Kinetics of dissociation of ferric chloride complexes. Stability constants

2801

Kinetics of Dissociation of Ferric Chloride Complexes

(16) J. Kirkwood and J. Shumaker, Proc. Natl. Aced. Sei. U.S.A., 38, 863 (1952). (17) C.Tanford, "Physical Chemistry of Macromolecules", Wiley, New York, N.Y., 1961. (18) 8. Schoenborn, R. Featherstone, P. Vogelhut. and C. Suskind, Nature (London), 202, (1964). (19) C. Pyun and M. Fixrnan, J. Chem. Phys., 41, 937 (1964). (20)R. Simha, J. Appl. Phys., 23, 1020 (1952). (21) P. Cheng and H. Schachman, J, Polym. Sci., 16, 9 (1955). (22) G. Phillies, Sc.D. Thesis, M.I.T., 1973, unpublished. (23) S. Broersma, J. Chem. Phys., 28, 1158 (1958).

E. Hegesh and N. Gruener, Clin. Chem. Acta, 36, 679 (1970). D. Koppel, J. Chem. Phys., 57, 4814 (1972). R. Briehl and S. Ewert, J. Mol. Biol., 60, 445 (1973). P. Tartaglia and S. Chen, J. Chem. Phys., 58, 4389 (1973). J. Peterson and M. Fixrnan, J. Chem. Phys., 39, 2516 (1963). S. Rice and P. Gray, "Statistical Mechanics of Simple Liquids", Interscience, New York, N.Y., 1965. G. Adair, Proc. R. SOC.London, Ser. A, 120, 573 (1926). G. Scatchard, J. Am. Chem. SOC., 68, 2315 (1946). V. Riveros-Moreno and J. Wittenberg, J. Biol. Chem., 247, 895 (1972). K. Keller, E. Canales, and S. Yum, J. Chem. Phys., 75, 379 (1971).

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Kinetics of Dissociation of Ferric Chloride Complexes. Stability Constants of Inner- and Outer-Sphere Complexes H. A. Schwarz" and R. W. Dodson Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973 (Received June 10, 1976) Publication costs assisted by Brookhaven National Laboratory

The inner-sphere complex FeC12+ is selectively produced by the reaction of thallium(I1) chloride with Fe(I1) in pulse radiolysis experiments. The approach to equilibrium of this system indicates that at 25 "C and 1 M ionic strength the equilibrium mixture contains an appreciable component of the outer-sphere complex, Fe3+,C1-. The equilibration mechanism is Fe3+ C1- + FeC12+ (Kin = k J k - l ) , FeC12+ t C1- * {FeC12)+ ( K z ) ,Fe3+ C1- + Fe3+,C1- (KO,,), Fe3+,C1- C1{FeC12)+(K4 = h d h - 4 ) . It is found that Kin = 3.0 M-l, KOut= 2.2 M-l, K P= 1.3 M-l, k-1 = 7.3 s-l, and k-4 = 5.3 s-l. An interpretation of published data indicates that the extinction coefficient of F e C P varies only slightly with ionic strength and that Koutis also nearly independent of ionic strength between 1and 4 M while K,, increases by a factor of 5 in this range.

+

The equilibrium constant of the reaction Fe3+

+ C1- -+{FeC1J2+

where (FeC1I2+includes both inner- and outer-sphere complexes, increases markedly with ionic strength. It has been assumed that any outer-sphere complex effects in this reaction are negligible.1,2Information on the relative contributions of inner- and outer-sphere complexes can be obtained from the effects of Fe3+ and C1- concentrations on the rate of approach to equilibrium. The kinetic results a t 6 M2 and 9 M3 ionic strength do not require any outer-sphere complex. Kinetic data at 0.6 M ionic strength4 were interpreted as requiring approximately equal proportions of the two complexes a t equilibrium. The oxidation of iron(I1) by thallium(I1) chloride complexes selectively produces inner-sphere F e C P a 5The kinetics and the ratio of initial and final absorbances found for the approach to equilibrium at 1M ionic strength are reported here. They demonstrate the importance of outer-sphere complexes at 1 M ionic strength. Experimental Section The materials and the preparation of solutions were as described b e f ~ r e .The ~ , ~concentrations in the reaction mixture containing thallium were 2.5 X M TI(III), 1.00 X lop3 M Tl(I), and 1.00 X 10-3 M Fe(I1). The Fe(I1) concentrations in reaction mixtures without thallium were either 5.1 X low3or 10.2 X 10-3 M. All solutions contained 1.00 M acid.

