sulfate in Methanol-Water 40% Methanol 30% Methanol (weight %) (weight %) 10 c 104 (moles/liter) (moles/liter) 2.2748 52.11 0.9595 66.96 4.5601 45.72 2.6435 60 47 6.6662 42.00 6.1582 53.04 8.. 7040 39.38 9.9216 48.32 10.716 37.32 12.869 45.69 16.531 43015 20% Methanol 10% Methanol (weight %) (weight %) 104c A o 104 (moles/liter) (moles/liter) 2.0589 75.45 1.3726 97.22 5.8421 67.25 5.0088 88.44 11.814 60o13 10o598 80o81 17.857 55.58 17.950 74 56 23,318 52.60 24.1324 70~73 28. 154a 50.48 29,461a 68.24 aFor completeness of data, these points are included. However, the validity of applying theoretical calculations to them is questionable since, at these concentrations, $&>0.2 (see Appendix I).

33 Application of Data to Theory Conductance in Water The phoreogram (>~ vs c1/2 plot) of H2BDS is compared to that of H2S04 in Figure 1; Na2BDS, K2BDS and Na2S04 are similarly compared in Figure 2. The t, c data for Na2SO4 are those quoted by MacInnes (33) from the unpublished work of Shedlovsky and Longsworth. aTe old criterion for an unassociated electrolyte (34) is that its equivalent conductance data approach the limiting law tangent from above. H2BDS, Na2BDS and K2BDS all exhibit this behavior, indicating essentially no association. Because of this fact, the H2BDS, Na2BDS and K2BDS data were fitted to the extended equation for unassociated electrolytes. Since A = 0- s el/2 + E c log c + j c (14) for an unassociated electrolyte, and A - = A + S c - E c log c, (15) then A = o + J c. (16) Using the proper values for S and E (see Appendix 111), A is easily calculated. If the data fit the extended theory for unassociated electrolytes, a plot of A vs c (called the Fuoss plot) should give a straight line where JAo is the intercept and J the slope. In actual practise, since S and E are dependent on Ao, a JV from the phoreogram is chosen

34 430 420 Limiting Law Tangent O 41o 400oo H 390 O -0 410 0 Limiting Law Tangent 400 I...I 2 I3I _ 0 1 2 3 4 5 6 cl/2 102 (moles/liter)i/2 Fig. 1 —Phoreograms of m-BenzenediSulfonic Acid (bottom) and Sulfuric Acid (top).

35 140 o K2BDS w Na2SO4 (33). O Na2BDS Limiting Law Tangent 130 C\J 120 110 100 0 2 4 6 8 10 12 cl/ 10 (moles/liter)1/2 Fig. 2. —Phoreograms of Sodium m-Benzenedisulfonate, Potassium m-Benzenedisulfonate and Sodium Sulfate.

36 and the Fuoss plot is made. If the J\o obtained from this plot is different from that first chosen, this new A-A can be used to recalculate S and E and obtain' new values. This process is repeated until JA\ becomes consistent. Figure 3 shows the final Fuoss plots for Na2BDS and K2BDS. Deviations from linearity only occur at the highest concentrations. The slight downward curvature occurring at these concentrations could be due to any or all of several reasons: (1) a small amount of association, (2) non-inclusion of an extra viscosity correction due to large ions, (3) a general breakdown of the theory at these concentrations for unsymmetrical electrolytes (35). Despite the curvature at high concentrations however, this plot affords a very fine method of extrapolation for.A-O. Since the reason for making the conductance measurements on Na2BDS and K2BDS is primarily to obtain a value for o, the Fuoss plot is of great importance. The phoreograms of CuBDS and CuSO4 are shown in Figure 4 and their Fuoss plots in Figure 5. The CuS04 data were checked against the data of Owen and Gurry (10) for this salt, since they include hydrolysis corrections in their work. The excellent agreement can be seen in Figure 4. The figure also shows that the CuBDS data definitely approach the salt's limiting tangent from above in marked contrast to the behavior of CUS04. However, although the CuBDS curve approaches its limiting tangent from above, it then crosses the tangent and approaches ao from below the tangent.

37 150 O K2BDS o Na2BDS -_ _ Slope J 140 130 O 120 110 0 10 20 30 40 50 6o c 10 (moles/liter) Fig. 3 —Fuoss Plots of Sodium m-Benzenedisulfonate and Potassium m-Benzenedisulfonate.

