--
The Oxidation of Ascorbic Acid by Hexacyanoferrate(lll] Ion in Acidic Aqueous Media Application of the Marcus Cross-Relation Luis J. A. Mallins' and J. Barbosa da Ccsta lnstituto Superior de Engenharia de Coimbra. 3000 Coimbra, Portugal While theoretical aspects of the Marcus theory for electron-transfer reactions have deserved several articles in this Journal (1-41, there is a lack of experiments on its applica-. tion suitable for the undergraduate level. One reaction meeting this purpose is the oxaation of L-ascorbic acid (HzAsc) by the substitution-inert complex [Fe(CN)6I3- in acidic medium. The rate for this reaction was found to be first-order in the concentrations of both HzAsc and [Fe(CN)sI3-, and the overall second-order rate constant, hob., shown (5) to have an inverse dependence on [H+]over the range of pH examined. Moreover, the same kinetics are followed in the range of temperature 15-30 OC, thus allowing experimental activation ~arametersto be determined. Values of k,h. at a given temperature and pH, can easily be measured spectrophotometricallv bv followina the decrease in absorbance of [F~(cN)& at 418 nm a function of time. Relating these with the Droposed mechanism (5), the second-order rate constant for the rate-determining scep is obtained at a given remperature.'l'his, in turn, allows comparison with the value predicted on the basis of the Marcus cross-relation. Theory
Many kinetic and mechanistic investigations have been renorted on the oxidation of ascorbic acid bv a number of oiter-sphere metal ion complexes (5-81, phenbthiazine radicals (9). and excited states of metalcomplexes (I0,ll). In the present case we consider the oxidation by [Fe(CN)6]3-,with overall stoichiometry where Asc represents the dehydroascorbic acid formed. The empirical rate law, a t constant pH, is
The experimentally measured kOb,shows an inverse firstorder dependence on [H+], a t constant temperature and ionic strength. In addition, a plot of hob, vs. [H+]-I is found (5) . . to be linear with zero interce~t.This behavior surzests (5-9, 12) that ascorbate anion idthe kinetically important soecies. This is oxidized in the slow, rate-determining step (eq 4). A mechanism that is consistent with the kinetic data is (5-9),
[Fe(CN),I3-+ ASC'-%=
[Fe(CN),14- + Aac
(6)
Step 6 represents the fast oxidation of the ascorbate radical anion (pKrz = -0.45, (13)) yielding dehydroascorbic acid, a process that may be diffusion-controlled (7).An alternative pathway (7) that may also account for the disappearance of Asc'- is the disproportionation reaction, 176
Journal of Chemical Education
For this reaction an estimated rate constant in excess of lo8 M-Is-' has been reported (7) for [H+] = 0.1-1.0 M. From the above mechanism the rate of disappearance of [Fe(CN)@ can be derived, by applying the steady-state approximation to the concentrations of HAsc- and HAW, as
Under the experimental conditions of this work, k-,[H+] ka[Fe(CN)g-] and eq 8 becomes
>>
and by comparison with eq 2 gives
This relation allows the second-order rate constant kz to he determined, at a given temperature and ionic strength, once k,h values have been measured for different pH values. Our results show that k,b, can be reliably measured by using inexpensive and readily available equipment and adopting a somewhat simplified version of a previously used procedure (5). Experimental Reagents and Apparatus All chemicals were of the highest purity available and used as
received. Doubly distilled water was further purified by a previously described method (14).Absorbances were measured with a Bausch and Lamb Spectronic 20 using 1-cm-diameter glass cylindrical cuvettes. A constant-temperature bath was provided by a tank fitted with a Haake Model E 52 constant-temperature circulator, which enabled the temperature to be thermostated to within *0.5'C. The pH, which varied in the range 0.50-2.50, was measured with aRadiometer Copenhagen PHM 61 pH meter, fitted with a combined electrode. The pH meter was calibrated with appropriate buffers2 (15) prior to each measurement. Procedure
Staek solutions: sodium perchlorate (2 M), perchloric acid (0.5 and 1.0 M), K3[Fe(CN)6](8.0 X 10-3 M), and L- ascorbic acid (4.0 X 10WM, freshly prepared3). About50 mL of solution of appropriateionic strength (1.0 M), and pH (0.50-2.50) is prepared by mixing the above stock solutions, two
' Author to whom correspondence should be addressed.
