Kinetics of the iron (II)-iron (III) electron exchange reaction in ice media

J. lnorg. Nucl. Chem., 1963,Vol.25. pp. 1139to 1140. PergamonPressLtd. Printedin Northern Ireland

KINETICS OF THE IRON (II)-IRON (III) ELECTRON EXCHANGE REACTION IN ICE MEDIA R. A. HORNE Arthur D. Little, Inc., Acorn Park, Cambridge, Mass. (Received II October 1962; in revisedform 4 March 1963) Almtraet--Electron-exchange has been observed between cations in ice media. The overall reaction rate constant for the Fe(II)-Fe(III) electron-exchange reaction at --78°C in the eutectic frozen from an aqueous solution initially 0-55 M in HCIO4 is 2'1 ± 0-3 x 10-s sec -~M-1. As in liquid water the process is first order in each reactant. The rate is the same in the presence of chloride ion as in the presence of perchlorate ion. The rate decreases with increasing acidity. The results indicate that electron-transfer can occur over very great distances in aqueous media by a water-bridging mechanism. SOME time ago DODSON a n d DAVIDSON(1) discussed the possibility t h a t t h e m e c h a n i s m o f the F e ( I I ) - F e ( I I I ) electron-exchange r e a c t i o n m i g h t involve electron-transfer via t h e solvent molecules in a q u e o u s media. Subsequently REYNOLDS a n d LUMRY t~ a n d KLOTZ, et aL ta~ suggested t h a t the r e a c t i o n m i g h t p r o c e e d via a G r o t t h u s s t y p e m e c h a n i s m involving h y d r o g e n t r a n s p o r t a l o n g extended bridges o f suitably oriented water molecules. T h e i m p o r t a n c e o f the role o f solvent in electron-exchange has also been recognised b y LIBBY, (4) WEISS, (5) PLATZMAN a n d FRANK, (6) a n d MARCUS. t7) Experiments in h e a v y water ts'9'l°) a n d in n o n - a q u e o u s a n d mixed solvent m e d i a m'12"13) while yielding evidence which a p p e a r s to give the water b r i d g i n g t h e o r y support, have n o t given a n y i n f o r m a t i o n which alone provides a basis for distinguishing u n a m b i g u ously w h e t h e r the F e ( I I ) - F e ( I I I ) exchange proceeds b y a c o m p l e x a n i o n b r i d g i n g o r w a t e r - b r i d g i n g mechanism. EXPERIMENTAL The materials used, the preparation of the stock solutions, and the methods of analysis have been described in detail by SILVERMANand DoBSoN~14~. The radioactive Fe(C10,)s solution was prepared from ~gFe C13-HC1 solution obtained from Oak Ridge National Laboratory. ¢1~R. W. DOBSONand N. DAVlDSON,J. Phys. Chem. 56, 855 (1952). (See discussion) (~ W. L. REYNOLDSand R. W. LUMRY,d. Chem. Phys. 23, 2460 (1955). ~s) I. M. KLOTZ, J. AVERS,J. Y. C. Ho, M. G. HOROWrrZ and R. E. HEIN~Y, J. Amer. Chem. Soc. 80, 2132 (1958). ~4)W. F. LmBY, J. Phys. Chem. 56, 863 (1952). ~s~j. WEISS,J. Chem. Phys. 19, 1066 (1951). ce~R. PLATZMANand J. FRANK,Physik 138, 411 (1954). ¢" R. A. MARCUS,J. Chem. Phys. 24, 966 (1956); 26, 867, 872 (1957). ~s~D. BONY, F. S. DAINTONand S. DUCKWORTH, Trans. Faraday Soc. 55, 1267 (1959). ~'J J. HODIS and R. W. DOBSON,J. Amer. Chem. Soc. 78, 911 (1956). ~10)N. SUTIN, J. K. ROWLEYand R. W. DOBSON,J. Phys. Chem. 65, 1248 (1961). ~la~R. A. HORm~ Ph.D. Thesis, Columbia. (1955). cx2j N. SUTIN, J. Phys. Chem. 64, 1766 (1960). ~lS~A. G. MADDOCK, Trans. Faraday Soc. 55, 1268 (1959). ~'~ J. S1LVERMANand R. W. DOBSON,J. Phys. Chem. 56, 846 (1952). 1139