38 0 CuBDS O CuS04 140 )O cuso4 (10) Limiting Law Tangent 130 120 CJI O 110 100 0 00 80 a 2I I I I 1 0 2 4 6 8 10 cl1/2 102 (moles/liter)l/2 Fig. 4 —Phoreograms of Copper m-Benzenedisulfonate and Copper Sulfate.

39 FI CuBDS 180 O CuS04 Slope J 170 16o a 150 1. 140 130 120 110 0 10 20 30 40 50 6o c 104 (moles/liter) Fig. 5 —Fuoss Plots of Copper m-Benzenedisulfonate and Copper Sulfate.

This raises some question concerning association or specific effects, or both. Nonetheless, the Fuoss plot (Figure 5) of CuBDS is a straight line, indicating it may be an unassociated electrolyte. Again, as with the Na+ and K+ salts, deviation from linearity occurs only at the highest concentrations. Further examination shows that the seemingly odd behavior exhibited in the phoreogram (Figure 4) is simply a result of the E and J terms of the extended equation~ Over the valid range of concentrations (see Appendix I), the term E c log c is always negative, and the J c term positive. As opposed to the case of the 1:1 electrolyte, the higher charge types have E and J terms which are extremely large and therefore, these terms in the extended equation become the determining factors in the shape of the curve even at very low concentrations. For these high valence type salts, E c log c is more important at low concentrations and J c at higher concentrations. The extended theory thus predicts that the phoreogram of an unassociated 2:2 salt should cross the limiting law tangent just as the phoreogram of CuBDS does. It is interesting to consider this behavior in more detail. The limiting law and the extended law have two points in common: c = 0 and c = cx (cx is the crossover _ _ _ x point). At the crossover point,

41 A ~/- S c72 =Ao - c1/2 + E c log + log (17) x x x (limiting law) (extended law) and thus log c = - J/E. The value of c is therefore x x characteristic of a given electrolyte. Between c = 0 and C = c- x _A _ -A (18) extended law limiting law E c log c + J c (19) and AA-must have a maximum value, An This maximum max value should occur at a concentration such that: log cmax = -(.4343 + E) (20) and at c max J =E c log c + Jc (21) max max max max Table VI gives the values of cx, cmaxnd A ____ maxmax for KC1 and CuBDS calculated from the above equations as compared to these values when taken from a large phoreogram. The KC1 values are those of Fuoss and Onsager (15) who first noticed this consequence of the theory. As seen, the Aa for the 1:1 electrolyte is so max small as to be essentially not measurable, and cx and cmax are almost at the lower limit of the experimental concentration range. However, this behavior is quite sensitive to charge type and, due to the large size of the E and J terms

42 TABLE VI The Crossover Parameters 4 4 AA, 104c 104 A x Salt x max max Calc. Plot Calc. Plot Calc. Plot KC1 1.8 - 0.7 0.002 - CuBDS 26.1 25.5 9.6 10.1 1.3 P.5 for a 2:2 electrolyte, a detectable is observed. max The agreement between the observed and calculated values of these quantities in the case of CuBDS is additional evidence that this may indeed be an unassociated 2:2 electrolyte. The Fuoss plot of CuS04 (Figure 5) in contrast to that of CuBDS, shows the behavior of an associated electrolyte when an attempt is made to fit its conductance data to the equations for an unassociated electrolyte. When treated as an associated electrolyte, the Ka obtained for CuS04 (see the following section for the method employed in calculating Ka) is 1.91 x 102 This is smaller than the value of 2.32 x 102 obtained by Owen and Gurry (10), who used the Shedlovsky method for determining Ka (36). This method forces the theoretical curve to approach the limiting law tangent from above by multiplying the S cl1/2 term of the limiting law equation by the factor _A/JV. The extended theory curve for an unassociated 2:2 electrolyte however, drops below the limiting law tangent and approaches'Ao from below the tangent. Therefore, the difference between the