A solution of KH tartrate (saturated at 25 OC), a 0.05 M KH phthalate solution. an equimolar (0.025 M) solution of KH2P04and Na,HPO., and further checkedagainst a solution of 0.05 M KH3(C20,)2 2H20.which have been assigned pH values of 3.56, 4.01, 6.86, and 1.68, respectively, at 25 OC. Solutions do not need to be deoxygenated if freshly prepared ascorbic acid solution is used.
equal 20-mL portions withdrawn and transferred to separate beakers
wrapped with aluminum foil to avoid exposure to light. To one of these solutions is added with mining 5 mL of KZ[Fe(CN)$ solution, and to the other 5 mL of ascorbic acid solution. Two 3-mL portions of ascorbic acid buffer mixture are withdrawn and transferred to separate cuvettes. One of these is used as the blank, and the other is wrapped in aluminum foil and placed in the thermostated bath. Similarly, 3 mL of the K3[Fe(CN)e] solution is transferred to a cuvette; covered with aluminum foil, placed in the thermostated bath, and left for -20 min. Equal amounts of the ascorbic acid and K3[Fe(CN)~] solutions in the beakers are mixed and the pH determined before and after reaction. Although protons are released in the reaction, there is negligible change in pH under the acid wnditionsemployed. The spectrophotometer is calibrated at418 nm with the hlank. and after thermal eauilibration the ascorbic acid and K21FeiCN)cl solutions in the thermostated cuvettes are mixed..stoo~~",.... ~~.",..~-. .~~ . watch started. and the K:,IFe,CN)c]absorption is measured at this navelength (G,,~ = 1012 W ' ~ m - os ~ lsoon as posiihlc after mixing. The cuvette, wrapped in aluminum foil, is then returned to the thermastated bath. Further readings are taken at regular intervals until a degree of reaction of -80% is reached. As advised above, the cuvette should not be left in the spectrophotometer cavity because after 20 min the temperature of the solution inside rises by -5 'C, which introduces a considerable error in the determination. Moreover, continuous irrndiatmn hy the lamp indllrek photolssis of [FdCN)sl3- and [ F ~ ( C N I # (formed both thermal and photo. chemically) I161the phutopmducts beginning to ~nterferewith the readings after 15-20 min in the cavity. ~~~~
~~~~
~
~
~~~
~
~
~~~
~
~~~~
= ing step, from the Arrhenius plot of Fig. 2, yielding 4.27 i 0.02 kcal mol-I and AS8 = -28.29 f 1.28 cal mol-I K-I a t 25 O C . These values compare favorably with those ohtained for the oxidation of ascorbic acid by other iron(II1) metal complexes (6).T h e recent availability (7,8) of the rate constant for the self-exchange electron transfer for the couple (HAsc./HAsc-) together with the experimentally measured (19, 20) self-exchange rate constant for the couple
~
~
Results and Discussion Using t h i s procedure leads t o good linear plots of IFelCN)?-l vs. time for degrees of reaction in excess of i0%, th; confirming the overkl second-order kinetics. T h e straieht lines for these d o t s were obtained by least-squares. values of kobaevolved from this treatment are collected in Table 1. A t all temperatures, plots of k,b, vs. [H+]-I were linear over the p H range studied, with intercept zero (see Fig. 1). T h e resulting slopes Klkz, together with the relevant values of K1 at p = 1.0 M (17).are collected in Table 2. They were ohtained by a least-squares method t h a t minimizes the sum of t h e squares of t h e perpendicular distances of the points from t h e best line (18).This same procedure was used to obtain the activation parameters, for the rate-determin-
Figure 2. AnheniuJ plot fw the second-order rate constant k2.
Table 1. Values of k-
at 293.15, 298.15, and 303.15 K and at Different Acldltiesa
Table 2.
Rate Data lor the Reactlon of [Fe(CN).IS- (8.0 X
lo-'
M) wHh L-Ascorblc Acld (4.0 X lo-* M) at p = 1.0 M (NalHCI04)
T(K)
K,k2 (min-') Intercept (M-'min-')
293.15 5.80 f 0.03 298.15 7.08 f 0.10 303.15 9.08 f 0.11
0.59 11.91 0.42f 23.26 0.02 f 6.56
IOSK7 (MIB
10-2k2(M-'SF')
10.0 10.6 11.9
9.67 11.13 12.72
Figure I. Plots of k v s . [H+]-'at = 1.0 M and 20% (0). 25 'C(O), and 30 "C (V).
Dale from ref 77.