1140

R.A. HoRr,m

The conduct of the experiments and the separation procedure were similar to those described by SILVERg_ANANDDODSON~15~. TWOsolutions, both 10 ml in volume were prepared. They were of the same ionic strength and concentration of added anions, but one contained the tagged Fe(III) perchlorate and the other the Fe(II) perchlorate. Both solutions were chilled at 0°C. Five reaction mixture samples were prepared next by adding 1 ml of each solution to small test tubes, stoppering the tubes, shaking well and rapidly, and immediately immersing in a dry-ice-acetone bath (-78°C). Freezing was complete in less than 30 sec. A dry-ice-chloroform bath was used for the --67°C runs, a dry-icecarbon tetrachloride bath for the runs at -23°C. At regular time intervals, one of the tubes was removed from the bath, quickly crushed, and tube and contents dumped into a room temperature quenching solution of ~,~-dipyridyl buffered with sodium acetate to give a pH of 5. Next the Fe(III) was precipitated as the hydroxide by adding excess NH4OH. The mixture was filtered through a sintered glass filter using a suspension of CaCO3 in conc. NH~OH as a filtering aid. A sample of the filtrate containing the Fe(II) was counted as a solution in a Nuclear-Chicago well-type scintillation counter. Efforts to dissolve and count the Fe(III) precipitate did not give reproducible results. In runs at 0°C the two 10 ml solutions were mixed and 2 ml. liquid samples pipetted off at regular time intervals. RESULTS The overall reaction rate constant, k Rate -----k(Fe(II))(Fe(III))

(1)

was calculated from half-lives tl/2 determined from McKAY plots and the expression k = 0.693/[(Fe(II)) + (Fe(III))]tl/~

(2)

as described by SILVER~N and DOBSON.~14~ Activities were corrected for the decay of the 59Fe. As might be expected, the induced exchange was greater in the present experiments in ice than in earlier studies in liquid water. ~11'x4~ The experimental error, estimated from the maximum spread of the points in the McKAY plots, was 20 per cent. Typical McKAY plots are shown in Fig. 1. At --78°C the exchange runs were followed for as long as 52 hr. (not shown in Fig. 1). Attempts to follow the exchange for even longer periods of time were frustrated by the onset of erratic results for which spectrophotometric analysis showed the slow oxidation of the Fe(II) to be responsible. As the reaction mixture freezes, relatively pure ice separates out and the remaining electrolyte solution becomes more concentrated until the eutectic temperature is reached, whereupon, as shown by separate experiments, the composition remains constant, and the still-liquid solution solidifies. A corrected overall rate reaction constant, k', was calculated from: k' -----0.693/C{[Fe(II)] + [Fe(III)]}tx/2

(3)

where C is the ratio of concentration of the principal electrolyte component in liquid solution at the eutectic to the initial concentration before freezing. The former value was calculated from the freezing curves of the appropriate system. A separate experiment was performed to test for any further segregation of iron species in the eutectic mixture. An aqueous HC104 solution of the same composition as the eutectic and containing Fe(llI) was slowly frozen. Before solidification was complete, samples of the solid and of the remaining liquid were removed. Spectrophotometric analysis showed that the Fe(III) concentrations in the solid, liquid, and in the original liquid solution were all the same, indicating no further macroscopic segregation of the iron species upon solidification of the eutectic. No evidence was observed for microscopic segregation of a concentrated solution or crystals of (a) a single valence state of iron, (b) one valence state of iron contaminated with the other

Kinetics of the iron (II)-iron (III) electron exchange reaction in ice media

1141

6000 5000 4000 - 7 8 ° C (0) >: 1~> I
3000

2000 I-. LU I-Z ,..;z

Z

-23°G (I)

(K|

iO00

800

tO"C (el

600 IcP 400 L 0

5

I0

15

20

25

50

T I M E , hours

FIG. I.~McKAY plots f o r t h e i r o n (II)-iron (III)electron-exchange reaction at 0,--23, --64 and -78°C.