43 data for an associated electrolyte and the extended theory curve is less than the difference between that data and the Shedlovsky curve. It is not surprising then, that the value of Ka for CuS04 obtained by using the extended theory is lower than the Ka obtained by Owen and Gurry. Table VII gives a summary of parameters for H2BDS, the BDS salts and CuS04. TABLE VII Experimental Parameters m-Benzenedisulfonic Acid, m-Benzenedisulfonate Salts and Copper Sulfate 0 Salt Jx1 0 3 a Jo -3 + A H2BDS 412.3 - - 6.65 5.0 Na2BDS 109.99 59.88 50.11a 1.775 4.5 K2BDS 133.52 60.00 73.52a 1.975 4.1 CuBDS 114.55 59.94 54.6 8.35 5.0 CuS04 134.1 79.8b 54.3 10.51 5.7 CuS04 133.6c 79.8C 53.8c avalues from Harned and Owen (37) bValues from MacInnes (38) CValues from Owen and Gurry (10) The X o of the BDS= ion is estimated from the Jo values of the Na+ and K+ salts using Kohlrausch's Law (39) and the A~'s of the well characterized Na+ and K+ ions.

The value for Ao of BDS thus found is used to estimate the Ao of Cu++ The Ao of Cu++ obtained from the _o of CuS04 + + and the A~ of the S04 ion is 0.3 conductance units lower than that from the oA of CuBDS, compared to a difference of 0.8 units from the \ that Owen and Gurry obtained in treating CuS04 by the Shedlovsky method. 0o It is interesting that the order of values of a for H2BDS, Na2BDS and K2BDS agree qualitatively with the 0o order of values of a obtained for HC1, NaCl and KC1 when their activity coefficient data are fitted to the extended forms of the Debye-Huckel theory. No comparison is availo ++ able for the a for the Cu salt, but it is at least reasonable as compared to the values of a for the H+, Na + 0 and K values. The reason for the higher a value for CuS04 over CuBDS is not immediately apparent. The successful fitting of the conductance data of CuBDS to the extended equation, with the result that it appears to be a completely unassociated salt, made most intriguing the possibility of discovering a strong 3:3 electrolyte. The same pattern as was used in treating the BDS salts was used on the NTS- salts. The acid conductance was used to qualitatively show whether hydrolysis of the anion would be important; it proved not to be. The conductance data for H3NTS are very close to the limiting law tangent and so the acid was treated with the extended equation for unassociated electrolytes. The Fuoss plots of Na3NTS and

45 K3NTS (Figure 6) show the same type of behavior as the corresponding BDS salts, the plots being curved at higher concentrations. Figure 7 shows the phoreogram of LaNTS. Although the limit of validity of the extended theory is, at best, about 1 x 10-3 M, it is seen that over a large range of concentrations, the conductance of LaNTS shows a behavior qualitatively similar to CuBDS. However, the Fuoss plot of LaNTS (Figure 8) looks more like that of CuS04 than CuBDS (Figure 5). Besides this, the slope is so large that it is even difficult to guess what A0 might be. The data of LaNTS were therefore fitted to the equation for associated electrolytes and the association constant obtained is 1.73 x 103 Table VIII gives a summary of parameters for H3NTS and the NTS salts. TABLE VIII Experimental Parameters 1,3,6-Naphthalenetrisulfonic Acid and 1,3,6b-Naphthalenetrisulfonate Salts Salt jo A\0 0 xl -3 o JxlO a(0) H3NTS 421.8 - 1 33.8 6.2 Na3NTS 121.55 71.44 50.11a 9.85 6.2 K3NTS 145.05 71.53 73.52a 11.95 6.4 LaNTS 137.5 71.5 69.1b 157.9 10.0 aValues from Harned and Owen (37) bValues from Spedding and Atkinson (40)

46 O K3NTS C) Na3NTS Slope J 180 170 0~ 160 CM " f S0 0 13o 120 0 5 10 15 20 25 30 c 10 (moles/liter) Fig. 6 —Fuoss Plots of Sodium 1,3,6-Naphthalenetrisulfonate and Potassium 1,3,6-Naphthalenetrisulfonate.

47 14o 120 Limiting Law Tangent aH o 10 0 0cO 6o 80 1 2 4 5 6 o 1 2 3 4 5 6 Fig. 7 —Phoreogram of Lanthanum 1,3,6-Naphthalenetrisulfonate.

48 200 O o 6o -I CMO: 16o O O 140o - 140 O 0 1 2 3 4 56 c 10 (moles/liter) Fig. 8.-Fuoss Plot of Lanthanum 1,3,6-Naphthalenetrisulfonate.

