KINETICSOF
THE
HYDROLYSIS OF THE DICHROMATE ION
+
ln(r2/yl) K , where K represents a combination of various mass spectrometer constants. Over the regions where eq 9 and 10 are valid, straight-line behavior of the function will be observed when plotted vs. atom fraction. This behavior is shown by the Fe-Ni system and within experimental error by the Fe-Co system.
Acknowledgments. The authors wish to thank the
1409
American Iron and Steel Institute for their generous support of this work. It was carried out in the Laboratory for Research on the Structure of Matter which is generally supported by the Advanced Research Projects Agency, Office of the Secretary of Defense. M. J. Ginsburg and Dr. R. C . Svedberg made substantial contributions to design of the heating and control equipment.
The Kinetics of the Hydrolysis of the Dichromate Ion.
111. Environmental
Effects on Rate Constants and Activation Energies’
by Berta Perlmutter-Haymanand Yael Weissmann Department of Physical Chemistry, Hebrew University, Jerusalem, Israel
(Received July 18, 1966)
The rate of the hydrolysis of the dichromate ion in the absence of bases and other nucleophiles is accelerated by a number of “inert” salts and is decelerated by tetraethylammonium salts and by certain neutral substances. The acetate-catalyzed hydrolysis is subject to specific cat’ionic effects as would be expected of a reaction between two anions. The activation energy is 7.5 kcal and is constant between 1 and 4 5 O , whereas the activation energy for the uncatalyzed reaction decreases with increasing temperature. The rate of the uncatalyzed reaction is somewhat higher than that calculated from data on isotopic exchange.
Introduction In continuation of our investigation of kinetic salt effects, we considered the acetate-catalyzed hydrolysis of the dichromate ion to be a suitable reaction; it involves two anions and is first order with respect to each of them.2 However, the contribution of the uncatalyzed reaction to the observed rate is not negligible under our experimental conditions. For an accurate determination of the salt effect on the catalyzed reaction, a knowledge of the same effect on the uncatalyzed reaction is therefore desirable. Although for technical reasons this knowledge could not be obtained for all the salts employed, the results obtained for the uncatalyzed reaction seemed interesting in themselves and further environmental effects on this reaction
were therefore investigated. Activation energies for the two reactions were measured as a help toward understanding the mechanism.
Experimental Section The course of the reaction was followed spectrophotometrically, as described previously.2 All experiments were carried out under conditions where the reaction is pseudo-first order and the back reaction can be neglected. The temperature in the cell compartment was kept (1) Taken in part from a thesis t o be submitted t o the Senate of the Hebrew University by Y. Weissmann in partial fulfillment of the requirements for a Ph.D. degree. (2) B. Perlmutter-Hayman, J . Phys. Chsm., 69, 1736 (1965).
Volume 71, Number 6 April 1967
1410
constant by circulating water from a thermostat (constant-temperature “Forma Temp”). When the temperature differed from room temperature, care was taken to measure it in the spectrophotometric cells themselves and not only in the thermostat. The two values differed by as much as 3”. The acetates employed were either analytical reagents or were prepared in solution of the desired concentration by exactly neutralizing the appropriate hydroxides by acetic acid of known concentration.
