J . Phys. Chem. 1990, 94, 41 16-41 19
4116
An Equilibrium and Kinetlc Study of the Methylene Blue-Ferrocyanide Reaction in Acid Medium John R. Sutter* and Wynetta Spencer Department of Chemistry, Howard University, Washington, D.C. 20059 (Received: June 12, 1989; I n Final Form: December 5, 1989)
-
The reversible noncomplementary, two-electron oxidation-reduction reaction between ferrocyanide and methylene blue to yield methylene white and ferricyanide has been studied in acid medium: 2Fe(CN):- + B+ + Ht 2Fe(CN),3- + HW. The kinetics were investigated by using the temperature jump technique. A mechanism is presented that is consistent with the data and the thermodynamic standard equilibrium constant has been estimated.
Introduction The kinetic study of a noncomplementary, multiequivalent redox reaction usually results in the investigation of a fairly complicated reaction mechanism. The present study of the methylene blueferrocyanide reaction producing methylene white and ferricyanide is no exception. The methylene blue monomer is reduced to the methylene white in two steps, the first leading to the production of a radical intermediate, which can be protonated. The skeletal sequence for this reduction of methylene blue showing the structures of the organic species involved is
The spectrophotometric determinations were performed on a Beckman DK-2A ratio recording spectrophotometer with a thermostated cell holder. The temperature jump apparatus used in this investigations has been described earlier.3 Stopped flow experiments were performed on an Aminco-Morrow appratus. The data were collected by using an Aminco-DASAR A / D converter, a microcomputer, and a nonlinear least-squares fitting program to process the equilibrium and kinetic results. The stoichiometry and equilibrium constant for the reaction, written in one of the thermodynamically equivalent forms as 2Fe(CN)64-
+ €3' + H+ = 2Fe(CN)63- + H W
were determined spectrophotometrically. The absorbance due to the total amount of methylene blue, B+(total), present in a solution of known H + was first measured at 610 nm and known amounts of Fe(CN)64- were added. The absorbance at 410 nm, the absorbance maximum of Fe(CN)63-, which was added initially in some experiments, was then also monitored. Using equations, extinction coefficients, and the monomer-dimer equilibrium constant previously deter~nined,~ we calculated the apparent equilibrium constant, Kapp
B+ melhylene blue
B' unprotonaled radical
Kapp= [ Fe"'] 2[HW(total)] / [ Fe"] 2[B+(total)]
W unprotonated methylene white
The formulas shown here are those from a number of contributing structures that could have been chosen and are shown as unprotonated species. The mechanism, to be presented later, shows that ideally three relaxations may be observed. That, coupled with the expected information to be gained from the proton dependence, should have yielded further detailed kinetic information on the behavior of radical intermediates. Only one relaxation was observed, however. The H+ dependence did provide some interesting though unexpected results. Diebler investigated a similar, although somewhat more complicated, reaction some years ago.' Experimental Section The purification and handling of the methylene blue (Fisher, USP) has been described elsewhere.2 Sodium ferrocyanide (Matheson, Coleman and Bell), sodium ferricyanide (Fisher, ACS), potassium nitrate (Mallinckrodt, AR), and hydrochloric acid ( B and A, ACS Reagent) were used without further purification. ( I ) Diebler, H. Ber. Bunsen-Ces. Phys. Chem. 1963, 67, 396. (2) Tzung, C.-Y. Anal. Chem. 1967, 39, 391.
