J. M. NOTLEYAND h/I. SPIRO
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The standard free energy of formation of a solvated salt MX is then given by A F ' M X ( ~ O I ~=) AFOA~X(B)- n5E'
Values for the standard free energies of formation have been calculated for the corresponding solvated salts and are listed in Table V. The standard free energies of formation for the silver halides were obtained from Latimer. 26 Heats of solution for LiC1, NaC1, KC1, CsCI, and NaBr previously reported, when combined with the heats of formation of the crystalline salts26 and free-
energy data obtained in this work, give the standard partial molal entropies for the corresponding salts. These entropies are also listed in Table V. The entropy given for LiCl is in considerable doubt since the heat of solution used in its evaluation is only an estimate. Acknowledgment. The authors are grateful to the U. S. Atomic Energy Commission, which supported this work through Contract AT-(30-1)-3019. ( 2 6 ) W. M. Latimer, "The Oxidation States of the Elements and their Potentials in Aqueous Solutions," 2nd ed, Prentice-Hall Ino., New York, N. Y.,1959.
Transference Numbers and Ionic Conductances in Formamide at 25'1
by J. M. Notley and M. Spiro Department of Chemistry, Imperial College of Science and Technology, London S.W.7, England (Received October 27, 1966)
The cation and anion constituent transference numbers of potassium chloride were measured at 25" at five concentrations from 0.01 to 0.1 N by the direct moving-boundary method, using as solvent formamide specially freed from ionic impurities. The addition of water had little effect on the results. The limiting transference numbers were combined with equivalent conductances from the literature to give individual ionic conductances in formamide. Ionic solvation numbers were calculated from them by means of the Robinson and Stokes modification of Stokes' law. The conductances and viscosities of 24 uni-univalent salts in formamide, measured by Davis, et al., were reexamined so as to give limiting conductances and viscosity B , coefficients. The concentration dependence of conductance in formamide was found to be strongly affected by the viscosity correction.
Introduction To attain a better understanding of ion-solvent interaction, we need accurate data on the properties of electrolytes a t infinite dilution and, if a t all possible, on the properties of single ions because cation-solvent and anion-solvent interactions are different. For most properties of electrolytes, the fraction to be attributed to the individual ions is uncertain except in the case of conductance where an unambiguous assignment can be made by means of transference numbers. UnThe Journal of Physical Chemistry
fortunately, although there are accurate conductance data for dozens of nonaqueous solvents, transference numbers of comparable accuracy exist only for a few: methanol2 (dielectric constant, Q 31.5), ethanol3 (E (1) Presented in Sept 1965 at the 16th Meeting of C.I.T.C.E. in Budapest, Hungary. (2) J. A. Davies, R. L. Kay, and A. R. Gordon, J . Chem. Phys., 19, 749 (1951); J. Smisko and L. R. Dawson, J . Phys. Chem., 59, 84 (1955). (3) J. R. Graham and A. R. Gordon, J . Am. Chem. SOC.,79, 2350 (1957); J. Smisko and L. R. Dawson, J. Phys. Chem., 59, 84 (1955).