BERTAPERLMUWER-HAYMAN AND YAELWEIBSMANN
0.8
‘+ p
0.6
0.4
0.2
.y
$
0.0
il
- 0.2
- 0.4
Results “Uncatalyzed” Reaction. This reaction has to be investigated in the presence of a buffer since otherwise the hydrogen-ion-catalyzed reaction would make a large and varying contribution to the observed rate.2 On the other hand, every buffer catalyzes the r e a ~ t i o n . ~We , ~ achieved pH values between 7.0 and 7.8 by using phosphate buffers at concentrations between 0.002 and 0.010 M and extrapolated the results to zero buffer concentration. In the case of Mg2+, the pH had to be somewhat lower in order to prevent precipitation. The pseudo-monomolecular rate constant is thus increased by the contribution of the acidcatalyzed reaction. This error was estimated semiquantitatively from the pH and from our previous value2 for k H + at an ionic strength of -3 X and was taken into account. (Since k ~ decreases + with increasing ionic strength,2 this calculation probably yields an upper limit for the error and thus a lower limit for the rate constant. The entire error being -10% at most, the uncertainty in its estimation cannot seriously affect our results.) The values thus obtained for kH20 at various concentrations of NaCl, NaN03, KazS04, KCl, KN03, MgClZ, (Et)4NBr, KBr, LiC1, sucrose, and dioxane are shown in Figure 1. (Experiments with Ca2* and Sr2+cannot be carried out in the manner described because the phosphates precipitate.) Figure 2 shows the dependence on 1/T of log koHnO (where I G O H , ~ is the value of ~ H * Oextrapolated to zero ~ O0.1 M solutions of ionic strength) and of log ~ H for KN03, of (Et),NBr, and of dioxane. The temperature range was between 1 and 45”. Except for (Et)4NBr where E, = 12.7 =k 0.5 kcal molee1, the lines are parallel within the limit of experimental error and all exhibit a marked curvature. Whereas the energy of activation over the whole range is 10.0 f 0.5 kcal mole-’, it changes from about 9.2 in the high-temperature range to about 12.6 in the low-temperature range. This gives an approximate temperature coefficient of 160 cal mole-1 deg. (Previous authors3report no such temperature dependence; the value of 9.6 kcal mole-’ (a)
The Journal of Physical Chemistry
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Concentration.
Figure 1. The dependence of log ~ H on ~ O the concentration of added substances. Full circles indicate that three or more points coincided within the limit of experimental error. (In the case of divalent electrolytes, “concentration” refers to cation concentration.)
1.8
n‘ 1.4 + 8 1.2 s 1.0 1.6
.y
M
0.6
-
0.4
-
0.2
-
0.8
i 4
.y
3.1
.,
3.2
3.3
3.4 3.5 (1/T) x 10’.
3.6
3.7
Figure 2. Arrhenius plots for @, the acetate-catalyzed reaction and for the %ncatalyzed” reaction in the presence of: 0.1 M Et,NBr; 0,0.1 M dioxane; 0, zero ionic strength; and in the presence of 0, 0.1 M KNOa.
which we calculate from their Figure 1 is, however, in reasonable agreement with our results.) (b) Acehate-Catalyzed Reaction. For each of the cations, Li+, Na+, K+, Mg2+, Ca2+, and Sr2+,several series of experiments were carried out; in each series, (3) P. Moore, 8. F. A. Kettle, and R. G. Wilkins, Inorg. Chem., 5 , 220 (1966). (4) B. Perlmutter-Hayman and M. A. Wolff, J . Phys. C h m . , 71, 1416 (1967).
KINETICSO F THE HYDROLYSIS O F THE DICHROMATE ION
the concentration of the cation in question was kept constant, whereas the acetate concentration was varied by substituting nitrate for acetate. (At the lowest acetate concentration it was found necessary to add a very small amount of the appropriate hydroxide to the reaction mixture, so as to obtain a pH of -9 before mixing with dichromate. Owing to the hydrogen ions present in the undiluted dichromate solution, the pH decreases immediately after mixing and during the whole course of the reaction will lie between 6.8 and 8 where the contributions of both H f and OH- to the rate are negligiblea2) The observed rate constant, kpseudo, was plotted against the acetate concentration ; the appropriate value of kHzO,the rate constant for the uncatalyzed reaction under the same conditions, was inserted a t the point [Ac-] = 0. (The value of k H z O for Ca2+ and Sr2+ was assumed to be equal to that of Mg2+ at the same concentration. The uncertainty thus introduced is not serious.) The secondorder rate constant, k A c - , was calculated from the slope. The results are shown in Figure 3. (The rate constant in the presence of 0.2 M Na+ is about 8% lower than that reported in our previoiis work.2 This discrepancy between two different series of experiments does not seem unreasonably large.) The influence of anions was investigated in the presence of 0.2 M K + and 0.05 M Ac-. Nitrate a t a concentration of 0.15 M was substituted by 0.15 M C1-, 0.15 ill Br-, and 0.075 M Sod2-. The reaction rate remained unaffected. The influence of nonelectrolytes was investigated in the presence of 0.05 M KAc; sucrose up to 0.5 A4 was found to have no influence, whereas dioxane (0.1 and 0.5 M ) exerted a slight decelerating effect on kpaeudo (see Table I).