+ +

The anions present were C104- and C1-. The solutions were deaerated with argon. The pulse radiolysis equipment and thermostat were described earlier.5,6A deuterium arc was used as the light source, and absorbances were measured at 340 nm (near the F e C P peak) except as otherwise noted. The optical path length was 6.1 cm. The reaction mixtures were a t 25.0 "C when pulsed. The dose delivered in each pulse produced 1.8 X M Fe(II1) in solutions containing thallium. A higher dose, producing 15 X 10-6 M Fe(III), was used for solutions not containing thallium. Results The pulse radiolysis of solutions containing thallium and chloride produces Tl(I1) by Cl2- oxidation of Tl(1) and hydrogen atom reduction of Tl(II1). The Tl(I1) rapidly equilibrates with chloride to form complexes.6 All forms of Tl(I1) oxidize Fe(I1) to Fe(II1) but its higher chloride complexes produce exclusively inner-sphere FeC12+.5 All reactions of Tl(I1) are complete in s, leaving a solution with F e C P present at a concentration exceeding the equilibrium concentration. In the subsequent approach to equilibrium, the absorbance of the solution is observed to decay by first-order kinetics, that is: A=

(A0

- A,)e.-kt

+A,

(1)

The blank against which the absorbance is measured is the solution just before the radiation pulse. The half-life of this The Journal of Physical Chemistry, Vol. 80, No. 25, 1976

2802

H. A. Schwarz and R. W. Dodson

decay is less than 0.1 s. There is also a slow production of Fe(I11j by


2Fe(II)

+ H202 + 2H+

-

2Fe(III)

TABLE I: Rate Constants and Final to Initial Absorbance Ratios for Ferric Chloride Approach t o Equilibrium in 1 M Acid Solutions at 25 “C

+ 2H20

This reaction contributes less than 20% of the total Fe(II1) and its half-life is 12 s under our experimental condition^.^ Consequently its effect is negligible. The absorbance of the solution was followed for a t least 3 half-lives. The parameters Ao, A , , and k were evaluated by a least-squares fit of the data to eq I. The standard deviations of the observed absorbances from the calculated values were less than fO.OOO1 absorbance unit, or generally about f 0.5% of the initial absorbance. Four pulses were given to each sample. The initial and final absorbances decreased by about 3% with each pulse. This effect is largely due to the back reaction of Tl(I1) with FeC12+.The rate constant, k , should be independent of this reaction, and R , the ratio of A , to Ao, is expected to be much less sensitive to number of pulses than A()and A Indeed, there was no discernible effect of number of pulses on either k or R. Values of k and R are given in Table I. We have found that inner-sphere FeC12+ in excess of the equilibrium amount can also be produced in the absence of thallium by the reaction of Clz- with Fe(I1). Jayson et a1.,8in a pulse radiolysis study of deaerated solutions containing Fe(I1) and C1-, did not observe any slow decay attributable to FeC12+. Their Fe(I1) concentration was a factor of 10 smaller than ours, and it is likely that hydrogen atoms reduced the FeC12+product instead of reacting with Fe(I1). Table I includes some rate constants measured in the absence of thallium. The amount and rate of Fe(I1) oxidation by the hydrogen peroxide produced during the radiation pulse were measured separately by following the absorbance change of the solution between 1and 5 s after the pulse. The contribution of the hydrogen peroxide reaction to the absorbance change during the FeC12+relaxation is not negligible in this case, primarily because of the higher Fe(I1) concentration. The data were corrected for the hydrogen peroxide effect before fitting to eq I. Rate constants calculated without this correction were 3 to 10% higher than those tabulated. Values of R (Le., A,/AO) for the ferrous solutions without thallium were higher than those in the presence of thallium by a factor of about 3. This effect is expected, as the pathway forming FeCIz+ in the system is only one of several modes of production of Fe(II1). The values of R were also scattered, probably because of reaction of hydrogen atoms with FeC12+or with traces of oxygen in competition with the slow reaction

0.0100 b

0.0100c 0.0172 0.0441 O.050b

+ Fe(I1) + H+

-

H2

+ Fe(II1)

Discussion The rate constants for the approach of FeC12+to equilibrium, given in Table I, do not increase linearly with chloride concentration, as would be expected if a single inner-sphere complex were involved. The curvature of such a plot is negative, whereas participation of a second inner-sphere complex, FeC12+,would produce positive curvature. Furthermore, the ratio of the initial slope to intercept is 2.2 M-l. If the outersphere complex were negligible in comparison to the innersphere complex, then the slope would be expected to be 5.2 M-l, the stability constant for monochloro Fe(II1) species.2 We will discuss the results in terms of the following reactions: Fe3+