valence state, or (c) a mixed salt containing both valence states in roughly equal amounts. Situation (a) would represent a separation of the reactants and would result in no or exceedingly slow exchange; situation (b) would result in a large induced exchange and incomplete reaction; and, situation (c) would result in rapid exchange, the exchange probably being complete within the time of mixing (i.e. 100 per cent induced exchange). None of these possible results were obtained, in particular, although the induced exchange in the present experiments was somewhat larger than in similar exchange experiments at higher temperatures, the amount of induced exchange was well within the limits calculated from the estimated freezing and thawing times. As a check upon the techniques used, a number of experimental runs were made in liquid, aqueous HC104 media at 0°C. The results (Table 1) are in good agreement with values reported by earlier investigations. A number of runs were made at --78°C, the lowest temperature studied. Since this temperature is well below --58°C, the eutectic temperature of the H20-HCIO 4 system, the medium is solid. The results are summarized in Table 2. The constancy of the overall reaction rate constant, even though the relative concentration of the reactants was varied, justified the assumption that at low temperatures the reaction continues to be first order with respect to both reactants. These same kinetics have been found to obtain in liquid aqueous media in the presence of all anions hitherto studied ~la'14,15,16aT) and in ethanolic media. ~11~ The rate of the Fe(II)-Fe(III) electron exchange was also measured at --22 and t151 j. HUDIS and A. C. WAHL, J. Amer. Chem. Soc. 75, 4153 (1957). (18) G. S. LAURENCE,Trans. Faraday Soc. 53, 126 (1957). ~171R. A. HORNE, J. Phys. Chem. 64, 1512 (1960).

1142

R.A.

HORNE

TABLE 1 ,--RATE OF THE F e ( I I ) - F e ( I I I ) ELECTRON-EXCHANGE REACTION IN AQUEOUS 0"55 M HC104 MEDIA AT 0 ' 0 ° C HC104 Conc. (M)

Fe(II) conc. (M)

Ionic strength

0"55 0"55 0'55 0'55

0'55 0"55 0"55 0"55

0"55 0'40 0"55

0"55 0"50 0"55

13"5 13"5 13"5 6"50

X X X X

Fe(III) conc. (M)

10 -5 10 -5 10 -5 10 -5

6'0 6"0 6"0 6"00

X X X X

Half-life t~ (sec)

10 -9 10 -5 10 -e 10 -9

3"30 2'94 3"06 6'78

X X X X

Reaction rate constant (sec -1 mol e -a)

103 103 l03 l0 P

1'48 1"24 1"60 1"44 1"44 :]: 0.10 1"35 1"48 1"31

SILVERMANAND DODSONt14~ HUDIS AND WAHL txS~ HORNE c17~

TABLE 2.--RATE OF F e ( I I ) - F e ( l l I ) ELECTRON-EXCHANGEREACTIONIN SOLID AQUEOUSHCIO4 MEDIA AT - - 7 8 ° C

Initial concentrations Temperature °C --78 --78 --78 --78 --78

Fe(II) M 13.5 13.5 4.6 6.5 6.5

× X × X X

Fe(III) M

10-s 10-5 10-5 10-8 10-~

5.5 5.5 5.5 5.5 5.5

X X × X X

Halflife tl~ sec

10-8 180,000 10-8 241,000 10-5 385,000 10-5 490,000 10-8 222,000

Overall reaction rate const, k sec-x M -1 2.7 2.0 3.4 2.3 2.6

X X × X X

Final concentrations Fe(lI) (M) 16.9 16.9 5.8 8.1 8.1

10-3 10-3 10-9 10-3 10-3

× x x x x

Fe(IlI) (M)

10-4 10-4 10-4 10-5 10-4

6.9 6.9 6-9 6.9 6.9

x x × X x

k' sec-x mole -~ 10-5 10-s 10-5 10-4 10-4

2.3 1.6 2.7 1.8 2.1

× x x x ×

10-a 10-a 10-s 10-a 10-a

2.1 4- 0.3 x 10-8

2.6 4- 0.4 x 10-~ (Initial Concentration of HCIO 4 = 0.55 M) (Initial Ionic Strength = 0.55)