0022-3654/90/2094-4116$02.50/0
The concentrations are the analytical concentrations of the indicated species and H W represents the monoprotonated form of reduced methylene blue, methylene white (leucomethylene blue), the bridged nitrogen being protonated. In all the experiments, care was taken to exclude oxygen to prevent the reoxidation of H W to.'B Solutions were prepared in a nitrogen-purged plastic glovebag and placed in stoppered spectrophotometer cells prior to measurement. Table I shows the results of the equilibrium constant determination. At an ionic strength of 0.5 M, a hydrogen ion concentration of 0.025 M, and a temperature of 20 "C, Table I shows a reasonably constant Kapp. The kinetics of this equilibrium system were studied by using the temperature jump technique. Solutions were prepared in the same way as in the equilibrium studies except that the final mixture was vacuum outgassed prior to a relaxation experiment to minimize cavitation. Table I1 gives the total concentrations of all species present as well as the observed relaxation times. Only one relaxation was observed under all experimental conditions. As was expected, no single-step mechanism could be found that was consistent with the data. Although the relaxation times were reproducible, from *5 to lo%, it must be pointed out that the equilibrium constants calculated from the concentrations given in Table I1 were usually in poor agreement with those calculated by using the data collected in the equilibrium runs. This is to be expected for a stoichiometric equation as complex as this, for a 10% error, which is reasonable, in the concentration of methylene blue calculated from a relaxation curve at 610 nm will result in (3) Reich, R. M.; Sutter, J. R. Anal. Chem. 1977, 49, 1081. (4) Spencer, W.; Sutter, J. R. J . Phys. Chem. 1979, 83, 1573
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 4117
Methylene Blue-Ferrocyanide Reaction
TABLE I: Equilibrium Measurements on the Methylene Blue-Ferrocyanide Reaction'
run
H+,M
2eh 4eh 2c 3c 5c I oc I2c 6eh 7eh 9eh I Oeh 1 leh I2eh I4eh l5eh
0.01 0.02 0.025
0.03 0.04 0.05 0.06 0.07 0.08 0.10 0.12
methylene blue, M X IO6
Fe(CN)6", M x 104
methylene white, M X lo6
8.85 8.26
6.14 6.43 1.04 6.16 10.3 64.4 104.0 6.39 6.42 6.43 6.42 6.62 6.42 6.1 1 6.6 1
1.95 2.54 0.78 2.59 3.63 8.23 9.21 2.83 3.12 3.06 3.38 3.76 3.55 3.76 3.94
10.0
8.21 7.17 2.57 1.59 7.98 7.68 7.75 7.42 7.04 7.25 7.04 6.86
Fe(CN):-, M X IO6 3.90 5.08 1.57 5.18 7.26 16.5 18.4 5.65 6.24 6.1 1 6.76 7.52 7.10 7.52 7.88
KaPPT
x 105 0.92 1.92 1.79 2.23 2.52 2.10 1.81 2.78 3.84 3.57 5.05 6.89 5.99 8.09 8.61
'The equilibrium constants are at least the average of duplicate runs. All measurements done at 20 OC and an ionic strength of 0.5 M. The concentrations given are the analytical concentrations of the species listed.
TABLE 11: Relaxation Times for the Methvlene Blue-Ferrocvanide Reaction' methylene Fe(CN)t-, run H+,M blue, M X lo6 M x 103 0.020 8.95 0.257 If 9.07 0.240 2f 7.42 0.740 3f 8.44 0.706 4f 0.706 8.57 5f 7.04 2.00 6f 2.01 7.68 7f 7.78 2.01 8f 8.46 2.03 9f 5.64 6.08 1Of 1If 5.77 6.02 12f 6.79 6.08 6.41 6.02 13f 14f 6.53 6.02 10.0 15f 6.69 10.0 6.79 16f 10.0 17f 6.41 20.0 I8f 4.88 20.0 19f 6.28 30.0 2Of 4.42 30.0 5.92 21f 0.140 10.8 4.70 22w 10.8 23w 4.59 10.7 4.49 24w 0.809 0.04 12 25h 7.68 0.808 6.92 0.140 26h 2.43 0.0653 27h 7.55 2.43 6.92 0.0891 28h 2.43 0.130 29h 6.41 2.43 5.97 0.160 30h 2.43 0.190 31h 5.39 7.30 4.75 0.100 32h 0.130 7.30 4.1 1 33h
methylene white, M X IO6 1.85 1.73 3.38 2.36 2.23 3.76 3.12 3.02 2.34 5.16 5.03 4.01 4.39 4.27 4.1 1 4.01 4.39 5.92 4.52 6.38 4.88 14.0 32.8 51.6 3.12 3.88 3.25 3.88 4.39 4.83 5.41 6.05 6.69
Fe(CN)6)-,
M
X
IO5
0.519 0.449 0.883 0.887 1.07 1.41 1.50 1.69 3.51 2.55 4.34 5.37 8.11 12.0 7.22 9.33 13.0 5.91 13.0 6.0 13.1 3.83 7.59 11.4 0.624 0.776 1.94 2.21 2.32 2.41 2.52 3.94 4.07
l i t , s-' 1.51 1.59 2.63 2.84 2.84 5.17 5.32 5.76 7.31 12.9 11.3 11.3 12.3 11.4 18.0 19.9 20.9 26.4 33.2 38.1 37.4 12.9 11.9 12.0 2.19 2.58 4.53 4.37 4.34 4.87 4.71 8.88 8.49
'The relaxation times are the average of two or three measurements on the same solution. All measurements at 20 "C and an ionic strength of 0.5 M. The concentrations given are the analytical concentrations of the species listed. The letter designations in the run numbers show which concentration is principally being varied.
a change in the calculated equilibrium constant by as much as a factor of 3. In this case all the concentrations would have been calculated from a kinetic trace with its included noise band. Thus a direct comparison of the value of Kappfrom the two kinds of experiments was not wholly satisfactory.