+ C1- + FeC12+ (slow)

Kin = k l / k - I

The Journal of Physical Chemistry, Vol. 80, No. 25, 1976

(1)

0.50 0.58

0.040 0.049

0.030 0.042

0.70

0.85

0.074 0.132

0.069 0.133

0.93 0.93 0.93 0.93

0.218 0.213 0.210 0.213

0.216 0.216 0.216 0.216

0.99

0.443 0.590 0.666

0.438 0.585 0.668

8.1 8.2

0.O5Oc 0.08gd 0.089 0.08ge 0.090

8.7 8.7 8.6 8.9 9.1 9.2 12.0 15.4 17.4

0.100b 0.1ooc

0.300 0.600 0.900

g.

H

7.4 7.5 7.3 7.4 7.7 8.1

0.0051

0.0082

1.00

1.00

I’ The fraction of Fe(II1) produced as inner-sphere chloride complexes. No thallium present, 5 X 10-3 M Fe(I1). c No thalM Fe(I1). 320 nm. e 370 nm. lium present, 1 X

+

FeC12+ C1Fe3+

+ C1-

Fe3+,C1-

KZ

(FeC12)+(fast) Fe3+,C1- (fast)

(2) (3)

+ C1- + (FeClZ}+(slow)

(4)

Only three of the four equilibria are independent, as is noted by expressing K4 in terms of the others. FeC12+is the innersphere complex and Fe3+,C1- is the outer-sphere complex. The symbol (FeC12)+represents the sum of the inner-inner complex, FeC12+, and the inner-outer complex, FeC12+,C1-, assumed to be in rapid equilibrium. Mechanistically, reactions 2 and 4 probably involve only FeC12+,C1- and could be written

+

FeC12+ C1Fe3+,C1-

FeC12+,C1- (fast)

+ C1- + FeC12+,C1-

(2f)

(slow)

(4’)

FeC12+,C1- + FeClZ+ (fast)

+

(5)

+

from which K2 = Kz’(1 K5) and k-4 = kP4’/(1 K 5 ) .Reaction 2’ is an ion pair formation and will be diffusion limited. Reaction 4’is similar to reaction 1with just the addition of a chloride in the outer sphere. Consequently it is reasonable to expect it to be slow. Reaction 5 is assumed to be fast by analogy with the corresponding reaction of FeOH2+,C1-.Y By “fast” is meant equilibrium is established in less than 0.01 S.

Hydrolyzed species are present in small proportions. Consequently the equilibrium constants and particularly the rate constants (which are strongly acid dependent1,2)are composite constants. Such effects do not influence the interpretation of the data inasmuch as all experiments were performed a t constant acid concentration. The ratio of final to initial absorbances, R , is determined by the first three equilibria. If it is assumed that the innersphere complexes are solely responsible for light absorption in this region, then

Kinetics of Dissociation of Ferric Chloride Complexes

where f is the fraction of the total iron species formed as inner-sphere complexes. For solutions containing thallium, f can be calculated from5


0.37 X 104[C1-] + 2.4 X 107[c1-]2 + 2.3 x 109[C1-]3 + 1.7 x 1010[C1-]4 f= 0.67 + 5.6 X 104[C1-] + 5 X 107[c1-]2 + 2.3 X 109[C1-]3 + 1.7 X 1010[C1-]4 which is the ratio of the rate at which Tl(I1) reacts with Fe(I1) to produce F e C P to the total rate of production of Fe(II1). The value off is near one for most of the chloride concentrations used here (as may be seen from Table I). Note that eq I1 does not contain extinction coefficients. This is the result of assuming only inner-sphere complexes absorb light. In other words, R should be wavelength independent. This is tested a t three wavelengths, shown in Table I. There is perhaps a slight increase in R a t shorter wavelengths, as might be expected if Fe3+,C1- is absorbing light with the peak of its spectrum further out toward the UV. Equation I1 can be rearranged to

y = Kj,

+ KInK2[C1-](1 - R f )

0.I

0

0.2

0.3

[CI-] ( I - R f ) Figure 1. Test of eq 3 which expresses the chloride dependence of the ratio of final to initial absorbances. Ionic strength is 1 M, temperature

25

‘C.