TABLE 3.~-TEMPERATURE DEPENDENCE OF THE RATE OF THE F e ( I I ) - F e ( I I I ) ELECTRON EXCHANGE REACTION IN AQUEOUS 0 ' 5 5 M . HC104 MEDIA*

O ve ra l l r e a c t i o n ra t e c o n s t a n t Initial c o n c e n t r a t i o n s Temp (°C)

State

21 '6 14.7 7.3 0 '0 --22 --23 --64 --6 4 --7 8

L L L L L+S L÷S S S S

Fe(II)

Fe(III)

Half-life t~ sec

D a t a of SlLVERMAN AND DODSONtlal Average from Table 1 6.5 4- 10 -s 5'5 1.35 x 10 -4 5"5 1'35 x 10 -4 5'5 6-5 x 10 -5 5"5 Average from Table 2

* Initial c o n c e n t r a t i o n

x x x x

10 -e 10 -6 10 -6 10 -6

9"4 7"6 2"2 8"9

x x × x

I0 a 104 104 104

k (sec -I m o l e -1) 9"97 5"34 2"73 1.44 1'03 0.65 0'22 0.11 2'6 x 10 -3

k' (see -I m o l e -1) 9"97 5"34 2"73 1.44 0"14 0.088 0'018 8"7 x 10 -a 2.1 x 10 -~

Kinetics of the iron ( I I ) - i r o n (III) electron e x c h a n g e r e a c t i o n in ice m e d i a

1143

-23°C, and -64°C. These results, together with the --78°C results and earlier work of SILVERMANand DODSON, 114~ a r e summarized in Table 3 to give a total temperature range of +22 to --78°C. The overall reaction rate constant of the reaction at --78°C in a medium initially 0.55 M in HC1 was measured and found to be 1.9 × 10-3 sec-1 mole -x after correcting for electrolyte concentration upon freezing. Within experimental error, this value is the same as for HCIO4. (See Table 2) The acid dependence of the reaction rate was also investigated at --78°C. The results are summarized in Table 4. Inasmuch as the phase diagram for the ternary system HC104-NaC104-H~O is not known, attempts to try to make an electrolyte concentration correction is probably not worth while in those cases where HC104 and NaC104 were present in comparable amounts. TABLE 4 . - - A c t D

DEPENDENCE OF THE RATE OF THE F e ( ! D - F e ( I I I ) ELECTRON-EXCHANGE REACTION IN ICE MEDIA AT - - 7 8 c c

Initial electrolyte concs.

Overall reaction rate constant Initial concentration

HCIO4 (M) 0-55 0-275 0.003

NaCIO4 (M) 0"00 0.275 0.53

Half-life

t4/2 Fe(ll)

Fe(III)

sec

k

k'

(sec 1 mole-l)

(sec-4 mole x)

2.6 × 10-2 4.6 × 10-2 9.1 × 10-z

2.1 × 10 3

Average from Table 2 1.35 × 10-4 5.5 × 10-" 1.08 × 105 1.35 × 10 4 5.5 × 10 s 5.4 × 104

4.8 × 10-8

DISCUSSION

In the presence of a complexing anion, X -m the rate of the Fe(II)-Fe(III) electron exchange reaction can be presented by aa) R = ~ ~ k.,n(FeX~-mn)(Fe *+)

(4)

X~=0

which is valid for all catalysing anions hitherto studied for values of n up to at least two. In chloride media (4) becomes: R = k0(Fea+)(Fe2+) + kl,o~(FeOH2+)(Fe 2÷) -k kl,cl(FeCl~+)(Fe 2+) q- k2,cl(FeC12+)(Fe2+) + . . .

(5)

Using values of the specific reaction rate constants and hydrolysis and complex formation constants used or measured by SILVERMANand DODSONt14)and extrapolating to --78°C, one finds that the contribution of chloride complexes to the exchange has become negligible, a conclusion in agreement with the observation that at this temperature, the overall specific reaction constant is the same in aqueous HC1 asinaqueous HC104. The results in Table 4 show some acid dependency indicating that the kl ,o~(FeOH~+)(Fe 2+) term in Equation (5)is still making a contribution at--780C. The acid effect, however, is very much less than at 0°C. When the proton concentration is reduced from 0-55 to 0.003 M, the overall reaction rate constant doubles, while at 0°C, SILVER~N and DODSONt14) found a twelve fold increase in going from 0.55 to 0.016 M. ns) R. A. HORNE, Nature, Lond. 181, 410 (1958).

