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The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
formation of such bonds is accompanied by an increase in entropy. This effect is due to the preliminary breaking of the hydrogen bond existing between the cation and a solvent molecule. (2) These anions also form hydrogen bonds with citric acid. Cl- and HSO, can become solvated twice. However chelation of these ions by one citric acid molecule is not important. In acetonitrile the complexation of the anions is accompanied by an increase of the entropy. This can again be explained by the necessary rupture of the hydrogen bond between the cation and the solvent molecule. (3) The formation of a first hydrogen bond by the anions weakens the electron donor power of their other basic sites. This effect rather depends on the perturbation of the electronic structure of the anion brought about by the first bond than on its stability. Acknowledgment. The authors are indebted to N. V. Citrique Belge for financial support of this work and to Mrs. Th. Zeegers-Huyskens for fruitful discussions. Supplementary Material Available: Raw experimental data for the ligand cohcentration, dissociation constants, and corrected values of the dissociation constant for variations in the dielectric data ( 5 pages). Ordering information is available on any current masthead page.
P. L. Huyskens and Y. 0. Lambeau
References and Notes I.M. Koithoff and M. K. Chantooni, J . Am. Chem. Soc., 91,4681 (1969). D. J. Pirson and P. L. Huyskens, J. Solution Chem., 3, 507 (1974). J. 6.Ruiinda and Th. Zeegers-Huyskens, "Proceedings of the 12th European Congress on Molecular Spectroscopy", 1975, Elsevier, Amsterdam, 1976. E. R. Ralph and W. R. Glikerson, J. Am. Chem. Soc., 86,4783 (1964). L. Onsager, Phys. Z., 28, 277 (1927). P. Huyskens and Y. Lambeau, J. Phys. Chem., following paper in this issue. R. M. Fuoss and F. Accascina, "Electrolyte Conductance", Interscience, New York, N.Y., 1959. See, for instance, C. J. James and R. M. Fuoss, J. Solution Chem., 4, 91 (1975). J. E. Lind, Z. Zwonelik, and R. M. Fuoss, J . Am. Chem. Soc., 81, 1557 (1959). J. F. Coetzee, G. P. Cunningham, D. K. McGuire, and G. R. Padmanabhan, Anal. Chem., 34, 1139 (1962). J. T. Denison and J. 6.Ramsey, J. Am. Cbem. Soc., 77, 2615 (1955). 6.Chenon and C. Sandorfy, Can. J . Chem., 36, 1181 (1958). R. H. Nuttaii, D. W. A. Sharp, and T. C. Waddington, J. Chem. Soc., 4965 (1960). S. Y. Lam, C. Louis, and R. L. Benoit, J. Am. Chem. Soc., 98, 1156 (1976). (a) M. K. Chantwni and I.M. Kolttwff, J. phys. Chem., 77,527 (1973): (b) M. K. Chantwni and I. M. Kokhoff, J. Am. Chem. Soc.,92, 7025 (1970); (c) ref 2; (d) this work; (e) I. M. Kokhoff and M. K. Chantooni, J. Am. Chem. SOC.,97, 1376 (1975). (f) Determined using the same method as for citric acid, at L = 4 X mol dm-3 and to L = 8 X mol dm-3. P. Huyskens, J. Am. Chem. SOC.,99, 2578 (1977).
Ionic Conductances and Walden Products of Anions Mono- and Disolvated by Citric Acid in Acetonitrile P. L. Huyskens" and
Y. 0. Lambeau
Department of Chemistty, University of Leuven, 200-F,Celestijnenlaan, E 3030 Heverlee, Belgium (Received February 14, 1978) Publication costs assisted by N. V. Citrique Selge
From conductance and viscosity measurements of acetonitrile solutions at various temperatures, the overall formal Walden products W = A? of tetraalkylammonium salts were determined in the presence of various concentrations L of citric acid. The values WO at zero ionic strength were obtained by linear extrapolation of W against the square root of the concentration of the ionophore. From WO the formal Walden products w-of anions C1-, HSO,, Br-, NO3-, and I- were computed. These values decrease with increasing concentration L of the ligand, on account of the ion's greater degree of solvation. From this variation it is possible to deduce the addition constant kl- of the first of molecule citric acid on the anions. These values are in good agreement with those deduced in a previous work from the effect of the acid on the dissociation constant of trialkylammonium salts. Using the addition constants kl- and kf determined in this last work it is possible to compute from the formal products w- the proper Walden products w< and wf of the mono- and disolvated anions. These values, of the order of 15-18 and 10 ohm-l cm-2 CPmol-', respectively, are in good agreement with those calculated on the basis of Stokes' law with a model of two or three joined spheres using the crystallographic radii of the anions and of the ligand.