(111)

+

where y = Rf{1 (Kin + Kout)[C1-])/[C1-].The sum Kln + K,,Ut is 5.2 M-l at 25 “C and 1 M ionic strength.2 A plot of y vs. [Cl-](l - R f ) is shown in Figure 1,from which K,, = 3.0 M-l, K2 = 1.3 M-l, and Kout = 2.2 M-l (by difference). Values of R computed from eq (11) with these stability constants are given in Table I for comparison with the observed results. Note that two points at the lowest chloride concentration are not included in Figure 1. The nature of the function y is such as to grossly overemphasize the experimental errors a t these concentrations. Also, reaction of chlorine atoms with Fe(I1) and back reaction of Tl(I1) with F e C P would cause the method of computing f to yield values which are too large. Such effects become negligible a t higher chloride concentrations. The effects of several assumptions merit consideration: (i) The above mechanism does not include a complex with two outer-sphere chlorides, Fe3+,2C1-. If such a complex is included and assumed to have negligible absorbance, then y = K,,

+ KInK2[C1-][1- Rf(1 + r ) ]

where r is the ratio of Fe3+,2C1- to {FeC12)+.The data preclude a value of r greater than 0.2. The intercept, K,,, is not significantly affected by any r , but if r is chosen as 0.1, for instance, Kz would be calculated to be 1.5 M-l. (ii) The inclusion of a finite extinction coefficient for Fe”+,Cl- leads to a lower estimate of Kin. For instance, a choice of 200 for e(Fe3+,C1-) would result in an estimate of 2.8 M-l for Kin. (iii) I f f is assumed to be 1a t [Cl-] > 0.04, K,, would be estimated as 3.3 M-l. It should be noted that Kz is defined for the formation of (FeCl# from FeC12+.The more usual definition of the second stability constant would be K2’ =

I(FeC121+1 {[FeClZ+] [Fe3+,Cl-])[Cl-] or Kz‘ = K2Ki,/(Kin Kout),which is 0.8 M-I (but still does not include any outer-outer, or Fe3+,2C1-, complex). The estimate of K2 from the slope of the line in Figure 1 will be influenced by any medium effect due to the replacement of

+

+

31-

1

-4

p/

0 Flgure 2,Test of eq 5 which expresses the chloride dependence of the rate constant k. Ionic strength is 1 M, temperature 25 ‘C:(0)thallium present, ( 0 )thallium absent.

C104- by C1-. Such an effect is of much less consequence in estimating the intercept, Kin. The value of 0.8 M-l for Kz’ agrees well with the conclusion of Rowley and Sutin that Kz’ is about 1 M-1.2 Reactions 1to 3 do not suffice to explain the chloride variation of k . Reaction 4 offers an additional pathway for introducing or removing chloride from the inner coordination sphere. Reactions 1 to 4 lead to the following expression for the rate constant for approach to equilibrium: 1

1

+ Kz[C1-]

In deriving this equation it was assumed that pseudo-firstorder kinetics apply, which will be the case if either [Fe(III)] >> [Cl-] or [Cl-] >> [Fe(III)].The latter is true in our experiments, so k / q = 12-1

+ k-&2[Cl-]

(VI

The Journal of Physical Chemistry, Vol. 80, No. 25, 1976

2804

H. A. Schwarz and R. W . Dodson

TABLE 11: Ionic Strength Variation of Inner- and OuterSphere Stability Constants of Monochloro Fe(II1) Comulexes Derived from Average Extinction Coefficients

+

Kin Kout,"

I,M

E"

1.00 3.00 4.00 5.00 6.00

1380 1710 2090 2520 2710

tin

25OOc 2620

2670 2730 2790

M-1

Kin, M-1

Ktiut,

5.2 9.8 17.3 36.3 110

2.9 6.4 13.5 33.5 107

2.3 3.4 3.8 2.8 3d

M-1

Reference 2, 340 nm. Linear interpolation between 1 and 6 M, 340 nm. ' Reference 5. Assumed.