TRANSFERENCE XUMBERS AND IONIC CONDUCTANCES IN FORMAMIDE
24.3)) dimethylf~rmamide~ ( e 36.7), and nitromethanes ( e 36.7) at 2.5’ and liquid ammonia (e -22) at much lower temperatures.6 Since no accurate transference numbers were available for solvents of dielectric constant higher than that of water, we set out to determine them in formamide at 25’ ( e 109.5,’ viscosity 7 3.30 CP*)* When this project was planned, the transference numbers of KCl in formamide were known to a few units per cent from emfg and Hittorf’O work and from reasoning based on Stokes’ law.” During the course of our research a further Hittorf study of the same system was published.12,lZa We have instead used the much more accurate moving-boundary method. Experimental Section All runs were carried out in an oil-filled glass-sided thermostat at 25 f 0.01’ kept constant to h0.002°. The general transference technique is described by Spiro,13 the optical assembly being illustrated in his Figure 12 and the rising boundary cell in his Figure 15. However, a new current regulator was designed and the circuit is shown in Figure 1. The E L 360 pentode was chosen because it can stand applied potentials as large as 4500 v; most other valves are not recommended by their manufacturers for use above 550 v. The current through the E;L 360 is-controlled by the voltage across resistance B amplified by the EF 91 valve. The potential source consisted of 20 120-v dry batteries. Currents from 30 pa to 2.5 ma could be selected by setting the range switch at A in the appropriate position and by the proper choice of the grid bias potential on the EF 91 valve. The impedance of the regulator ranged from 150 to 1000 megohms, so that a change of 1 megohm in the resistance of the cell during a run altered the current by only 0.1-0.7%. During an experiment the current was determined a t regular time intervals by measuring the potential drop across a standard 1000-ohm resistor in series with the cell. A series of preliminary experiments was carried out to find suitable following solutions for a leading solution of KC1 in formamide. Autogenic experiments, attractive because of their inherent simplicity, failed to throw up a viable system: cadmium, silver, and thallium anodes were ruled out by virtue of the known insolubility of their chloride salts, mercury became covered with ;t gray deposit and gave no visible boundary, produced a visible but curved boundaw and copper, which formed a curious thick boundary, was unsuitable be(ZUlse it dissolves spontaneously in formamide containing- oxygen _ - and because its electrode reaction produoes a mixture of cu(I)and Cu(II).14 Sheared boundaries were more successful. Visible
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cation boundaries were seen between KC1 and LiCl (falling boundary) or PbClz (rising), but not between KC1 and NaCl (falling) or BaClz (rising). Anion boundaries appeared when the following salt was potassium picrate (KPic) (rising) or potassium benzene sulfonate (rising) though not when it was HCOOK (rising or falling), CH,COOK (rising or falling), or K I (rising). Potassium iodate reacted with the solvent. The cation and anion boundaries selected for quantitative study were KC1 + PbClz and KC1 + KPic; they were easy to see even at very low currents. Of the several possible electrodes investigated, those of the CdICd(OOCCH3)z type, while nongaming, were rejected because of slow volume changes caused by diffusion. ’ 6 Platinum anodes a t low current densities did not gas either, but there is some difference of opinion in the literature16 as to the product formed and this affects the calculation of the volume correction. Silver was finally chosen as the nongassing anode and silver chloride (made by dipping a platinum electrode repeatedly into the molten salt) as the nongassing cathode. Experiments confirmed that the expected electrode reactions
+ C1- +AgCl + eAgCl + e- +Ag + C1Ag
proceeded quantitatively in formamide solutions. (4) J. E.Prue and P. J. Sherrington, Trans. Faraday Soc., 57, 1795 (1961). (5) 5.Blum and H. I. Schiff, J. Phys. Chem., 67, 1220 (1963). (6) E. C. Franklin and H. P. Cady, J. Am. Chem. SOC.,26, 499 (1904); J. L. Dye, R. F. Sankuer, and G. E. Smith, ibid., 82, 4797 (1960); 83, 5047 (1961); J. B. Gill, Chem. Commun. (London), 7 (1965). (7) G. R. Leader, J. Am. Chem. Soc., 73, 856 (1951). (8) G. F. Smith, J. Chem. Soc., 3257 (1931). (9) T.Pavlopoulos and H. Strehlow, 2. Physik. Chem. (Frankfurt), 2, 89 (1954). (10)L. R. Dawson and C. Berger, J. Am. Chem. SOC.,79, 4269 (1957); C. Berger, Ph.D. Dissertation, University of Kentucky, 1952. (11)L. R. Dawson, E. D. Wilhoit, and P. G. Sears, J. Am. Chem. SOC.,79, 5906 (1957). (12)R. Gopal and 0. N. Bhatnagar, J. Phys. Chem., 68, 3892 (1964). (l2a) NOTEADDEDIN PROOF.G. P. Johari and P. H. Tewari, J. Phys. Chem., 70, 197 (1966),published a third set of Hittorf results while the present paper was in press. (13)M. Spiro, “Determination of Transference Numbers,” Chapter 46 in A. Weissberger, Ed., “Physical Methods o f Organic Chemistry,” 3rd ed., Interscience Publishers, New York, N. Y.,1960. (14) H.R&ler, 2. &’Zelctrochem., 16, 419 (1910). (15) M. Selvaratnam and M. Spiro, Trans. Faraday Soc., 61, 360 (1965). (16)K. Schaum and H. Schneider, Ber., 56, 2460 (1923); S.Tajima and N. Baba, Electrochim. Acta, 7 , 355 (1962); D. E. Couch, ibid., 9,327 (1964).
