KINETICSOF
March 5, 1964 [CONTRIBUTION FROM
THE
THE
OXIDATION OF CHROMIUM(II) BY IRON(III)
829
CHEMISTRY DEPARTMENT, BROOKHAVEN NATIONALLABORATORY, UPTON, NEW YORK]
The Effect of Chloride Ions on the Kinetics of the Oxidation of Chromium(I1) by Iron(1II)l BY G. DULZAND N. SUTIN RECEIVEDOCTOBER4, 1963 The kinetics of the oxidation of chromium(I1) by iron(II1) in the presence of chloride ions have been investigated by the use of flow techniques. Since the formation of FeClz+ from Fe3+ and C1- proceeds relatively slowly, it proved possible to estimate the rate constants for the various chloride-catalyzed paths by adding chloride to only the chromium(I1) solution on the one hand, and to both the chromium(I1) and iron(II1) solutions on the other. The results are consistent with the rate law: R = k1(Cr2+)(Fe3+) k2(Cr2+)(FeOH2+) ka(Cr2+)(FeCI2+) ks(Cr2+)(Fe3+)(C1-)where R is the rate of the oxidation-reduction reaction and kl = 2.3 X l o 3 F-' sec.-l, k2 = 3.3 X lo6 F-' sec.-l, k d = 2 X lo7 F - l sec.-I, and kb = 2 X lo4 F - 2 set.-' a t 25.0' and ionic strength 1.00 F. It was found t h a t CrCI2+ is produced in both chloride-catalyzed paths. The natures of these two paths are discussed.
+
+
+
The products of the reaction were separated chromatographiThe chloride-catalyzed oxidation of chromium(I1) ally.^ Aliquots of the reaction mixture were withdrawn from the by iron(II1) has been studied by Taube and Myers2 stopping syringe and added to a Dowex 50W-X8 cation-exchange and by Ardon, Levitan, and T a ~ b e . Taube ~ and column. The (H20)aCrC12+and C ~ ( H Z O )were ~ ~ +eluted with 1 F Myers found t h a t both (H20)5CrCl2+and C r ( H ~ 0 ) 6 ~ + and 3 F perchloric acid, respectively, and the chromium( 111) in the fractions was determined as described elsewhere.s were produced in the oxidation and that their relative amounts depended upon the chloride and hydrogen ion concentrations of the solutions. They proposed Results that the (H20)6CrC12+arose from the reaction of (H2Order of the Reaction.-The chromium(I1)-iron(II1) O)sFeC12+ with C r ( H 2 0 ) 6 2 +and t h a t this reaction reaction was found to be first order with respect to each proceeds via an inner-sphere activated complex conof the reactants. Plots of log [6(a - x ) / a ( b - x)] us. t , taining a Fe-C1-Cr bond. This interpretation has where a and b are the initial concentrations of the reacbeen questioned by Zwickel and T a ~ b e . By ~ studying tants and x is the concentration of product a t time t, the chloride-catalyzed oxidation of Cr(H20),?+ by gave straight lines. The values of the second-order Fe(Hs0)63+a t -SOo, where the formation of (H20)6rate constants in 1.00 F HClOd a t 25.0", calculated FeC12+ from Fe(H20)63+and C1- proceeds relatively from the slopes of these lines, are presented in Table slowly, Ardon, Levitan, and Taube have shown reI . Individual determinations of the rate constants cently that (H2O)5CrCl2+ is produced even when differed from the mean by less than 5%. The aver(H20)5FeC12+is not present prior to the reaction. age of the values presented in Table I is (7.7 0.1) However, they did not study the oxidation of CrX lo3 F-l sec.