1144

R.A. HORNE I0' T x

T _-

~

Liquid

0

+ Solid

Solid

iO o

Z Z 8 IO'l w

z 0 I-

,o I o

10 4

xk~ dora of Silverrnon and Dodson ok' present doto

w

g I0";

Q~ 0

'%o

I

;o

.

I

5o

103/T, *K -~

FIG. 2.--Temperature dependence of the iron (II)-iron (III) electron exchange reaction. In Fig. 2, the corrected overall reaction rate constant is plotted on a logarithmic

scale vs. the reciprocal of the absolute temperature. Values of the specific reaction rate constant, k, as determined by SILVERMAN and DODSON(14) are also plotted. By

substituting into the integrated form of the Arrhenius Equation d(ln k') dT

-

Ea RT 2

(6)

one finds that the slope of the resulting straight line corresponds to an activation energy of 8.4 kcal/mole which is in good agreement with values reported earlier and

summarized by

HALPERN. (19)

A very important feature of the curve in Fig. 2 is the absence of any discontinuity or break at --58°C, the eutectic temperature, as the remaining electrolytic solution freezes. The absence of such a feature suggests: (a) there is no change in mechanism as one proceeds from a liquid to a solid medium, (b) the rate of the reaction is not diffusion controlled, and (c) if the mechanism of the electron-exchange is related

to the mechanism of proton mobility, then the proton mobility must, apart from a temperature effect, be the same in ice as in liquid water. LAIDLER(20) has suggested that the Fe(II)-Fe(III) electron-exchange reaction in aqueous media is a diffusion-controlled process. In the absence of any information to the contrary (such as a change in order or change in the temperature dependence of the rate), it is reasonable to assume that the mechanism of the rate-controlling step of the Fe(II)-Fe(III) exchange process does not generically differ in liquid water and 119) j . H A L P E R N , Quart. Revs. 15, 207 (1961). (See Table 1, p. 211.) (20) K. J. LAIDLER,Canad. J. Chem. 36, 138 (1959).

Kinetics of the iron (II)-iron (III) electron exchange reaction in ice media

1145

in ice. Unfortunately, there is a paucity of information concerning the diffusion rates of highly solvated polyvalent cations and their complex ions in both liquid water and ice. LAIDLER(2°) USeS a value of 1"2 × 10-5 cm 2 sec-1 for the diffusion constant of ferrous and ferric ions in water of 25°C. Their diffusion constants in ice are not known. We have performed a simple diffusion experiment in which we tried to detect movement in a pure ice-frozen FeC13 solution boundary at --78°C. In sixty days, the boundary moved less than 0.5 cm, thus indicating that the diffusion constant of Fe(III) chloride complex ions is less than 10-7 cm 2 sec-1. The self-diffusion of water in liquid water and in ice has been measured, (21,~2,23) however, and the ratio of the diffusion constants is: D~t~O.L,25oc 2"4 × 10-5 DH~o,s,ooc

- - 2-4 × 105

(7)

1.0 × 10-x°

The ratio of the diffusion constants of hydrated Fe(II)-Fe(III) species in water and ice should be greater than the above ratio for the self-diffusion of water, especially if the ice is at --78°C, rather than 0°C. For solid-state diffusion in metals, (24) D ranges a r o u n d 10 -1° c m 2 sec -1 and is sometimes as small as 10-17 cm 2 sec-1. The present process in ice should be of comparable or even greater slowness, thus 10-16 cm 2 sec-1 does not appear to be an unreasonable estimate for the diffusion constant of highly solvated cations in ice. Such an estimate leads to a value of roughly 101° for the ratio OFe(II) or Fe(III'), water 25°C to DFe(II) or Fe(III), ice-78°C• The rate constant of a reaction is proportional to the sum of the diffusion coefficients of the reactants. (z°) If the electronexchange is diffusion controlled, the ratio of the reaction rate constants in water and ice should be equal to the corresponding diffusion coefficient ratio. The present experiments show that such is not the case. kwater'•5°c ~ 5 × 103