Volume 65
Number 2
February 1988
177
([Fe(CN)6]3-/[Fe(CN)fi]4-)makes a Marcus calculation possible. The most useful development of Marcus theory for adiabatic outer-s~hereelectron-transfer reactions is that which enables the calculation of a cross-reaction rate constant ( k d from the eauilibrium constant [KIT)and the rate constants of the corresponding pair of self-exchange reactions (ku and kzz) (21,221, Under certain assumptions (22) the expression for f is
where Z is usually taken as the collision frequency between two uncharged particles in solution (10" M-ls-'). Klz is calculated from the reduction ~otentialsof the couoles involved under t h e conditions of measurement; for (IFe(CN)f13-/IFe(CN)d4-) the value of 0.448 V vs. NHE was a'dopted ikeasured a G 5 OC in p = 0.5064 M with 0.50 M NaC104 (23)) and for the couple (HAscIHAsc-) the value of (0.71 f 0.01) V vs. NHE estimated for p = 1.0 M from pulse radiolysis data (7,13) is used. The rate constant kll, for the couple ([Fe(CN)6]3-/[Fe(CN)fi]4-),has been experimentally measured both a t low (19) and high (20) cation concentration. I t was found (19, 20) that the value of kll depends mainly on the nature and concentration of the cation and not on the anion or ionic strength. While several mechanisms were proposed to account for the catalytic effect of the cations, ion association is thought to play a major role. For a high concentration of Na+ ions (1.75 M) avalue of kll = (5.8 f 0.9) X lo4 M-Is-' was measured a t 32 OC by 14N NMR spectrometry4 (20). Recent studies (7,8) involvingthe oxidation of ascorbic acid, by a number of outer-sphere metal oxidants, led to estimates of 1X lo5 and 3 X lo5 M-Is-' for the self-exchange rate constant, kzz, of the couple (HAsc.1 HAsc-), under the experimental conditions of this work. Use of the latter value together with the parameters above and the Marcus cross-relation (eq 11) yields acalculated value of kz = 5.0 X lo2 M-Is-' at 25 OC in good agreement with the experimental value. A satisfactory agreement is also obtained with kzz = 1 X 105 M-Is-', giving k2 = 3.0 X 102 M-Is-' a t 25 "2. In either case a successful application of the Marcus cross-relation is illustrated with this calculation. A further check on the validity of the Marcus calculation performed above is made by using the Marcus expression (21, 22) for the rate constant kz,
k,
= Z exp (-AG;/RT)
(I3)
where AG; is the free energy of activation for the electrontransfer step, usually approximated by (2)
+
AG; = AG: AG:
+ AG:
(I4)
AG; represents the free-energy change required for the activated complex to be formed from the reactant encounter complex. In the Marcus formalism the activated complex is a hypothetical state born out from the necessity of the chargeprocess to conform to the Franck-Condon energy restrictions, and is best discussed by referring to the potential energy diagram of the reaction (2). Accordingly, prior to the electron-transfer event the donor and acceptor orbitals must have equal energy. This energ equalization is achieved by expending free energy (AG$ to carry out the necessary changes in the ligand geometry (inner-sphere reorganization). This, in turn, promotes a rearrangement of the outer solvation sphere of the reactant ions in the activated complex, for which a free-energy change AG, is required (outer-sphere reorganization energy). An additional free en-
178
Journal of Chemical Education
ergy is expended in bringing the charged reactants to the encounter distance in the activated complex (AG,). Now, the free energy of activation from Marcus theory (eq 13) is related to th;~experimentally derived free energy of activated
where k and h are the Boltzmann and Planck constants, respectively. Therefore, the calculated value of AGI a t 25 "C from eqs 13 and 15 with k2 = 5 X lo2 M-Is-', as calculated above, is AGX = 13.77 kcal mol-'. This is in good ameement with the experimental value, derived from the activation parameters, a t the same temperature AGt = 12.70 kcal mol-l. Finally we note that the value of kz = 1.22 X 103 M-Is-' measured previously a t 15 OC (5) in the presence of K+ ions (p = 1.0 M), is higher than our value even a t 25 OC (see Table 2). This is expected on the basis of Marcus theory since the reduction ~ o t e n t i a lof the c o u ~ l e(IFe(CNhl3-/ [Fe(CN)6I4-)is highe; in the presence of K'+iods (23) addkll = 5.5 X lo4M-Is-' a t 15 "C. which is close to that found for the same concentration of ~ a ions + a t 32 OC (20). In conclusion, we present a simple, yet reliable, experimental procedure that allows the measurement of the rate constant for the rate-determining step in the oxidation of ascorbic acid by [Fe(CN)6]3,-.This provides a good opportunity for the student to confirm experimentally the previously proposed mechanism for the overall reaction and enables the student to perform a Marcus calculation on the same system. We feel this is important since the undergraduate student is now exposed to these aspects of the Marcus theory for electron-transfer reactions (25,26). Acknowledgment .