-l. (H20)62+ by (H20)5FeC12+or identify the products of this reaction. We have studied the kinetics of the TABLE I oxidation of chromium(I1) by iron(II1) in the presence of chloride ions a t 25.0' and find that the chlorideTHEORDEROF THE CHROMIUM(II)-IRON(III) REACTIONIN catalyzed reaction proceeds via two paths a t this 1.00 F PERCHLORIC ACIDAT 25.0" temperature; one of these paths involves (H20)b[cr(r1)1 x 104, [ F e ( I I I ) I X 105, k X 10-8, FeC12+ as a reactant and the other does not. The F F F-1 sec. -1 former reaction is very rapid and both paths produce (H20)5CrC12 +. 1 78 6.51 7 8
*
Experimental Chemicals.-Thallous perchlorate and sodium perchlorate were prepared as described elsewhere.6 Iron( 111)perchlorate ( G . Frederick Smith Chemical Co.) and chromium( 111) perchlorate (Amend Drug and Chemical Co.) were purified b y recrystallization from perchloric acid. Solutions of chromium(I1) in perchloric acid were prepared by electroreduction of the chromium(111) a t a lead cathode.6 Perchloric acid (70%, Baker Analyzed Reagent) and hydrochloric acid (38%, Baker and Adamson) were used without further purification. The reactant solutions were prepared with triple distilled water in a n argon atmosphere (General Dynamics, N. Y.). The argon was purified by passing it through an activated copper column a t 120' ( B T S catalyst, Badische Anilin-und Soda-Fabrik AG, Ludwigshafen am Rhein, Germany). The chromium( 11) solutions were standardized by adding aliquots to excess thallium(II1) in 2 F hydrochloric acid and determining the thallium( I ) produced by a coulometric method.' Procedure.-The kinetics were studied by the use of the flow apparatus which has been described previously.* The disappearance of iron( 111) was followed spectrophotometrically; wave lengths of 336 mp and of 260 to 300 mg were used to observe the FeCIZ+and Fe3+,respectively. (1) Research performed under the auspices of t h e U. S Atomic Energy Commission. ( 2 ) H. Taube and H . Myers, J. A m Chem. S o c . , 76, 2103 (1954). (3) IM Ardon, J. Levitan, and H Taube, i b t d . , 84, 872 (1962). (4) A. M . Zwickel and H. Taube, ibid., 83, 793 (1961). ( 5 ) G. Dulz, Ph.D. Thesis, Columbia University, Kew York, N. Y., 1962. (6) R. F l a t t and F. Sommer, Helu. Chzm. A d a , 26, 684 (1942) (7) R . P. Buck, P. S . Farrington, and E . H. Swift, A n a l . Chem., 24, 1195 (1962). (8) G. Dulz and N. Sutin, I n o r g . Chem., 2 , 917 (1963).
1 94 3 73 3 93 9 27 9 27 9 27 9 27 9 40 9 43 9 75 18 9 19 0 19 0 19 1 28 4 37 3 38 8 38 9
6.51 6.51 6.51 6.51 13.0 26.0 52.0 6.51 26.0 3.25 6.51 6.51 6.51 3.25 3.25 3.25 7.51 6.51
7 7 7 7 7 8 7 7 7 7 7 7 7 7 7 7 7 7
8 7 9 3 6 2 9 7 6 6 4 7 5 6 4 7 5 5
The Effect of Acid.-The effect of acid on the reaction was studied in mixtures of sodium perchlorate and perchloric acid a t a total ionic strength of 1.00 F . The results are consistent with the rate law
+
R = kl(Cr2+)(Fe3+j kz(Cr2+)(FeOH2+)
(1)
Since K h , the equilibrium constant for the hydrolysis (9) J. A. Laswick and R . A . Plane, J . A m . Chem. Soc., 81, 3564 (1959).
G. DULZAND N. SUTIN
830 reaction Fe3+
- d(FeCIZ+)= -k3(Fe3+)(C1-) dt
+ HzO e FeOH2+ + H + =
ki i- kzKh/(H+)
(2)
where k = R/(Cr2+)[Fe(III)]. The value of Kh is a t 25.0' and ionic strength 1.00 F.l0 1.69 X We have plotted k as a function of l / ( H + ) in Fig. 1.
