1554
HENRY S. FRANK
substituent is large and directed away from the ring. Unfortunately, because of the uncertainties involvedlg detailed calculations of the change in ionization potentials are not practical. It is evident, however, that there are no gross inconsistencies between the predictions of the model and the observed ionization potential variations.
Vol. 67
Acknowledgment.-The authors are indebted to Dr. N. D. CoTgeshall for several enlightening discussioiis and to Dr. A. B. King for his helpful commelzts during the preparation of the manuscript. lye are also grateful to Messrs. J. P. Rlems, P. W. Mazak, C. J. Ullrich, and H. T. Best for assistance in obtaining aiid plotting the data.
SIKGLE ION ACTIVITIES ASD ION-SOLVEKT IXTERACTIOK IN DILUTE AQ‘C‘EBUS SOLUTIOSS BY HENRY S.FRAXK Departmcnt of Chenazstry, I’niverstty of Pattshurgh, Pzttsburgh 13, Pennsylvania Received March 11, 1963
-4return is proposed to the ascription of physical significance t o single ion activities in electrolyte solutions and illustrations are given of two cases ahere this seems to lead t o meaningful results. In 0.1 iVf HC1 Y E + seems to be about 5% greater than YC,-, in rough agreement with predictions from the previously postulated difference in degree of hydration of H + and C1-. In dilute solutions of tetraalkylammonium iodides .fI- appears to he larger, and sometimes much larger, than f x a ~ + . It is suggested that this is a real phenomenon, and an explanation is offered in terms of the structure-promoting influence of R,S+ cations and the structure-breaking effect of I-. For the convenient tabulation of numerical data relating t o single ion activities a new property of ionic solutions is proposed, to be called the mean ionic activity deviation, denoted by ,a, and defined as 6, = (f+:+!f-”-)l/~. When used with the mean ionic activity coefficient, f+, this makes accessible the single ion activity coefficients through the identities f+ = (f,6,)’/2v+ a n d f - = (fi/6i)u/2y-.
Introduction Although it is now over 30 years since single ion activities were showni to be inaccessible to exact thermodynamics, it has never quite been possible to do without these quantities, and an uneasy compromise has been struck in their regard. That is, it has been agreed not to call any given quantity a single ion activity a t the same time that the idea of such an activity has still been used freely in various kinds of derivations,2 and elaborate procedures have been worked out for getting refined values of pH3--i.e., of an effective u H + . This is not a very satisfactory situation, and one of the purposes of the present essay is to propose that single ion activities and activity coefficients be reinstated as acceptable working quantities. Special care will be necessary to ensure adequate recognitioii of the inherent uncertainty of any numerical value assigned, but the advantages to be gained seem considerable in the reopening of avenues of investigation, and of interpretation, of ionic solution phenomena. One such avenue has recently been followed4 in the use of acl- in studying the binding of counterions in polyelectrolyte solutions and several others are explored below. That there is no difficultv in defining a single-ion activity coefficient in terms of a thought process may be illustrated, among other possibilities, by the fact that this is what is done when the Giintelberg charging process is employed in deriving the equations of the Debye-Hiickel theory. The problem has thus been one of accessibility only, and this, in turn, reduces to (1) E. A. Guggenheim, J . Phys. Chem., 33, 842 (1929); 34, 1540 (1930). (2) See, for example, (a) D. A. &IacInnes. “The Principles of ElectriY., 1961, Chapter 13; (b) J. G. Kirkwood chemistry,” Dover, New
Thermodynamics,” McGraw-Hi11 Book a n d I. Oppenheim, “Ch Co., New York, N. Y., 1961, Chapters 12 a n d 13. (3) See, for example, H. S. Harned a n d B. B. Owen, “The Phyeioal Chemistry of Electrolytic Solutions,” 3rd. Ed., Reinhold Publ. Corp., New York, N. Y., 1058, Chapter 10. (4) S. Lapanje, J. Haebig, H. T. Davis, a n d S. A. Rice, J . Am. Chem. Soc., 88, 1590 L1961).
that posed by the impossibility of the exact evaluation, by thermodynamic methods, of liquid-j unction poteiitials.2a The last-named fact has an interesting implication, namely, that to assert that nothing can be known about single-ion activities is equivalent to stating that nothing can be known about liquid-junction potentials. Since the latter statement is very far from being true, it is both possible and legitimate toniake, and to act upon, the converse statement that anything that can be known or guessed about a liquid-junction potential can be made to provide a piece of information, or an estimate, about a single-ion activity. This is the principle which has been employed in obtaining pH values3 and in the evaluation, referred to above14 of the activity of chloride ion in certain electrolyte solutions. I n these applications, experiments are devised in which the potential difference across a liquid junction is imagined (a) to be negligible, (b) to be calculable, or (c) not to change (or to change only trivially) as the test solution is altered in certain ways (for instance, is made to run from high dilution, where the single-ion activity coefficient must be near unity, to the finite conceiitration of interest). If the errors in such assumptions were zero, one would have exact values of the single-ion activities, or activity ratios, involved. Correspondingly, any estimate of the numerical error the assumptions contain is, when translated, an estimate of the error-limit to be ascribed to the single-ion activity measurement. This in turn makes it possible, by standard thermodynamic means, to evaluate, within the corresponding (estimated) limits of error, a variety of other “noli-thermodynamic’’ quantities of interest. Single-Ion Activities in 0.1 M HCl.-An an example of what can be done, take the carefully considered values of 1.085 and 1.092 assigned, respectively, by Hitchcock and Taylor5 and Bates, Pinching, and Smith6
SISGLEION ACTIVITIES
July, 1963
for the p H of 0.1 M HCl. The latter is on a molality basis, and the former becomes 1.086 when corrected to the same basis. These make log YHt = -0.086 or -0.092; but y+ for this solution is reported as 0.7964,' giving for log yi, that is for l/z(log Y H + log y c i - ) the value -0.099, corresponding to log YCI- = -0.1 12 or -0.106. Thuslog ( y ~ + / y ~ lequals -) 0.026 or 0.014, and Y H + / ~ C ~equals I .062 or 1.033. Horn greatly these numbers are in error is, of course, a question. It seems likely, however, that they are more than qualitatively correct, and that, in 0.1 M HC1 at 2 5 O , the single-ion activity coefficient of H + is in fact about 5% higher than that of C1-. I n support of this coiiclusioii it may be noted that Robinson and Stokes,s in their discussion of the influence of hydration on stoichiometric activity coefficients, have ascribed a hydration number of about 8 to HCI, and consider that this is almost entirely cation hydration. A simple extension, however, of their derivation (in fact, a return to the form given earlier by Bjerrum9) supplies expressions for the influence of single-ion hydrations upon single-ion activity coefficients. The result for a 1-1 solute, correct to first-order terms in m, is
+
In y+h
=
In y-h
=
3h+
+ h55.51
3h-
-2 -771
+ h+ -55.51
2
m
(1)
where h+ is the cation hydration number, i e . , the number ~f molecules of water which a cation removes from its solvent function, and h- the hydration number of the anion. Using eq. 1one obtains
Ag, AgI, R S I ( c ) , I