Financial support from INIC (Lisbon), under Projecto de InvestigaqXo 85lCEX12, is gratefully acknowledged.
Literature Cited 1. Newt0n.T. W. J. Chzm. Educ. 1966.45.571. 2. Lewis, N. A.J. Chem. Educ. 1380,57,478. 3. Nefa,P.J. Chem.Educ.1981.58.110. 9. Scott, R. A.; Mmk,A.G.; Gray, N. B. J. Chem. Educ. 1985.62.932. 5. Mehmtrtr, U.S.:Aglawal, M. C.; Musbran, S. P. J . Phys. Cham. 1969.73.1996. 6. Pelinetti.E.:M~ntssti,E.;Pramaum,E.Inorg.Chsm.1978,17,1181. 7. Macmtney, D. H.:Sutin, N. Inorg. Chim. A m 1983, 74,221. 8. McAuley,A.;Speneer,L.; We8t.P. R. Can. J. Chem. 1985,63,1198. 9. Pelizretti,E.:Meisel,D.;Mulae, W.A.;Neta,P.JAm. Chem.Soc. 1973.101,6954. 10. Kri8hnan.C. V.: Sutin,N. JAm. Chem.Sor.1981.103,2141. 11. Kurirnura. Y.;Yokota, H.;Muraki. Y. Bull. Chom. Soc Jopon 1981.54.2450. 12. Gupta. K. S.; Gupta, Y. K. J. Chem. Educ. 1984,61,972. la. ~te~~ken,s.:~~ta,p. J . P ~ Y ~1319.83.1134. .C~~~. I t Armsrego, W.; Pertin, D. R.; Perrin, D. D. Puriiicarion o i Loboretory Chemirals: Pergarnon: Oxford, 1966. 15. Meitos.L.Xandbook ofAnolyticolChemislgl:McGram-Hill: New York, 1963:pp 1113. 16. R O ~ ~ , S . E . : AJ ~. ~ I~ O ~ , ~P .~1983,77,131. ~ . c ~ ~ ~ A ~ ~ ~ 17. K ~ ~ ~ ~ ~ , M . : Y ~ ~J. ~c ~~ ~~~ ~~ ,. TI.M. M s .~ ;1~82,423. ~Y . ~ D~ ~~ ~I ~~, ~s ~. 18. York. D. Con.J. Pkys. 1364 44, 1079. 18. Campi0n.R.J.:Deck,C.F.;King,P., Jr.: Wahl,A.C.Inarg. Chem. 1967.6.672. 20. Shpores M.; Ron, G.:Laewemtein, A ; Navon, G. Inorg. Chem. 1965.4.361. 21. Marcua,R. A.Ann.Rou.Pky8. Chem. 1964.15.155. 22. R ~ Y ~ o IW. ~ . L, . : L U ~R. ~ ~. . ~ ~O I E ~~D C ~ , OhT~ ~~ ~ ~~ I l ~N ~~sW :Y ~ORT ~~.~ ~ ~ I ~ : 1966; p 117. 23. Kalthoff, I. M.:Tomaicek,W. J. J. Phys. Chom. 1935,29,945. ,25.,west on.^. E..;,J ~ .Si.,N.I Chrm. lw5, 14,213, ; C ~ W ~ ~ A. , H~. h ~ ~ i ~ ~ ~ ~ i ~ t i e ~ ; ~ ~ ~ ~ NJ. 1972:p 205. 26. Douglas, B.: McDanid. D. H.:Alexander. J. J. Concepts and Modela of Inorganir W ~ S YN ~ W york, 1983: p 378. chsmiatry;
'
Activation parameters for this self-exchangereaction are only available for K+ ions (1.75 M) between 25 and 40 OC. If the same activation energy is used for Na+ (1.75 M), an estimate of kll = 4.9 X 10' M-'s-' at 25 "C is obtained, the difference being within the experimental uncertainty of the determination.Consequently we have used the value measured at 32 "C.