where k4 is the rate constant for the reaction of ( & 0 ) 6 FeC12+ with Cr2+. Preliminary experiments in which chloride was added to both the chromium(I1) and iron(111) solutions on the one hand [(Hz0)6FeC12+ present a t its equilibrium concentration prior to the oxidationreduction reaction], and to only the chromium(I1) solution on the other [no (H20)5FeC12+present initially], established that the reaction of Cr2+with (H20)6FeC12+ proceeded much more rapidly than any other oxidation-reduction reaction in the system and t h a t it also proceeded much more rapidly than the formation and dissociation of (H20)sFeC12 +. Cnder these conditions eq. 4 reduces to d( FeC12 t, -_ __ dt
0' 0
I
I
10
5
I I
15
I / ( H +I, F - I Fig. 1.-Effect
of acid on the rate of the chromium(I1)-iron(II1) reaction a t 25.0".
From the slope and intercept of Fig. 1 we calculate t h a t k l = (2.3 0.2) X lo3 F-' set.-' and k2 = (3.3 f 0.3) X 106 F-l sec.-l at 25.0" and ionic strength 1.00 F . The Effect of Chloride.-In order to determine the effect of chloride on the kinetics of the chromium(I1)iron(II1) reaction, it is necessary first to consider the rate of formation and dissociation of (Hz0)6FeC12f. Connick and Coppelll have studied these reactions and have calculated values of k3 and k-3 defined by the equation
+ C1-
k3
Fe(H20)b3+
(H20)bFeC1z't k..
+ kLa(FeC12+) + ka(FeClz+)(CrzC) (4)
is < ( H + ) , we obtain k
Vol. 86
(3)
a
using a value of K3 determined by Rabinowitch and Stockmayer. l 2 We have reanalyzed their data using the value of K3 determined recently by Woods, Gallagher, and King"3 and obtain k3 = 19.4 F-' sec.-l and kL3 = 6.7 sec.-l a t 25.0' and an ionic strength of 1.00 F.I4 I t should be noted that k3 and kL3 are overall rate constants and include the contributions of the acid-dependent paths. In the presence of chromium(I1) the rate of disappearance of (H20)sFeCl2+is given by the expression (10) R . 51 51ilburn and W C Vosburgh, J . A m . Chem Soc., 7 7 , 1352 ( 19.5.5
(11) R E. Connick and C. P Coppel. ibid., 81, 6389 (1959) (I?) E Rabino'witch and W . H . Stockmayer, ibid., 64, 33.5 (1942) (13) Sr 51 J hl Woods, P K Gallagher, and E L. King, I n o r g . Chem , 1 , 5 5 (1962) ( 1 4 ) T h e values of ks which we determined in the course of these studies are in excellent agreement with those obtained b y Connick and Coppel.
=
k~(FeClz+j(CrZtj
(5)
Consequently, the reaction of C r 2 +with ( H ~ 0 ) 6 F e C 1 ~ + could be followed directly a t 336 mp, where (HL0)5FeC12+ is the only absorbing species. The concentrations used in these studies were: [ F e ( I I I ) ] = 2.79 X 10-j F,[Cr(II)] = 5.20 X 10-j F and 3.52 X 1 0 - 5 I;, (HC1) = 0.10 F , and (HC104) = 0.90 F The value of k4 was found to be 2 X lo7 F-I set.-' a t 25.0' and ionic strength 1 00 F . I t is readily seen that under the above conditions k4(FeCl2+)(Crz+) >> k-3(FeC12+) and k4(FeC12T)(Cr2T)= 10k3(Fe3-)(C1-) even after 90yo of the FeC12+ has reacted, as is required for eq. 5 to be valid. If the chloride is added to only the chromium(I1) solution and if there is a chloride-catalyzed path which does not involve (H20)5FeC12+ as a reactant, the rate of disappearance of Fe(II1) is given by the expression - d[Fe(lll)' dt
=
+ kz(Cr2+)(FeOH*')+ k3(Fe3+)(C1-)+ k6(Fe3+)(C1-)(CrZ+)( 6 )
k,(Crz-)(Fe3t)
where the steady-state approximation for the concentration of (H20)6FeC12+ has been made. Provided [Cr(II)] >> [Fe(III)] and (Cl-) >> [ F e ( I I I ) ] , a pseudo-first-order rate constant for the reaction can be defined as k = [kf ~ k d h / ( H + j -k kb(C1-)](CrZt) -t ka(CI-) ( 7 )