Volume 70,Number 6
May 1966
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J. M. NOTLEY AND M. SPIRO
Figure 1. Circuit diagram of electronic current regulator. Resistances marked with an asterisk are high-stability ones with a 1% tolerance, and k stands for kilohms.
ThusI3 the corrected transference numbers a t any normality, CKCI,are given by the equat,ions
Carbide 3A Molecular Sieves and deionized by means of a mixed bed of Amberlite ion-exchange resins loaded, respectively, with H f and HCONH- ions. Details of TgKC1= TgKC'(obsd) - C K c l A V the purification process are given elsewhere.19 The (anode or cathode closed) purified solvent, fp 2.3', could be tapped off in liter quantities and had a water content (160 ppm or 0.009 TCIKC1 = TCIKC'(obsd) C ~ C I A (anode V closed) M ) and specific conductance (2 X ohm-' cm-I) where lower than any in the literature. The specific conductance of the solvent slowly increased on standing and it AV = V A & l - V A g - TgKC1vg~lKC1 was therefore measured, whenever a run was carried From molal and partial molal data in the l i t e r a t ~ r e ~ ~ J *out, on a sample of the same batch of formamide that and the average transference number found in this had been used to make up the KC1 solution. This was paper, we obtain the value used to calculate the solvent correction which was less than 0.25% for the most dilute solution. AV = +0.0019 1. f-'
+
BDH AnalaR KC1 was dried a t 160'; a sample of acidity. Lead showed only a trace (ca. chloride was prepared by mixing solutions of AnalaR lead nitrate and hydrochloric acid, washed, dried at 110' and then more fully at 250' under a stream of dry HC1 gas, and finally allowed to cool under dry nitrogen. Potassium picrate was formed by adding a solution of AnalaR potassium hydroxide to a hot solution of AnalaR picric acid; the solid which appeared on cooling was twice recrystallized from water and dried at 120'. The salts dissolved rapidly in formamide if a shaking machine was used, although lead chloride had first to be shaken to a dry powder before the solvent was added. The solutions were made up at 25' in calibrated Pyrex volumetric flasks and transferred to the cell by pressure of dry nitrogen. BASF formamide (fp 2.25') was dried with Union The J O W of~ Physkal Chemistry
Results The results of 40 transference runs are summarized in Table I. At each concentration of KC1, and for each type of boundary, the transference numbers were found to be independent of current when the latter was changed by a factor of 2 and independent also of a variation of a t least 15% in the normality of the following electrolyte. Further purification of the solvent by triply recrystallizing it had no effect either. The average deviation from the mean transference number was 0.0004. The sum of the cation and anion transference numbers is seen to be close t o unity in all (17) L. G. Longsworth, J . Am. Chem. SOC.,54, 2741 (1932). (18) R. Gopal and R. K. Srivastava, J . Phys. Chem., 66, 2704 (1962). (19) J. M.Notley and M. Spiro, J . Chem. SOC.,B , 362 (1966).
TRANSFERENCE NUMBERS AND IONIC CONDUCTANCES IN FORMAMIDE
1505
Table I : Summary of Transference Measurements on KC1 in Formamide a t 25’
CKCl
0.01017 0.02008 0,05002 0,08027 0.1005 a
1O’CPbClz
7.2-10.0 17 .0-20.0 43-51 47-65 79-95
Current, ma
0.08-0.15 0.15-0.29 0.38-0.75 0.64-1.22 0.75-1.50
With volume and solvent corrections applied.