As for the BDS= salts, the Na+ and K+ salts were used to find Ao of the NTS ion. The XO of LaNTS is not in good agreement with that expected from the limiting ionic conductances of the cation and anion. However, it was noted from the phoreogram of LaNTS that when the lower concentration points were included (that is, those points which were actually dropped from the calculations because Ls>3% Lsolution), the curve then seemed to be approaching a higher Ao (about 140) value; this value would be in better agreement. Nonetheless, the disagreement between the Jo_ obtained from the addition of Ao and \O, and the Ao obtained by treating the LaNTS data with the extended equation for associated electrolytes, may well be an indication that the extended theory cannot be applied to 3:3 electrolytes. The a values of H+, Na+, and K+ for all practical 0 purposes, are constant. But the a obtained for LaNTS is considerably higher. This may again be an indication that the theory has been pushed beyond the limit of its validity. Conductance in Mixed Solvents Although the conductance data for CuBDS in water were successfully fitted to the equation for an unassociated electrolyte, caution still had to be exercised before suggesting that the conductance theory showed this electrolyte to be completely unassociated, or conversely that the electrolyte proved the validity of the theory. For 1:1 electrolytes, the size of the J term varies between about 50 and 100; for 2:2 electrolytes, it becomes

50 about 5000 to 10,000. Therefore, for 1:1 electrolytes which are associated to any appreciable extent, a Fuoss plot would easily indicate that the electrolyte could not be fitted to the equation for unassociated electrolytes. Similarly, for the 2:2 which is strongly associated, the Fuoss plot would not be linear. However, for a 2:2 electrolyte which might be only slightly associated, the size of the J term would obscure the small degree of association and the Fuoss plot would still be linear, except at the higher concentrations (35). The data for CuBDS fit this last example almost exactly: the J term is large and suspicion is aroused since, at the highest concentrations used, curvature appears on the Fuoss plot. For a case such as this, conductance measurements in mixed solvents may serve as the experimental technique needed to check whether this kind of electrolyte is or is not associated to some degree in water. At the same time, such measurements would indicate whether the theory handles the transition to associated electrolytes smoothly. By changing the solvent mixtures, varying degrees of association are forced and association constants may be obtained by applying the A, c data to the equation for associated electrolytes. If a smooth extrapolation of these constants back to pure water can be performed, then some significant information is obtained. Depending on the reliability of the extrapolation, an electrolyte, if it is

51 indeed unassociated in water, would yield an extrapolated K of zero or very close to zero. a Because of the tedious hydrolysis corrections required in arriving at the sets of A, c data when CuBDS was used, it was decided that the mixed solvent conductance work would be performed on MnBDS; the Mn++ ion requires no hydrolysis correction. In water, MnBDS shows the same type of behavior as CuBDS. The phoreogram of MnBDS as compared to that of MnSO4 is shown in Figure 9. As with CuBDS, the data for MnBDS approaches the limiting law tangent from above, then crosses the tangent and approaches Ao~ from below the tangent. The Fuoss plot for MnBDS (Figure 10) shows a straight line except at the highest concentrations used. Thus, the same conclusions can be drawn for MnBDS as for CuBDS: the conductance data in water can be successfully fitted to the equation for an unassociated electrolyte, but the slight curvature at the high concentrations indicates the need for mixed solvent techniques in an attempt to determine whether any small degree of association is taking place. To test both the consistency of the treatment of 2:2 electrolytes and the method of extrapolation, the conductance of an electrolyte known to be associated in water was also measured in the mixed solvents. For this work, MnS04 was chosen; again, no hydrolysis corrections are needed for this salt. If the extrapolation technique is valid (and the theory applies to mixed solvents), the extrapolated K a

140 0 MnBDS C) MnS04 Limiting Law Tangent 130 c) X \ 0 100 0 0 90 0 2 4 6 8 10 c1/2 lO (motes/liter1 3/ Fig. 9 —Phoreograms of Manganese m-Benzenedisulfonate and Manganese Sulfate.