The disappearance of iron(II1) was followed using wave lengths in the range 260 to 300 mp and values of k were calculated from these measurements. These values are plotted in Fig. 2 as a function of the chromium(I1) concentration a t chloride concentrations of 0.05 and 0.10 F. It is seen that the data satisfy eq. 7 reasonably well. From the slopes of these lines we calculate that k5 = (2.2 i 0.4) X 104 F-2 set.-' a t 25.0' and ionic strength 1.00 F. These measurements thus provide evidence for a chloride-catalyzed oxidationreduction path which does not involve (HzO)5FeCl2+ as a reactant. Evidence for such a path a t -50' has been obtained previously by Ardon, Levitan, and Taube.3 In order to determine the chemical form of the chromium(111) produced in the oxidation-reduction reactions, the products in the following reaction mixtures were investigated: (a) [ C r ( I I ) ] = 2.0 X 1 0 P 4 F , [ F e ( I I I ) ] = 1.04 X 10-* F, (HC1) = O.Oi3 F, (HC104) = (1 925 F; chloride initially in both the chromium(I1) and iron(II1) solutions (b) [Cr(II)] = 4.7 X 1OY3F , [Fe(III)] = 1.04 X lo-? F,(HCl) = 0.075 F , (HC104) = 0.925 F; chloride initially in only
KINETICS OF
March 5 , 1964
THE
OXIDATION OF CHROMIUM(II) B Y IRON(III)
the chromium(I1) solution. It was found that the chromium(II1) species produced in reaction a consisted of 99% CrC12+ and 1% Cr3+ while those produced in reaction b consisted of 31% CrC12+and 69% Cr3+. Since (FeC12+) >> (Cr2+) in reaction a , and if it is assumed that the reaction of FeC12+ with C r Z + produces only CrC12+,it follows that
Substitution in eq. 8 of the rate constants determined above gives (CrClz+)/[Cr(III)] = 0.998, which is in excellent agreement with the observed value of 0.99. If i t is assumed t h a t the reaction path involving Cr2+, Fe3+, and C1- (but not FeC12+) also produces only CrClZ+,and if a steady-state assumption for the concentration of FeC12+ is made, the yield of Cr3+ in reaction b is given by
In
[kdcl-)
+ (ki 4-kzKh/(H+) f k d C 1 - ) ] ( C r 2 + ) d k d C1-1
4- (H20)6CrClf+ [( H*O)sFeH20-Cl-Cr( H20)5]
+
or
[( H20)5FeHz0-CrC1(Hz0)4] 4+
+
+
Fe(H20)gZ+ ( H Z O ) ~ C ~ C(12) ~~+
It is not possible t o distinguish between these two formulations on the basis of the evidence available a t present. In order to account for the formation of (H20)6CrC12+, reaction 11 would have to proceed via an (outer-sphere) activated complex in which the chloride was bonded directly to the chromium. Since Fe(Hz0)63+ does not undergo. substitution readily, it is likely that reaction 12 also proceeds via an outersphere complex, although the possibility of a waterbridged inner-sphere activated complex, with chloride acting as a nonbridging ligand, cannot be ruled out. I
I
I
I
I
(9)
where (Cr2+)ois the initial concentration of chromium(11). Equation 9 predicts that the yield of (Cr3+) should be 7 3 f 395, which is in satisfactory agreement with the observed value of 69y0. If it is assumed t h a t the reaction path involving Cr2+, Fe3+, and C1- does not produce CrC12+, then the yield of CrC12+ should be 12%, which is much lower than the observed value. The value of (Cr3+)/[Cr(III)]was also calculated by numerical integration on an IBM 7094 computer without making the steady-state assumption for the FeCIZ+ concentration. The ratio calculated by this procedure agreed within 0.1% with that given by eq. 9.
