DISCHARGE OF
Dec. 20, 1939
\'ARIATION
REACTION 6379
TABLE I PSEUDO-FIRST-ORDER RATECONSTANT SULFATE IONCONCENTRATIOS~
O F THE
WITH
[S04-lm
M E T A L I O N COMPLEXES WITH PRECEDING CHEMICAL
2350 k' X 102, min. -1
275' nb
[S04-lm
k' X 102
n
0,05 .08
3 . 7 =t 0 . 4 2 0.07 8 . 7 =I= 0 . 4 2 3.2 1 .10 7 . 7 Zt 0 2 .10 2 . 8 =I= . 4 3 .15 5.6 f 3 2 ,125 2.2 .1 2 .20 4.9 f 1 2 3 ,225 4 . 2 =I= 0 2 .l5 2 . 0 i. .1 ,175 1 . 8 =t .03 2 .25 3.8 f4 2 .20 1.5 f .2 5 .30 3 . 3 Zt 3 2 .21 1.5 1 .3l(satd.) 3 . 5 =I= 1 2 IW 200 300 400 500 600 (S0;l' x 10' .22 1.6 1 .25(satd.) 1 . 6 =I= 0 . 1 3 Fig. 1.-Plot of reciprocal rate data us. [SO,-]2 t o determine k and K . a Initial S20,' concentration 0.01, 0.02, 0.03 m a t 235'; 0.02 m a t 275'. Nitrogen flow rate: 0.21 l./min. n = number of runs. Fig. 1. It should be noted that the sulfate ion TABLE I1 concentration increases during the reaction and, RATE AND EQUILIBRIUM COXSTANT DATAFOR REACTIONS therefore, the values for K obtained from these OF PYROSULFATE ASD DICHROMATE WITH FUSED NITRATE graphs may be slightly smaller than the true value. Comparison with the Dichromate-Nitrate Rek (min.-l) T," C . Ksro:T,'C. Kcrzo;-" action.-Since the dichromate and the pyrosulfate 0.038 235 0.026 250 8.5 X reactions have the same slow step and were studied 0.096 275 0.038 300 3 . 8 X lo-'* under similar conditions, the rate constant obAH, = 13 kcal. AH = 5 kcal. AH = 50 kcal. tained in this study can be used to calculate the From extrapolation of data in ref. 2 and F. R. Duke and M . L. Iverson, J . Phys. Chem., 6 2 , 417 (1958). equilibrium constant for the former. The result
+
TABLE I11 SOLUBILITY OF Xa2SOd IN NaN03-KN03 EUTECTIC T , OC.
Solubility (m) X 102
235 250 275 300
25 =I= 1 2 8 . 2 =I= 0 . 7 3 4 . 2 =I= . 8 42.1 iz . 5
The plots of equation 7, 1/k' vs. the square of the initial sulfate ion concentration, are shown in
[ COXTRIBUTION FROM
THE
(see Table 11) shows that Cr20,-- is a much weaker acid than S~07--. The rate of the dichromate reaction was brought into the measurable range by adding heavy metal ions to precipitate the chromate as i t is formed. The large over-all apparent activation energy for the dichromate reaction (cu. 63 kcal.) is partly compensated by the increase in solubility of these chromate salts with temperature. AMES, IowA
COATES CHEMICAL LABORATORY, LOUISIANA STATE UXIVERSITY]
Kinetics of Discharge of Metal Ion Complexes with Preceding Chemical Reaction BY HIROAKI ~ I A T S UlaD PAVL A , DELAHAY AND MARCOS KLEINERMAN~~ RECEIVEDMAY4, 1959 The kinetics of discharge of complexes with preceding formation of an intermediate by a purely chemical reaction are treated for faradaic impedance measurements and the galvanostatic and potentiostatic methods. Contributions from charge transfer and the preceding chemical reaction can be separated from experimental data. Analysis is given ( a ) for variations of the faradaic resistance (series equivalent circuit) and faradaic capacity with 1/w1/2 ( w = 26,s = frequency), ( b ) for po0 tential-time curves, and (c) for current-time curves. The contribution from chemical kinetics vanishes for l / w 1 / 2 or t = 0, and the exchange current density can be computed from simple equilibrium considerations. The chemical kinetics componeiit of the faradaic resistance is constant for large values of l/w1/2 or t .
the exchange current for direct discharge being so low that reaction 1 followed by discharge of MY,+(H- m ) is faster. The intermediate complex
composition can be determined from variations of the exchange current with concentration of complexing agent, all other concentrations remaining constant. This method, which is similar to reaction order determination in chemical kinetics, was extended to electrode processes by Vetter3 and Geri~cher.~ These authors assumed that chemical equilibrium is achieved but this assumption, while
(1) (a) Research Associate, 1938-1959: on leave from the Government Chemical Industrial Research Institute, Tokyo. (b) Predoctoral fellow, 1957-1959. (2) F o r a review see, for instance, P. Delahay, Ann. Reo. Phys. Chem., 8, 229 (1957)
(3) (a) F o r a review see K. J. Vetter, 2. Elektrochem., 59, 596 (1955). (b) Also K. J. Vetter, "Transactions of Symposium on Electrode Processes," Philadelphia, M a y 1959, in course of publication. (4) (a) For instance, H. Gerischer, 2. Elektvochem., 61, 604 (1953). (h) For a review see H. Gerischer, Anal. Chem., 31, 33-39 (1959).