53 150 140o H 130 120 I/ 110 1 o 10 20 30 4o 50 6o c 10 (moles/liter) Fig. 10 —Fuoss Plot of Manganese m-Benzenedisulfonateo

for MnS04 should be compatible with the Ka obtained when MnS04 conductance data (in water) were fitted to the equation for associated electrolytes. The solvents employed were methanol-water mixtures. Methanol was chosen because dielectric and viscosity data on the complete range of weight percentage mixtures are available (see Appendix II). Sets of A, c data from the mixed solvent resistance measurements were obtained (Tables IV and V)o Figure 11 compares the phoreograms of MnBDS in pure water, two methanolwater mixtures and in pure methanol. That more and more association has been forced by changing the solvent from 100 water to 100% methanol is evident from the figure. From the A, c data, values for Ao, a and K for MnBDS and MnS04 in the various solvent mixtures may now be calculated by the method of Fuoss (35). The equation for the equivalent conductance of associated electrolytes is: A = a (Ao? s (co)l/C 2 + E ca log ca + J ca) (22) where all the terms are defined as on page,6 and in Appendix I. By introducing the mass action equation for association: Ka 1a 2 2 where f+ is the ~ctivity 6defficient, equation (22)-can be written:

55 o H20 O 20% methanol 120 k ] 60% methanol 100% methanol Limiting Law Tangent 100.... 80 60 2 60 40 i ~0 1 2 4 0 1 2 3 4 5 6 c1/2 102 (moles/liter)1/2 Fig. 11 —Phoreograms of Manganese m-Benzenedisulfonate in Methanol-Water Systems.

A. =0o _- S (cca)I/ + E ca log ca + J ca - KAf 2 cc. (24) The procedure for finding the three unknowns a, Ao 0 and a will now be outlined. 0 If the proper Ao and a were known, the value of a could be found for each IA, c point. First, an opening a is chosen from a81/2 (2'5) Next, a= A (26): ~ - S c is found. Using the value obtained for a from equation (26), a, a,..., a are calculated: 2 3 n os2-1 (2+7) A0t' S (ca) + / E ca log ca + J c S (ca )1/2 E Ca log Ca ca A 2 2 2 2 Osa. (29) n AS (can1) /+ E ca log Ca + J Ca n- n-td n-l until an On-l = ao; (30) this a is the fraction of ions unassociated in the solution.

57 With the value of a now determined, the following definitions are made:' — At + s (ca)1/2 _ E ca log ca, (31),A.:.t - _AAo, (3-2) Y A' (33) and x f=+ (34) where f+ is calculated from the Debye-Huckel theory using the proper a value. Equation (24) therefore becomes: y = J - KaX I (35) This procedure for determining a, assuming that a and _o are known, is the same as is used in the actual case when 0 a and J\. are not known. Note that the three unknowns are included in equation (3.5): J (that is, a) and Ka explicitly and \oA implicitly. Picking a reasonable series of a values, a correct JA must be found, and only when this correct A0~ is used in calculating a and y, is a plot of y vs x a straight line. If the trial value of o0 is smaller than the unknown (that is, correct) JO, the numerator of y approaches a positive constant as c decreases (x increases), and since the denominator of y is approaching zero in this case, the y vs x plot will

58 be sharply concave upward as c decreases. If the trial value of _o_ is too large, the numerator of y becomes zero before the concentration does, and the y vs x plot will be concave downward as the concentration decreases. Therefore, a series of A-0 values must be used before the correct one is found. With the proper Jo in the y vs x plot, the intercept J is obtained; this J must be made compatible 0 with the a value used in finding a and f+. Now these best Ao and J values can be used to find the best a and all the parameters are thus found. This procedure for finding A0, a and K is obviously an extremely lengthy process to follow manually for each system studied. A computer program was written to handle the problem of varying a, JA and a until the plot of y vs x was found to be linear. 0 Table IX presents the final Ka, -A and a values thus obtained. Having the values of Ka, the extrapolation of Ka to water for MnBDS may be attempted. As suggested by Fuoss (35), log Ka vs /D (D is the dielectric constant of the solvent) was plotted for both MnBDS and MnS04 (Figure 12) in the series of mixed solvents employed. Both the MnSO4 and MnBDS data show curvature at lower dielectric constant, but are close to linear as they approach the dielectric constant of water. The MnS04 data in the mixed solvents extrapolate very close to the K in water determined previously. A linear extrapolation of the high D points of

