Inorganic Chemistry
278 NOTES
A
0 200
1
I 220
240
260 Wovelenath
280
1 300 mp
Fig. 2.-Spectra of 2.5 X 10-6Jf Bi(II1) in 1-cm. cells: A, in 1 M HCIOa: B, in 1 ;M HCIOa and 0.45 M HJPO2; C, as BiI-2 in 1 iM HCiOa.
tion is correct, a straight line of unit slope results with an intercept of log pa. It should be noticed that the equation only applies to the case of two species being present, both absorbing, and so allows for absorption due to bismuth ions but does not allow for any contribution to the absorbance by iodide ions. It has been verified, by experiment, t h a t iodide does not absorb a t this wave length when present a t this low concentration. The plot of the results is shown in Fig. 1, in which the best straight line of unit slope has been drawn. This line agrees very well with the data, confirming t h a t the complex is indeed BiI+2. From the intercept, was found to be 4.79 X lo2, in good agreement with the previous method of calculation. Discussion
A comparison of the results reported here and those reported by previous authors reveals a number of important differences. The value of the stability constant is tenfold smaller than that reported previously (4.35 X lo3),which suggests t h a t an error may have been made by previous workers in recording the concentration of iodide. A comparison of the sixth solution in Table I where the iodide concentration was 4.0 X M and a solution in the previous paper where this concentration was given as 3.9 X lo-* 1 14 reveals approximately the same value for the absorbance. The failure of previous authors to observe precipitation from the more concentrated bismuth solutions cannot be as readily explained. From the solubility product of bismuth iodide, which has been reported as S. 1 X 10-19,,3one would expect precipitation from some of the solutions in Table I where none appeared and from the solutions prepared by Frolen. We have observed two effects due to the presence of hypohosphorous acid: first, a marked decrease in the rate of precipitation of bismuth iodide from supersaturated solutions and, secondly, the formation of a similar-appearing precipitate even in the absence of iodide ions. The
latter appears to be mainly metallic bismuth resulting from the reduction of the uncomplexed ion by hypophosphorous acid. Bombergeri has, in fact, shown i t possible to obtain a quantitative precipitation of metallic bismuth from perchloric acid medium by heating with hypophosphorous acid. It has been our experience t h a t hypophosphorous acid, once opened to the atmosphere, deteriorates rapidly, and this might be the cause of its reactivity having been overlooked. Experiments have also shown that hypophosphorous acid reacts with dilute solutions of bismuth without precipitation. The absorption band of bismuth is shifted to longer wave lengths and the absorbance is decreased (Fig. 2), suggesting t h a t a weak complex is formed. It was because of this t h a t the second series of measurements of the formation of BiI +2 was carried out in the absence of hypophosphorous acid. The good agreement between the results obtained in the two series of experiments, as evidenced by Fig. 1, confirms the suggestion t h a t the complex between bismuth and the acid is very weak. The absorption spectrum of the ion B i I f 2 has been found to have two peaks above 240 mp, as shown in Fig. 2, with a maximum absorbance a t 282 mp. In Fig. 1 the deviation of the lowest result from the line is suggestive of the formation of a second species, presumably Bi12+. The narrowness of the range of concentrations which are high enough to permit an appreciable fraction of this species to be formed and still low enough to avoid precipitation of bismuth iodide makes study of this species exceedingly difficult, and no confirmation of its formula or estimate of its formation constant could be made from our data. Acknowledgments.-This work was supported in part by the United States Atomic Energy Commission under Contract AT(30-1)-905. (7) D. R. Bomberger, A?zal. Chem., 3 0 , 1321 (1958)
C O X T R I B U T I O K FROM THE
MAXP L A N C K I X S I I T U I E
FOR PHYSICAL CHEMISTRY, G O E T T I N G E N , C E R X A S Y
The Kinetics of the Chromate-Dichromate Reaction as Studied by a Relaxation Method BY JAMES H. SWINE HART^^ AND GILBERTW. CAST ELL AN^^
Receaved J u l y 1 3 , 1963
In recent years the application of relaxation techniques to the study of fast reactions has received considerable attention. Eigen and de.Maeyer2have develvped the theory and experimental techniques for studying such reactions. However, little attention has been (1) (a) Department of Chemistry, University of California, Davis, California; (b) Department of Chemistry, Catholic University of America, Washington, D. C . (2) & Eigen I. and L. delfaeyer, “Techniques of Organic Chemistry,” A . Weissberger, E d . , Interscience Publ., New York, N. Y . , 1963, Vol. V I I I , Part 11, Chapter XVIII.
NOTES 279
VoZ. 3, No. 2, February, 1964 directed toward the simplicity relaxation theory lends to the study of slow reactions3 The conditions for using relaxation methods to evaluate the kinetics of a system are the following. First, the system must be in equilibrium. Second, when a perturbation is applied to the system to change the equilibrium, the change must be small enough so t h a t the rate equations can be linearized, t h a t is AG/RT