(8)

kice,.78°c

Protons have an anomalously high apparent mobility in liquid aqueous solution, and this phenomenon has been attributed to a Grotthuss type mechanism. (25) An ordered lattice is expected to facilitate this process; therefore, it has been suggested that the anomalous mobility of protons in ice should be very great, (26'27,~8'29) 0.1-0.5 cm 2 sec-lV -1. HF,rNMErS~3°) has made direct measurements of proton mobilities in protonated ice and obtained values ranging from 2.0 × 10-5 cm 2 sec-1 V -1 at --20°C to 2.2 × 10-4 cm 2 sec-1 V -1 at 15°C. That is to say, apart from the temperature dependence, he has found that proton mobilities in ice are comparable to those in liquid water. If both the anomalous mobilities of protons and the Fe(II)-Fe(III) 121)A. W. ADAMSONand R. R. IRANI, ,]7.Amer. Chem. Soc. 79, 2969 (1957). (2~) W. KUHN and M. THURKAUF, Helv. Chim. Acta. 41, 938 (1958). (2a~ D. C. DOUGLASS and D. W. MCCALL, J. Chem. Phys. 31, 569 (1959). (241 C. J. SMrrnELLS, Metals Reference Book, Vol 2, pp. 551 et seq. lnterscience, New York 0955). (25) E. HOCKEL, Z. Elektroehem. 34, 546 (1928). (~s) M. EmEN and L. DeMAEvER, Z. Elektroehem, 60, 1037 0956). (27) B. E. CONWAY and J. O. M. BOCKgJS, J. Chem. Phys. 28, 354 (1958) ~28~M. EmEN and L. DeMAYER, Proc. Roy. Soc., 247, A, 505 (1958) (2a) B. E. CONWAV, Canad. J. Chem. 37, 178 (1959) (a0~ F. Heinmets, Nature, Lond. 188, 925 (1960)

1146

R . A . HORNE

electron-exchange reaction arise from the same mechanism, possibly of a Grotthusstype as suggested by R~YNOLDSand LUMRY/2~ and if the process is greatly facilitated in ice, one might expect an abrupt increase in rate as the solution freezes. Figure 2 fails to show any break, and thus the present results appear to support the findings of HEINMETS3~°~ However, it should be cautioned that the present experiments and those of HEIlqMETS~3°~ necessarily involved highly impure ice. Furthermore, in the present experiments, the solutions were rapidly frozen; hence, the resulting ice is probably relatively disordered. In the present experiments, there are more t h a n 3000 water molecules for each Fe(II)-Fe(III) species. Estimates based on the concentrations involved indicated that in the solid medium, the reactants are separated by distances of roughly 100 A. This finding is to be compared with the earlier conclusion of HUDIS and WAnE~15)that the distance between iron nuclei in the transition state in the case of the fluoride catalysed exchange is large enough to accommodate one or more water molecules, and of HORNE~11)that the apparent dielectric constant of the medium which the reactants see is that of water, even in ethanolic solutions quite dilute in water. The ability of redox processes to occur over great distances through aqueous electrolytic solutions by water bridges may have considerable significance in explaining the mechanistic details of certain biologically important processes. The electrical properties of hydrated hemoglobin ~31~and the differences in oxidative susceptibility of free heme and hemoglobin in aqueous solution ~a~ may be due to Grotthuss-like transport processes. KLOTZet al. ~3~ have theorized that a number of important longrange biological electron-transfer processes might occur via water bridges. Acknowledgements--The author wishes to express his gratitude to the Research Projects Committee

of Arthur D. Little, Inc. for funding the present work; to Drs. A. G. EMSLIE,G. R. FRYSlNGER, J. H. B. GEORGE,H. O. McMAHoN,E. S. SrIANLEYof A. D. LITTLE,Inc. and Dr. F. HEINMETSof the Quartermaster Research and Engineering Cen, Natick, for their helpful discussions; and to Miss E. StmLIVANfor assistance with the experiments. csl~D. D. ELEYand D. I. SPIVEV,Nature Lond. 188, 724 (1960) ~ss~R. A. HORNE,Science, 130, 164 (1959).