59 TABLE IX Experimental Parameters Manganese m-Benzenedisulfonate and Manganese Sulfate in Methanol-Water Salt % Methanol K x 10 a() (weight %) a MnS04 0 1.33 133.2 5.0 10 2.37 104.9 5.2 20 4.39 85.8 5.8 30 8.81 74.7 8.0 40 17.1 68.9 8.2 MnBDS 0 - 113.3 5.4 10 0.08 88.3 5.4 20 0.16 72.1 5.8 30 0.21 63.9 5.5 40 0.56 60.8 5.7 60 5.13 64.1 8.2 80 14.9 74.2 7.3 100 81.7 61.6 8.0 MnBDS leads to the value of K of 4.5, corresponding to an ac a of about 0.995 at a concentration of 3 x 10-3 M. This value is entirely consistent with the previously obtained conclusion from the conductance data in water that MnBDS may be a completely unassociated electrolyte. From Table IX, it is apparent that the values obtained for a vary considerably and that there is a large general

'________I 1 _' i' — I i I —1-:)~_ 0 Scr 2 L r1 / 1 &- 0 I ___ MnBDS 1.0 1.5 2.0 2.5 3o 102 x 1/D Fig. 12 — The Association Constants of iManganese m-Benzenedisulfonate and Manganese Sulfate as a Function of Dielectric Constant.

61 jump in the value of a from 40% methanol to 60% methanol. 0 Fuoss has stated (35) however, that the a for a particular electrolyte should be nearly constant even in different 0 solvent mixtures, and that any variance in a only indicates the necessity for an extra viscosity correction due to large ions. The Fuoss method for applying this correction makes use of the Einstein volume (41) for large ions. The value of this correction for these salts, according to the Fuoss method, would then be about 1.4 Lt; this amounts to a change of about 150 in the J term. However, in order to keep a constant in the MnBDS mixed solvent work, the needed correction is closer to 20L~ J, or a change of about 2000 in the J term. It seems ill-advised to add such a large single correction without considering other factors which might 0 be causing the variance in a. Higher terms in the equation which had been dropped in the case of 1:1 electrolytes, for instance the c3/2 term, could possibly have some significance in the case of the 2~2 electrolytes. Also, recalling the 0 large value for a obtained for LaNTS, where Ka is quite 0 large, the reason for the variance in a may be the fact that the equation does not completely describe the behavior of strongly associated electrolytes. 0o In any event, when variation in a is witnessed, a correction of such large proportions cannot be attributed to one factor such as viscosity until the actual viscosity measurements have been made, The difficulty in this is that the measurement of viscosity in dilute solutions is of itself,

62 a major research project. Until these measurements are made however, the reason why a is not constant will be only speculatively evaluated. The )O values obtained for MnBDS in the various solvent mixtures deserve some comment also. Up to 40% methanol, the values for J.O decrease in such a manner as to make their Walden product, Loq (42), almost constant (I is the viscosity of the solvent). In 60, 80 and 100% methanol, the values of 0o for MnBDS vary such that the Walden product falls sharply and Loq in pure methanol is only about one-third Ao1 in pure water. This behavior is qualitatively similar to the behavior noted by others (43) for different salts in methanol-water solvent mixtures.

SUMMARY Within the concentration range of applicability, the conductance theory of Onsager and Fuoss for unassociated electrolytes has proved quite valid for the examined 1:2, 2:2 and 1:3 sulfonates in water. In addition, for these salts, generally consistent values for the closest distance o of approach of the ions, a, have been obtained, and the conductance data for the 2:2 sulfonates cross the limiting law tangent as predicted by the theory. The application of the Onsager-Fuoss extended theory to the associated 2:2 0 sulfates has also given reasonable results for J-~ and a. However, the associated 3:3 sulfonate studied did not give 0 Jo and a parameters in good agreement with the 1:3 salts. When MnBDS was forced to associate by employing mixed solvents, the association constants were obtained by use of the extended theory for associated electrolytes. The extrapolation of these constants back to the dielectric constant of water indicated that MnBDS was only slightly associated in water (a = 0.995 at 3 x 10- 3 M). In conjunction with the work on MnBDS, the higher association of MnSO4 in mixed solvents was studied; the results obtained from this salt exemplified the consistency of the extrapolation for both 2o2 electrolytes. The large variation in a

64 values found from the mixed solvent work raises the question of the roles of the viscosity correction for large ions and the inclusion of higher terms in the theoretical equation for 2:2 electrolytes. As indicated by their low field conductance, both CuBDS and MnBDS must now be designated as much stronger electrolytes than their corresponding sulfates. In connection with this, investigation of the high field conductances of CuBDS and CuS04 has been begun (44). These measurements have been used to give some indication of the extent of ion association in solution (45), and the initial findings indicate that, substantiating the low field work, CuBDS is less associated than CuS04 in water solutions. This preliminary result was obtained by comparing the experimental data of CuBDS and CuS04 with the Onsager-Wilson theory for the high field conductance of completely unassociated electrolytes (45). However, even with the conclusions drawn from the low field conductance studies in water and mixed solvents, this work has not shed any light on the actual question of what is involved on the microscopic scale in ion association. The Fuoss (5) and Denison-Ramsay (3) theories would predict that a plot of log Ka vs 1 D be linear: z z b b- 1 2 a a~~~~ D k T

