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POTENTIOMETRIC STUDIES I N M I X E D SOLVENTS
incorporation. and desorption have been shown not to occur.
Potentiometric Studies in Mixed Solvents.
6. The existence of a qualitatively similar efflect in Fe203, Crz03,arid ZnO has been demonstrated.
I.
The Determination of
Activity Coefficients and Junction Potentials Using Modified Gran Plots
by F. J. C. Rossotti and Hazel Rossotti Inorganic Chemistry Laboratory, Oxford University, Oxford, England
(Received M a y $6, 1964)
The suitability of various imixed aqueous-organic electrolyte solutions for use as media in potentiometric studies of equilibria was investigated. For systems of 0.6 M 1IX ( A I = Lif or E a + and X = C104- or SO8-) in water and 50% v./v. organic solvent (methanol, ethanol, or dioxane), AI+ was gradually replaced by H+. The resulting changes in activity coefficients and liquid junction potentials are discussed.
Complexes formed in aqueous solution between metal ions and ligands, which are conjugate bases of weak acids, are frequently studied by measuring the concentration, h, of' free hydrogen ions, using a suitable galvanic ce1L112 The results are best interpreted if activity coefficients of species participating in the cell reaction, and the potentials a t any liquid-liquid junctions, can be kept constant throughout the measurements. Mixed aqueous-organic solvent media are often used to increase the solubility of many metal complexes and also because of their intrinsic interest. 1Iany authors have combined an aqueous reference half-cell with a mixed solvent half-cell and 1 hus have introduced large liquid junction potentials. I n the present work, liquid junctions between aqueous solutions and mixed solvents have been avoided. As a preliminary to studying metal complex formation in mixed aqueous-organic solvents, two series of nieasurements were made a t 25" and ionic strength 0.5 M in each of the possible combinations of solvent S (water, 50y0v./v. methanol, 50% v./v. ethanol, and 50% v./v. dioxane), background cation 1\I+ (lithium, sodium), and background anion X-- (perchlorate, nitrate).
Series I . The mean stoichiometric activity cocfficient (YHYCI)"' was measured as a function of h using the cells
- glass electrode
-
H+, l I + , C1-, X- in S [>I+]4- h 0.5 M AgCl(s), Ag(s) (1) The activity coefficient product Y H Y C I is defined so thLat YHYCI 1 as (h t.[Cl-1) + 0 in each MX-S medium. A stoichiometric activity coefficient is obtained3 by dividing activity by total as opposed to free concentration and will accordingly differ froin the true activjty coefficient if the ion under consideration is partially associated. Series I I . The dependence of
-
E,
=
El? - R T / F In
+
YH
on h was determined using the cells (1) F. J. C. Rossotti and H. Rossotti, "The Determination of Stability Constants," McGraw-Hill Book Co., Inc., New York, N. y., 1561, Sections 4-1, 7-3-A. (2) J. Bjerrum, G. Schwarzenbach, and L. G. S i l l h , Ed., "Stability Constants." The Chemical Society, London, 1957 and 1558. (3) See ref. 1 , Section 2-2-C.
Volume 68, A'umber 12
December, l96g
F. J. c. ROSSOTTI b N D HAZEL ROSSOTTI
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From eq. 1,2, and 3
&I' (0.5 - h) M HfhM x- 0.5 M in S
MX 0.5 A4
&I+ 0.49
in S
Ag+ 0.01 M X- 0.5 A!! in S
RT E=Eo--ln
V Y ( V H - VI?) 4r2(V v ) 2
+
F
I
RT
- In
F
YEYC~
(4)
whence
E,=E--
RT In (V F
+ v) =
where the term
RT VY Eo' = EO - - In F 4r2 ~
is constant throughout a titration. The equivalence point may readily be obtained by a modification of Gran's method. The present procedure also gives values of YHYC1. The quant, [Cl-1 0.5 mM, indicating that Y1iYc1 = 1 under these conditions and hence presumably that lini YH = 1. The