Table I: Effect of Dioxane on the Rate in the Presence of 0.05 M KAc % Dioxane
0
0.88 4.40
0.05 X
D
78.5 77.9 75.1
kpaeudo X
8.3 7.7 6.0
10:
kAc- X loz
6.5 6.2 5.0
The influence of (Et)rNBr was measured in the presence of KAc at three different concentrations, 0.03, 0.05, and 0.10 M . From each measured value of kpseudo we subtracted that value of k H n O which corresponds to the given concentration of (Et)*NBr. The result was divided by the acetate concentration
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OA 0.5
1
I
I
I
I
I
I
I
I
fl
0.4
0.1 0.0
-0.1 0.1
0.2
0.3
0.4
Concentration.
Figure 3. The dependence of log kro- on the concentration of a, Li+; 0,Na+; 0 , K + ; W, Mg2+; 0, Ca2+; and A, Sr2+.
0.1
0.2
0.4
0.3 [EtrNBr].
0.5
Figure 4. The dependence on EtaNBr concentration of log hoin the presence of KAc: 0, 0.1 M ; 0,0.05 M; and W, 0.03 M; and 0 , log ~ H ~ o .
to yield k ~ ~ - Figure . 4 shows log k A o - vs. (Et)dNBr concentration. As can be expected in view of the accelerating influence of electrolytes, the values of k A c are higher the higher the acetate concentration. On the other hand, since the three lines are parallel within the limit of experimental error, the retarding influence of (Et)4NBr seems to be independent of the presence of electrolytes. The influence of (Et)4NBr on leHzO has been inserted in Figure 4 for the sake of comparison. The activation energy was determined in the presence of 0.1 M K f in the same temperature range as ~ been plotted against above. In Figure 2, log k ~ has l/T. From the straight line obtained we calculate an apparent energy of activation E , = 7.5 kcal mole-'. Volume 71 Number 6 April 1967 ~
1412
BERTAPERLMU’ITER-HAYMAN AND YAELWEISSMAN
1 0.2 - 1
Discussion (a) Acetate-Catalyzed Reaction. This reaction cannot be investigated a t very low ionic strength since a t low acetate concentrations (a) the pH is no longer sufficiently constant during any reaction and (b) the uncatalyzed reaction makes a very high relative contribution to the observed rate and any small experimental error in kpseudo is magnified in the calculation of kAc-. I n an attempt to estimate ~ O A ~ - , the rate constant at zero ionic strength, we tried a plot of log
+
log k ~ o -- 2.036~’/’/(1
IGO’A~-
8
* M 3
-1.8
-
-1.9
-
-2.0
1.20 1.25 1.30 1.35 (l/D) x 102.
against c for the three univalent cations Li+, Naf, and of log ~ H on ~ O the 5. The dependence of log 1,~ and E(+. This method is based on an e ~ t e n d e d ~ ?Figure reciprocal of the dielectric constant in dioxane-water mixtures. Debye-Huckel-Brq4nsted equation and has been found useful for a number of reactions between ions of unlike electric constant, D, calculated from values in the litersign,’ yielding straight lines sometimes up to suratureIa for 0 and 10% dioxane solutions, assuming a prisingly high concentrations.8~9 I n the present case, linear dependence of D on concentration. Figure 5 three concave lines were obtained which remained shows a plot of log k ~ us.~ 1/D. From the slope of separate even at our lowest concentrations and did not lend themselves to extrapolation. We can therefore .the straight line drawn through the three points we calculate the diameter of the activated complex to give only a rough estimate for k0nc-,viz. be 2.4A, which is a very reasonable value.14-16 0.5 k * ~ ~ -0.8 mole-‘ 1. sed-’ On the other hand, we have no explanation to offer Now in this reaction it clearly is not the ionic strength for the peculiar effect of tetraethylammonium bromide. which determines the rate, for a change in this quanThis effect is, however, paralleled to a certain extent by tity from 0.20 to 0.275, achieved by substituting sulthe effect of this substance on the reaction between fate for nitrate at constant potassium ion concentrapersulfate and iodide.I7 tion, has no influence on the rate constant. Rather it is the cations which are important. Their influence is (5) C. W. Davies, “Ion Association,” Butterworth and Co. Ltd., specific and follows the sequence Li+ < Na+ < I