65 But the plots of log Ka vs 1/D are not linear throughout; only approaching linearity in the high dielectric range. Also, the values for a, calculated for MnBDS, using the Bjerrum theory separate into two groups: from 10% to 40% 0 0 methanol, the a is about 15 A; from 60% to 100% methanol, 0o 0 the a is about 7.5 A. Not only is there a great variation o O in the values of a thus found (as there was in the a values from the Fuoss theory), but the order of their relative sizes is inverted from the order found using the conductance theory. The Bjerrum a's for MnS04 also vary considerably with pero centage methanol, and like the a's of MnBDS, change in the inverse order from the corresponding conductance values. The explanation for the differences in behavior in methanolwater from that predicted by the theories may be a specific solvation effect or a reflection of the changes in the physical properties of the methanol-water solvent itself. The results from this research investigation of the low field conductance of various salts in water and methanolwater, along with the questions raised, point to the need for a variety of physical measurements to help clarify the behavior observed. A conductance study of other salts and solvent systems, and viscosity measurements are the next steps in pursuit of the problem. In this laboratory, preliminary conductance experiments have been begun with dioxane-water solvent mixtures and with o- and p-benzenedisulfonate salts. To help clarify the general problem of ion association in these systems, ultrasonic absorption,

high field conductance, and near ultraviolet and visible spectra should be examined.

APPENDIX I Definition of Terms in the Limiting Law and Extended Law Equations for Unassociated Electrolytes In attempting to describe the behavior of an ioni.c solution when a field is applied, the problem is the determination of the ionic velocities. If there were no ionic atmosphere, the velocity of a reference ion, j, would be directly proportional to the external force applied. Since an ionic atmosphere exists around the ion in solution, two effects must be considered: 1. The electrophoretic effect: When an external field is applied, the ionic atmosphere, carrying solvent medium with it, moves in a direction opposite to the reference ion. Therefore, j is not moving in a medium at rest, and its net velocity is decreased. 2. The relaxation effect: Before the external field is applied, the atmosphere surrounding j is spherically symmetrical. Once the field is applied, j begins to move but the ionic atmosphere, attempting to re-form around j, does so in a time t, not equal to zero, therefore giving rise to an asymmetric atmosphere around j. This asymmetry 67

68 produces a field on j opposing the external field and therefore causes the velocity of j to be decreased. Taking these two effects into account, the limiting law for the equivalent conductance of unassociated electrolytes (assuming the ions to be point charges) in solution was derived by Onsager'(18): L =- L~O - s c1/2 (1) By considering these same two effects, but using a model in which the ions are represented by charged spheres rather than by point charges, and carrying the mathematical treatment further, Onsager and Fuoss developed the extended law equation for unassociated electrolytes:(15,16,17)~ -A~ - s cl/2 + E c log c + J c.(2) The constants S, E and J are given by the following equationsS = a* L~ + (3) a* (3a) 6 D k T (1 + q) c * (5b = Cc/2 8e (3b) 3rC c (10 ) E = EA- - E2 (4) O04343 E _ a b (4a) = 24 c~~~~~~~~~(a

69 o * 0.4343 E2 = ab / (4b) 16 c1 j = Aho + a, (5) 12 2b) h(b) + 0.9074 + In ( 1 (5a) 12 c b3 h(b) =2b + 2b - 1 (5b) * * 11~ a * 0 * r T>2 1 0 12 - 1/2.0170 + ln( 4j) (5c) 12 c 8 c where e = electronic charge = 4.8022 x 10 esu JK = reciprocal of the radius of the ionic atmosphere; defined by Debye and Huckel: [lo1000 D k T ~ Ci Zi N = Avogadrots number = 6.0238 x 1023 molecules/mole z = ionic charge D = dielectric constant k = Boltzmann constant = 1538031x 10-16 erg/degree molecule T = temperature, o A c- = concentration, moles/liter IZ 1Z21 (IO + ) 1 1/2 i lzil + IZ21) (1Z21 2 j 1211 2 = Faraday constant = 96,493 absolute coulombs/equivalent

70 = viscosity C = velocity of light = 2.9979 cm/sec 0 a = closest distance of approach of the ions, cm 2 b = Bjerrum parameter - 1 Z21 e a D k T Because of mathematical approximations used in the derivation of the conductance equations, the theory should not be fitted to data whose ( a>0.2 (46).