Discussion It is evident that the chloride-catalyzed reaction proceeds via two paths and that (H2O)&rCl2+ is produced in each of these paths. There does not appear to be much ambiguity concerning the reaction involving (Hz0)6FeCI2+, this path very probably proceeds via an inner-sphere activated complex as originally proposed by Taube and Myers (H20)jFeC12f
Fe(H20)2+
831
I
0
I
I
I
2 (Cr2+) x IO', F
3
4
Fig. 2.-Effect of chloride on the rate of the chromium(I1)-iron(111) reaction a t 25.0'; [Fe(III)] = 3.25 X F.
For purposes of comparing the rates of the two chloride-catalyzed oxidations, k4 may be converted to a third-order rate constant by multiplying it by Ka. We then obtain Ra = 6 X 107(Fe3")(C1-)(Cr2') F s e c . - '
for the rate of the chloride-catalyzed oxidation involving (H20)6FeC12+as a reactant (provided the equilibrium TABLE I1
+ C r ( H Z 0 ) 2 +-+ [ ( H Z O ) ~ F ~ - C ~ - C ~ ( H( +Z--f O)~] Fe(HzO)s2+ (H20)XrC12+ (10)
+
It is of interest that the ratio of CrC12+ to Cr3+ produced in this inner-sphere path is much higher than that calculated by Taube and Myers. The reason for this discrepancy lies in the fact that reaction 10 proceeds much faster than the formation of (H20)6FeC12+from Fe(H20)63+ and C1- under the conditions used by Taube and Myers. The nature of the second chloride-catalyzed path is less certain. Two formulations which are consistent with the rate law are
+
( H z O ) ~ F ~ ~ + C ICr(Hz0)e2+ + [(HZO),F~HZO-CI-C~(H (+ Z--+ ~)~] Fe(H20)e2+ (H20)jCrCl2+ (11)
+
(15) H . T a u b e , personal communication. I t should be noted that the value of ka did not become available until 1959.
COMPARISON OF
RELATIVERATE CONSTANTS FOR THE CHROMIUM(II)-CHROMIUM(III), CHROMIUM( II)-IRoN( III), A N D IROh'(II)-IROS(III) REACTIOSSAT 25.0' THE
7
Cr2 *Cr"'( H20)aX
X
Hz0 OH -
1 >8 X > 2 x 106b
c1-
Relative rate constants--CrZ Fe"'(Hz0)aX ?-
1 1 . 4 x 103 1 x 104
Fez Fe"'(Hz0)aX + -
1 1.1 x 1 0 3 ~ 6 2d
a A. Anderson and X. A. Bonner, J . A m . Chem. Soc., 7 6 , 3826 (1954). * D. L. Ball and E. L. King, ibid., 80, 1091 (1958). J. Silverman and R . W. Dodson, J . Phys. Chem., 56, 846 (1952). N. Sutin, J . K. Rowley, and R. W. Dodson, ibid.,65, 1248 (1961).
between Fe(HzO)a3+and C1- is maintained). The rate of the chloride-catalyzed oxidation which does not involve (Hz0)6FeC12+is given by Rs
= 2 X 104(Fe3+)(CI-)(Cr2+) Fsec.-'
832
G. DULZAND N. SUTIN
The path involving (H20)6FeC12+as a reactant thus proceeds about 3000 times faster than the chloridecatalyzed path which does not. These results provide additional support for Taube's conclusion that substitution in the inner coordination shell of the iron(III) is a requirement for marked chloride catalysis.16 The relative rate constants for the Cr(I1)-Fe(III), and Fe(lJ)-Fe(lll) reactions are 'Omcr(11)-cr(111)3
(16) H Taube, Advan Inovg C k e m R a d t o c k e m . , 1, 34. (1959).
Vol. 86
pared in Table 11. It will be seen that chloride has a larger effect than hydroxide on the rates of the Cr2+Cr(III) and Cr2+-Fe(III) reactions but not on the rate of the Fez+-Fe(II1) reaction. I t is of interest that the relative rate constants for the Cr2+-Fe(II1) reactions lie between those for the two electron exchange reactions. Acknowledgment.-It is a pleasure to acknowledge helpful discussions of this problem with Drs. R. W. Dodson and H. Taube.