The addition of an acid has totally opposite effects on the conductance of solutions of trialkyl- and tetraalkylammonium salts in acetonitrile. For instance, the addition of 4 X mol dm-3 of citric acid to a 2 X lob3M solution of Et3NH+Br- increases the conductivity K from 1.18 to 1.44 X 10". ohm-l cm-l whereas it decreases that of a 2 X M solution of Et4NtBr- from 3.36 to 2.96 X 10". ohmm1 cm-l. The reason for this behavior lies in the fact that in the first case the main effect of the acid is to increase the 0022-365417812082-1892$0 1.OO/O
dissociation of the salt, whereas for the highly dissociated tetraalkylammonium salts, the presence of the acid decreases the mobility of the ions. However, this last effect is not simple. On one hand, the addition of the acid triggers a change in the viscosity Q of the solution (passing from 0,347 to 0.356 CPin the case under discussion) and thus decreases the mobility of all the individual ions. On the other hand, some anions become solvated by the acid and in this case it is the nature of the moving entity itself which changes. 0 1978 American Chemical Society
Anions Solvated by Citric Acid in Acetonitrlle
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
1
In order to take the first effect into account it is useful to consider, not the ionic conductance Xi of the individual ions, but their Walden products, defined as
1893
W / o h n i ' c d c poise mol;'
A
15OC
25oc
wi = hiq
(1)
One can assume in effect that, for a given moving particle, the Walden product wi will remain constant when the changes in the viscosity or in the temperature of the medium are not substantial. In a previous work,l it was shown that the anions C1- and HS04- can bind up to two molecules of citric acid. The addition constants k i and kz- of the first and second molecule ligands respectively were determined. For Brand NO3-, kl- is smaller and the addition of the second molecule can no longer be detected. For I-, hl- is still an order of magnitude smaller. In solutions of such anions containing citric acid, one has thus to consider two or three kinds of moving anions: unsolvated anions (concentration co), monosolvated anions (concentration cl) and, on occasion, disolvated species (concentration c2). The formal Walden product w- of the anions in such solutions is related to these concentrations and to the proper Walden products w{, wl-, and w c of the individual species of the relation
In the presence of a concentration L of free ligand, this equation can be written
wow- =
+ wl-kl-L + w2-kl-k2-L2 1 + kl-L + kl-kl-L2
(3)
In this work we determine the values wo-, wl-, and, on occasion, wz-of C1-, HS04-,Br-, NO3-, and I- complexed by citric acid in acetonitrile, from the variation of the formal Walden product w- with respect to increasing ligand concentration.
I. Determination of the Formal Walden Product w -of the Anions at Zero Ionic Strength of the Solution A. Method. The ionic conductance Xi and the Walden product wi of a given ion depends on the presence of the other ions, which affects its mobility. According to the theory of FUOSS,~ the dependence of wi on the concentration [i] of free cations in the solution is given by the expression wi = wp - si[iI1J2+ ci[i] log [i]
+ ai[i] + bi[iI3l2 (4)
wp is the Walden product at zero ionic strength, and si, ci, ai, and bi are constants for a given ion, a given solvent, and a given temperatures3 The concentration of the cations [i] is related to the formal concentration F of the ionophore by the dissociation constant of the ionophore Kd, which in the case of tetraalkylammonium ions in acetonitrile is fairly large. We consider the experimental quantity W , which may be called the overall formal Walden product of the solution, defined by
Taking into account Fuoss' conductance equation (4) and the dissociation equilibrium of the ionophore, W varies
0 35oc
a 50
1
I 2
1
1
1
I
6
1
!
I
,
10 X l i 2
8
Figure 1.
with the formal concentration of the ionophore according to the expression
WY2
W = W - S P J 2+ A F - - F
+ CF log F + B P I 2 +
Kd
y is the activity coefficient of the ions. The fourth and the seventh terms take the uncomplete dissociation into account. The limiting slope of W vs. F1J2a t F 0 corresponds to the expression of Onsager4
-
-s = -0.8205
8250 w,- (DT )lI2
X lo6
(DV3J2
(7)
In this work we determine W by extrapolation of W against FIJz. The extrapolated value W is the sum of the formal Walden products of the anions wo and of the cations w+O. wf0 remains constant because it is not affected by the presence of the ligand and its value can be found in the literature. w4 can be computed by the difference w 4 = W - w+o (8) The formal Walden product of the anions depends on the concentration of the ligand, as a consequence of the variation in the extent of solvation. B. Experimental Section. The experimental methods are the same as in the previous work. Pr4N+C1-, an Eastman Kodak product, was crystallized from an acetone solution and dried in vacuo. Bu4N+HS04-(Aldrich) was crystallized from a methanol solution. Et4N+Br- and Pr4N+I-,Fluka purum, were crystallized from a methanol solution, adding diethyl ether. Et4N+N0