APPENDIX II Viscosity and Dielectric Data for Methanol-Water Systems (47) % Methanol m R x 103 D (weight %) (millipoise) 0 8.95 78.48 10 11.58 74.21 20 14. oo00 70. o01 30 15.31 65.55 40 15.93 60.92 60o 14.0o3 51.71 80 lo.o6 42.60 100 5.41 32.64 71

APPENDIX III Calculated Values for the Conductance Equation Terms of the Systems Studied Size Independent Terms for Water Systems System a* D* E1 E2 H2BDS 0.6085 156.41 6.3312 133.53 Na2BDS 0.7398 156.41 6.3312 133.53 K2BDS 0.7038 156.41 6.3312 133.53 H3NTS 1.0577 294.93 28.491 731.67 Na3NTS 1.4373 294.93 28.491 731.67 K3NTS 1.3264 294.93 28.491 731.67 2:2 electrolytes 1.8312 240.96 33.766 650.60 3:3 electrolytes 6.1803 541.74 384.62 4940.2 Size Independent Terms for 2:2 Electrolytes in Methanol-Water g Methanol a* I* E1 E2 (weight %) 0 1.8312 240.96 33.766 650.60 10 1.9915 191.52 39.933 562.43 20 2.1735 163.10 47.566 522.69 130 2.3990 154.14 57. 954 545.22 40 2.6775 153.65 72.182 606.57 60 3.4237 189.35 118.04 955.81 80 4.5790 290.99 211.14; 1964.6 100 6.8271 618.11 469.35 6222.1 72

Size Dependent Terms for Water Systems 0ystem 1. 62 1yte System 1 System H2BDS 4 13.372 129.6 H3NTS 6 78.64 -28.8 5 15.729 174.7 7 85.87 90.5 6 17.930 227.8 8 92.66 223.8 9 99.16 852.7 Na2BDS 4 13.372 150.1 Na3NTS 6 78.64 83.1 5 15.729 195.2 7 85.87 202.5 6 17.930 248.3 8 92.66 335.7 9 99.16 964.6 K2BDS 4 13.372 144.5 K3NTS 6 78.64 50.3 5 15.729 189.6 7 85.87 169.8 6 17.930 242.7 8 92.66 303.0 9 99.16 931.9 2:2 5 73.418 -79.6 1 3:3 6 964.88 -5696 electrolytes electrolytes 6 81.500 -37.5 7 1028.8 5867 7 88.848 20.6 8 o1086.o -5950 8 95.690 90.4 9 1138o2 -5965 10 1186.5 -5927

74 Size Dependent Terms for 2:2 Electrolytes in Methanol-Water % a21 a a 2 Methanol Methanol (weight (A) (weight (A) 0 5 731.418 -79.6 40 5 158.63 -292.5 6 81..500 -37.5 6 174.37 -283.5 7 88.848 20.6 i 7 188.49 -259.6 8 95.691 90.4 8 201.45 -224.8 9 I0,12. A 5 168.9 9 213.55 -181.8 10 5 86.09-43 -114.0 60 5 262.65 -654.0 6!92.286 -83.8 6 287.16 -664.8 7 101!. 76 -39.8 7 308.94 -652.2 8 112.62 14.1 8 328.80 -622.5 9 120.02 75.8 9 347.18 -579.6 20 5 103.76 -152.9 80 5 478.63 -1764.1 6 114.65 -131.6 6 520.39 -1837.1 7 124.49 -97.5 7 557.30 -1863.1 8 133.59 -54.0o 8 590.43 -1852.0 9 142.13 -3.4 9 620.96 -1814.8 30 5 126.82 -209.8 100 5 1097.3 -7187.8 6 139.79 -194.6 6 1185.3 -7595.9 7 151.44 -165.8 7 1262.1 -7880.9 8 162.18 -127.4 8 1330.8 -7994.9 9 172.25 -81.6 9 1393.3 -8053.9

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