TK=
10‘CKP is
0.4242 0,4233 0.4216 0.4204 0 .4201b
7.7-10.0 14.9-17.8 35-45 43-70 56-92
+
Table 11: Effect of the Addition of Water
CKCl
0.01017
0.008 0.053 0.10
0.1002
0.010 0.13
TK
TCi
0.5768 0.5767 0.5779 0.4201 0.4203
0.05-0.11 0.11-0.21 0.25-0.54 0.48-0.93 0.50-1.06
TCI”
0,5768 0.5771 0.5782 0,5792 0.5795
TK
+ Tci
1.0010 l.OOO4 0 9998 0.9996 0.9996
“Best” TK
0.4238 0.4231 0.4217 0.4206 0.4203
A run carried out with triply recrystallized formamide of fp 2.4’ gave 0.4203.
cases, an important check on the reliability of the measurements, and the “best” values in the last column were obtained by dividing the mean cation transference number by ( T K TcI).It is these values which are used in the calculations following. The figures in Table I1 demonstrate that the addition of small quantities of water was without significant effect on the transference numbers. This is consistent with earlier reports9a20that the presence of up to 1% of water (0.6 M ) had no appreciable effect on conductances and emf’s in formamide. It seems likely, therefore, that further drying of the solvent used in the present work would not have altered the results listed in Table I.
Water content, M
Current, ma
0.5795 0.5799
Discussion Comparison with Previous Results. The data are set out in Table 111, and the apparently large disagreement between different determinations requires some comment. The only indirect method is that based on the assumption that the ions Me8PhN+ and PhS03- are equimobile in formamide. There is no independent evidence to support this assumption; in water the limiting ionic conductances of the two ions21*22differ by 7% and, since one ion has a large polar group exposed to solvation influences while the other has not, no conclusions can be drawn as to their relative mobilities in other media. There is some hope that the re-
cently synthesized salt (i-Am)4N+B(i-Am)4- will prove to be more equimobile than others yet triedz3 but its solubility in formamide is unknown. The rather high transference number derived from cells with transference is probably accounted for by the fact that results obtained by this method are very sensitive to small errors in emf.13 The Hittorf method, too, based as it is on concentration differences, makes precision difficult. An uncertainty of as little as 0.2% in the concentrations of the electrode and middle compartments leads to an uncertainty of 4y0 in the final transference number if the concentration at each end of the cell changes by one-tenth during electrolysis. Dawson and Berger,’O who encountered some problems with potentiometric titrations for chloride in the presence of formamide, found that the cation transference numbers calculated from the anolyte and catholyte portions differed on average by 7%. Gopal and Bhatnagar12 measured the composition of the anode chamber only and determined the potassium content gravimetrically as the dipotassium sodium cobaltinitrite, a method which has not been recommendedt4 for work of high accuracy in the case of aqueous solutions. Both groups of Hittorf workers analyzed only one middle compartment and appear not to have varied the current or time of electrolysis for any given solution. Equal mixing between both electrode compartments and the middle section, brought about by diffusion, convection, or vibration, would therefore have remained undetected and led to low results. When all these points are borne in mind, the results in Table I11 are seen not to differ by more than can reasonably be attributed to experimental error. (20) F. H.Verhoek, J . Am. Chem. SOC.,58, 2577 (1936). (21)G.H.Jeffery and A. I. Vogel, J . Chem. SOC.,400 (1932). (22)M.J. McDowell and C. A. Kraus, J . Am. Chem. SOC.,73, 2170 (1951); P. G. Sears, E. D. Wilhoit, and L. R. Dawson, J . Chem. Phys., 23, 1274 (1955). (23) J. F. Coetzee and G. P. Cunningham, J . Am. Chem. SOC.,86, 3403 (1964); 87, 2529 (1965). (24) R.Belcher and A. J. Nutten, A d . Chim. Acta, 4,475 (1950).
Volume 70,Number 6
M a y 1966
J. M. NOTLEY AND M. SPIRO
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Table 111: Coniparison of Transference Numbers of KC1 in Formamide a t 25" Obtained by Different Methods Concn range, M
Method
Conductance of MeaPhN fPhSO3Cell with transference Hittorf Hittorf Hittorf Moving boundary
Results
0.415 0.45 T K O 0.406, b" T K O 0.419, b T K O = 0.409, b TKO = 0.427, b T K O
Not given 0.20-0,59 0.1-0.5 0.03-0.14 0.01-0.1
TK
= = = =
Ref
11 9 10 12 12a This paper
= 0.072
= 0.014 = 0.013
= 0.054
See eq 1.
Variation with Concentration. The "best" potassium transference numbers in Table I, when plotted against