It is now well established2 that discharge of certain metal ion complexes is preceded by a purely chemical reaction of the type
-
R I Y p + ( n - = z ) t- h I Y v + ( n - Y Z )
+ ( p - v)Y-Z
(1)
6380
H. LfATSUDA, P.D E L A H A Y
entirely justified under proper experimental conditions, cannot always be made. The kinetics of the chemical step are considered here for the discharge of metal ion complexes on amalgam electrodes for faradaic impedance measurements, galvanostatic and potentiostatic methodsb Extension to other electrode processes with similar kinetics is immediate. Current-Potential Characteristics.-The current density (positive for a net cathodic reaction) for - v z ) is the discharge of
where C , is the concentration of MY,+(n- u z ) a t the discharge site; Ca the amalgam concentration a t the electrode surface; Cy the concentration of complexing agent a t the discharge site; ks' the formal rate constant a t the standard potential E, for the charge transfer reaction, e.g., the discharge of MY,+(n- vz) (not the over-all reaction) ; E the potential in the European convention; Q the transfer coefficient; and F , R , T have their usual significance. Kinetic data can more conveniently be given a t the standard potential Eo for the overall reaction, e.&, the reduction of MY,+(" - PS) to the amalgam. Equation 2 is applicable except that E - E, and C , are replaced by E - Eo and C,/K, respectively, K being the instability constant for reaction 1. The common value of the current densities for the forward and backward reactions is equal to the exchange current density Io a t the equilibrium potential E e for the bulk concentration of reactants. Thus, by application of the Nernst equation a t E, there follows 1 0 = nFk.( Cpo)l-n ( CaolQ ( Cy'J)u-P(l-a) (3) where CPois the bulk concentration of - Dz), and CaQand Cyothe bulk concentrations of amalgam and complexing agent, respectively. Note (a) that Io does not include any kinetic parameter for the preceding chemical step and (b) that I Oand k , are formal kinetic parameters depending on the double layer structure (Frumkin). For correction of the double layer effect, see a previous paper from this Laboratory.6 By combination of eq. 3 with eq. 2, as written in terms of Eo and K , one obtains in the same fashion as in a previous paper7
where C,O is the bulk concentration of >iY,+(" - y 5 ' . This is the general current-potential equation for processes with preceding reaction 1. The concentrations C, and Ca of eq. 4 will be derived from the Fick equation modified for the occurrence of the preceding step of eq. 1. This approach is (5) For an analysis of polarographic waves c j . H. Matsuda, unpublished investigation. (6) M. Breiter, M. Kleinerman and P. Delahay, THIS J O U R N A L , 80, 5111 (1958). T. Berzins and P. Delahay, ibid., 71, 6448 (1955). See refer(7) ences therein.
AND
Af. KLEINERMAN
VOl. s1
based on the ideas originally developed by Koutecky and Brdickaa in their classical paper on polarographic kinetic currents. I t will be assumed that (a) the reaction site is a t x = 0, x being the distance from the electrode; (b) there is practically no concentration polarization of Y; and (c) the overvoltage, E - E,, except for the potentiostatic method, does not exceed a few millivolts. Equation 4 then can be linearized in terms of E by expansion in series of the exponentials. Thus C,. C, n F I = l o [c"o - --Go - -RT ( E - E,)] (Fj) for (E - E e ) > kt,Cyo(fi - u ) . In the first case Z,= 0 and the component
is independent of frequency. Ry comparison of Z r from eq. 9 with (RT/nF)(l/lo)of eq. 8 one can readily establish conditions under which 2, is negligible a t low frequencies. This case can be encountered since one easily has k b = lo8 set.-' mole-' 1.) cf. the case of cadmium cyanide discussed below) and Cyo = 0.1 mole l.-I, ie., for p - v = 1,w > kbCyo(* - u,
(8) J. Koutecky and R. Brdicka, Collection Csechoslou. Chem. Comm u m . , 12, 337 (1947). (9) H. Gerischer, Z. physik. Chem., 198, 286 (1951); 201, 55 (1952).
Dec. 20, 1959
DISCHARGE OF METALI O N
COMPLEXES WITH PRECEDING
and l/wc, is given by eq. 7 in which 2, is made equal to zero and the term in l/wl/z is the same as in eq. 10. Note that the term in l/Cpo in eq. 10 is practically l/C,OD'/2, i.e., rs a t sufficiently high frequencies depends on the equilibrium concentration of the discharged species and not on the kinetics of reaction 1. For l / w l / p --t 0, rr = (Rl'/nF). (1/10),e.g., rs solely depends on the exchange current when w += -. The influence of the kinetics of reaction 1 progressively decreases with increasing frequency, i.e., with decreasing ~ / L J ' / ~ . The foregoing analysis accounts for certain not yet fully explained observations on faradaic impedance. For instance, G e r i ~ c h e rfound ~ ~ it necessary to use very high salt concentrations ( 5 M sodium chloride) in measurements on the discharge of Cd(CS)c-- and Cd(CX)a- on a cadmiumamalgam electrode. Discharge of Cd( CN)4-- is preceded by transformation6v10 into Cd(CN)3-. Dissociation into Cd( C S ) ?also is observed'' a t sufficiently low cyanide concentrations. The rate of formation of Cd(CN)a- and/or Cd( C S ) 2increases with the foreign salt concentrations~I0 because kb( C y o ) P - y of the double layer effect, m d the conditio11 o is fulfilled at relatively low frequencies in 5 M sodium chloride. Furthermore, the chemical contribution is then quite negligible. Galvanostatic Method.-The exchange current in this method is determined from potential-time curves observed a t constant cell current in unstirred solution. An analysis was reported' previously for potential-time curves for direct discharge in which the effect of the capacity current (charging of the double layer) was considered. This correction for the capacity current also holds here. The concentrations C, and C, in eq. 5 are known from the Sand equation'* and a previous paper13 from this Laboratory. Thus ( K
