1528
Inorganic Chemistry
NOTES
It has been chosen as this value together with t = SO gives the best fit between calculated and experimentally determined stability constants for outer-sphere complexes’ of Cr3+ and e o 3 + as well as for the complex OVHzOSOa.) The same seems to hold for the hydrolysis reaction of the vanadyl cation. This reaction according to Rossotti and RossottiQ leads to the formation of a binuclear isopolybase 2V02+
+ 2 H n 0 k-2 (L’OOH)2*f + 2H+
(6)
I t is possible to study this reaction with the stoppedflow method.1° il rate law is found which formally allows for the bimolecular combination of two vanadyl-monohydroxo cations to the dimer
hydroxo complexes and certain inner-sphere redox reactions are expected to proceed via the same simple mechanism, which has long been known to operate in a general way with the complex-forming reactions of solvated cations and no special type of mechanism must be postulated for the olation reactions, which lead to binuclear isopolybases. So the suggestion of Eigen and a’ilkins12 can be confirmed although they used in their paper as a proof of their idea the direct comparison of bimolecular ( k l z for the iron reaction) and monomolecular rate constants ( k ~ exoh ~ 0 for FeOH2+ which was obviously wrong) which can only be compared directly, when K Ois approximately i M-l. (12) M. Eigen and R. G. Wilkins in “Mechanisms of Inorganic Reactions,” Advances in Chemistry Series, No. 49, American Chemical Society, Washington, 1). C., 1965, p 55.
i,?
2VOOH +
e (OVOH)?2+
(7)
kii
with kla = 2 X lo4 MV1sec-I (at p = 0.3 M a n d a t 25”) and k z l = 20 sec-I. Then by extrapolation to zero C O s T K I B U T I O S FROM THE REACTOR CHEMISTRY DIVISION, ionic strength we get k1a ( p = 0) = 8 X l o 3 sec-I. OAK RIDGENATIONAL LABORATORY, Applying eq 5 and taking from the formula of F ~ o s s , ~ OAK RIDGE,TENNESSEE 37830, M-I ( 2 5 O , d = 6 8). We A N D THE DEPARTMENT OF CHEXISTRY, Ko(+l,+l) = 8 X UNIVERSITY OF MAINE,ORONO,MAINE 04473 finally get k23 = lo5sec-’. Again from the hydroxyl ion catalyzed path of the complex-forming reactions of the vanadyl ion8I1l the Association of C d 2 +a n d Br- i n the Solvent exchange rate of water in the inner hydration sphere of KNO, Ca(NO& H2Ola the vanadyl-monohydroxo cation can be estimated as kHnoexoh(OVOH+)= 3 X lo4 sec-l. Since in this case, B Y J E R R Y BRAIJNSTEINlbAND HELENBRAUNSTEIN” too, the rate constant for the spontaneous water exchange and kz3 are of the same order of magnitude, we Received December 16, 1968 may conclude that also with the formation of the binuThe solution chemistry of electrolytes a t concentraclear complex (OVOH)22+ the rate-determining step is tions intermediate between anhydrous fused salts and the water exchange in the inner hydration sphere of the “ordinary” aqueous electrolytes has received little monomeric species OVOH(Hz0)4+. attention, in spite of its importance in the development It should be pointed out, however, that into the value of theories of electrolyte solutions. The temperature of ka3enter all possible oversimplifications or mistakes of dependence and water concentration dependence of the Fuoss model. I t is possible to apply the Fuoss equilibrium constants for the association model to all combinations of interacting species includCdZ+ Br- e CdBr+ (1) ing equally or oppositely charged ions and ion dipoles since in this model only coulombic interaction and the in the solvent {equimolar (Li,K)N03) HzO containvolume of the complex-forming species are considered. ing up to 50 mol % water have supported a quasilattice However, there always arises the question of the appromodel of competing association and hydration equilibpriate “contact distance.” The “contact distance” of ria., two tightly solvated cations could well be somewhat The present work is part of an extension of these greater than for solvated cation-anion complexes. studies to other solvent systems. Studies of transport Inserting 6 fi instead of 5 fi increases Ko(2+,2+) and properties4c5 and volumetric properties6 in Ca(NO&* decreases kza(Fe3+) by a factor of 5 and KO(l+,l+) 4H20 and in its mixtures with K N 0 3 have suggested and k23(11O2+) by a factor of 2, respectively. This that these hydrate melts may be considered as analogs gives a better fit of k23 and k I z 2 0 e s c h in both cases. of molten salts, consisting of nitrate ions and hydrated However, although the values of K Oused above may cations. I n this note me describe measurements of the thus be very approximate, it is quite clear that k23 and (1) (a) Research sponsored by the U. S. Atomic Energy Commission unk H p O e x & a t any rate are of the same order of magnitude. der contracts with t h e Union Carbide Corp. and with t h e University of Maine. (h) Oak Ridge National Laboratory. (c) National Science FounObviously the formation also of other binuclear dation Cooperative Fellow a t the University of Maine, 1964-1966.
+
+
+
(7) F. Basolo and R. G. Pearson, “Mechanism of Inorganic Reactions,” John Wiley &Sons, Inc., New York, N. Y . ,1960, p 380. (8) H. Strehlow and H. Wendt, I n o i g . Chem., 2, 6 (1963). (9) F. Rossotti and H. S. Iiossotti, A d a Chum. Sca?zd.,9, 1177 (1955). (10) B. Lutz and H. Wendt, t o be submitted for publication. (11) A. Schlund and H. Wendt, B e y . Buizseizges. P h y s i k . Cheiiz., 72, 652 (1968).
+
(2) J. Braunstein, Inoug. Chim. Acta Rev., 2, 19 (1968). (3) (a) J. Braunstein, J . Phys. C h e m . , 71, 3402 (1967); (b) P. C. Lammers and J. Braunstein ibid., 71, 2636 (1967). (4) C. T. Moynihan, ibid.,70,3399 (1966). (5) J. Braunstein, L. Orr, A. I