where Kin[Cl-I 1 Kout[C1-1 A plot of h/q vs. [Cl-] is shown in Figure 2,from which k - 1 = 7.3 s-l and h-4 = 5.3 s-l. The deviations from the line are somewhat larger than the experimental error, possibly because of medium effects. Unpublished results of Po and Sutin,lo in which h was measured in a stopped-flow apparatus a t chloride concentrations up to 0.5 M, are in agreement with our data to better than 2%. Values from the literature for k-l at 25 "C and 1 M ionic strength, 1 M acid, are 7.2411 and 6.8 s - ~ . ~ Campion et a1.12 report a value of 12 M-l s-l a t 3 M ionic strength for the Fe(I1) catalysis of F e C P decomposition.13 This pathway should be negligible at our concentrations, and indeed no effect of Fe(I1) on the rate constant is observed and lo-* M (Table I). between Rowley and Sutin2 measured Kin Kout in equilibrated systems and determined h by a stopped-flow method a t 6 M ionic strength under conditions such that [Fe(III)] >> [Cl-] and sufficiently low [Cl-] that [FeC12+]was negligible. Under these conditions, eq IV reduces to =1

+ K*[Cl-]

+

+

(assuming the outer-sphere complex contribution to Z is negligible). Their values are given in column 2 of Table I1 along with their values of Kin Koutin column 4.If it is assumed that KO,, is 3 M-l a t 6 M ionic strength, which is consistent with the above discussion, then from eq VI tin is 2790 a t 6 M ionic strength. The value of €in a t 1 M ionic strength is 2500.5I t is clear, then, that the much larger variation of Z with ionic strength, seen in Table 11, can be explained as due to varying proportions of inner- and outer-sphere complexes. In other words, eq VI can be used to calculate separate values for Kin and K,,t. In order to do this we will assume that t for FeC12+can be found a t the various concentrations by linear interpolation between the 1 and 6 M values. The values so computed are given in Table 11.The value of 2.9 for K,, a t 1 M ionic strength obtained by this method is in good agreement with the value of 3.0 reported above. Values of Kouta t 4 M and below are quite insensitive to the linear interpolation assumption. I t would appear that Koutis relatively insensitive to ionic strength in this region whereas Kinvaries by a factor of 5. Wendt and Strehlow4 reported that KO,, = 2 f 1 on the basis of pressure jump measurements of the rate of F e C P relaxation in 0.027 M H+. I t was necessary for them to assume that h-4 was negligible in comparison to h-1. We do not find this to be the case in 1 M acid, but it may be so a t their acid concentration where the overall rate of relaxation is much faster. I t is not clear whether the agreement of our value of Koutwith theirs is significant or fortuitous in view of the very different populations of hydrolyzed species in the two experiments.

+

Acknowledgment. We express our appreciation to Drs. J. K. Rowley and N. Sutin for helpful discussions. This research was carried out a t Brookhaven National Laboratory under contract with the U.S. Energy Research and Development Administration. References and Notes

+

They found h to be nearly linear in [Fe(III)] [Cl-1. The ratio of initial slope to intercept was 107 M-l, which on the basis of the above equation would be Kin.The sum Kin + KOutwas 110.In other words, Koutis negligible compared to Kin a t 6 M ionic strength. Rowley and Sutin gave extinction coefficients of the monochloro Fe(II1) species between 1 and 6 M ionic strength derived from spectrophotometric measurements. These are average extinction coefficients and are related to the extinction coefficient of the inner-sphere complex by

(VI)

The Journal of Physical Chemistry, VoI. 80, No. 25, 1976

(1) H. Coll, R. V. Nauman, and P. W. West, J. Am. Chem. Soc., 81, 1284 (1959). (2) J. K. Rowley and N. W i n , J. Phys. Chem., 74, 2043 (1970). (3) T. C. King and J. K. Rowley, J. Phys. Chem., 75, 1113 (1971). (4) H. Wendt and H.Strehlow, 2. Nektrochem., 68, 228 (1962). (5) H. A. Schwarz and R. W. Dodson, J. Phys. Chem., submitted for publication. (6) R. W. Dodson and H. A. Schwarz, J. Phys. Chem., 78, 892 (1974). (7) H. N. Po and N. Sutin, Inorg. Chem., 7, 621 (1968). (8) G. G. Jayson, E. J. Parsons, and A. J. Swallow, J. Chem. Soc., Faraday Trans. 1, 69, 1597 (1973). (9) R. E. Connick and C. P. Coppei, J. Am. Chem. Soc., 81, 6389 (1959). (IO) Unpublished work by H. N. Po and N. Sutin: private communication from N. Sutin. (11) H. N. Po and N. Sutin, as reported in ref 2. (12) R. J. Campion,T. J. Conocchioli, andN. Sutin, J. Am. Chem. Soc., 86,4591 (1964). (13) T. J. Conocchioli, G. Nancollas, andN. Sutin, J. Am. Chem. Soc., 86, 1453 (1964).

Kinetics of dissociation of ferric chloride complexes. Stability constants

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