Results and Discussion The Equilibrium Constant. It is necessary to determine a properly constituted and constant equilibrium constant in a reaction of this complexity, for without it any inference of mechanism would be open to doubt. A plot of the data in Table I shows that, as the hydrogen ion concentration is increased, K , r! increases, linearly at first, and then exhibits curvature in the Righer hydrogen ion region. This
behavior is attributed to a change in the concentrations of the variety of protonated species present in the solutions. Fe(CN)64(F), HFe(CN)b- (HF), and H2Fe(CN)62-(H2F), as well as the several protonated species of methylene white HW, H2W, and H3W. Protonated species have not been reported for ferricyanide, Fe( CN)63- (F,) .5,6 If the Kappequation is cast in terms of the analytical concentrations and the protonation equilibrium constants corrected to ( 5 ) Sillen, L. G., Martell, A. E.,Eds. Stability Constants of Metal-Ion Complexes; The Chemical Society: London; Special Publication 17, pp 101, 1I "n, . i
(6) Butler, J. N. Ionic Equilibria; Addision-Wesley: Reading, MA, 1964; p 447.
4118
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990
the ionic strength of the medium, the thermodynamic standard equilibrium constant, which is applicable at infinite dilute, becomes
fl = (K,,,/H+1[1
+ KIH++ +
+
monomer/dimer step
2B+ = B22+
(1)
protonation steps
F
+ H = H F K, = 1.87 x 103 HF + H = H2F K2 = 26.4 B'
+H
(3) (4)
W+H=HW
(5)
+ H = H2W H2W + H = H3W
K I N= 1.05 X IOs
(6)
K2, = 1.36 X lo6
(7)
independent redox steps
B+ + H F = HB'
+ F3
r8 = k,(B+)(HF) = k_,(HB')(F,) (8)
+ H2F = H2W + F3 + H 2 F = HSW + F, r l 0 = klo(HB')(H2F) = B'
HB'
(9)
k-10(H3W)(F3) (lo) thermodynamically dependent steps
B+ + F = B'
+ F3
r l l = kll(B+)(F)= k-,,(B*)(F3)
+ F3 B' + H F = H W + F3 HB' + F = H W + F3 HB' + H F = H2W + F, + F3 + H+ r16 = kl6(B+)(H2F) = B'+ F = W
B+
+ H2F = HB'
+
F=B'
I I
F3
11-8+4-2=0
(2)
+
8'
(8)
HF=HB' (3)
B* + H2F=HB*
(16) (12)
B*
B'
(13)
+
HF=HW
(4)
1
HB*
+ HpF=HaW
+
(3)1
((7) HF=H2W
(2)1
(14)
F3
F3
+
F3
+
F3
+
F3
+
F3
+
H'
16-8+3=0
12-9+6+5-3-2=0 13-9+6-3=0
I(7)
(10) HB' (15)
+
I(6)
B* + H2F=H2W
(9)
F3
+
F=W
(2)1 1~ + (3)(
+
HB.
15-10+7-3=0
I(6)
+ F=HW
+ F3
14-10+7+6-3-2=0
"Vertical numbered steps are the protonation reactions. The Htare not shown. The equations to the side show how the dependent reactions may be constructed.
The order in which these steps are presented is, of course, immaterial, although this particular arrangement did lead to a somewhat easier solution of the secular equation than some other orders that were tried in order ensure the correct reduction of the equation. The secular equation takes the general form lrogab - A6abl =
(2)
= HB'
HW
+
B'
+ K,wK2,(H+)211f~2/f42fi2)
where K, is the first protonation equilibrium constant for ferrocyanide, F H = HF; K2 for H F H = H2F? K,, and K2ware the constants for HW + H = H2W and H2W + H = H3W.' These constants were corrected for ionic strength by using the Davies equation to calculate the activity coefficients,f;, where the i indicates the charge type. The linear constants in the Davies equation were taken as 0.3 for charges one and two and 0.4 for charges three and four.8 The activity coefficient for the neutral species is unity. The corrected values of the constants K,,K2,K,,, and K2, used in this work are 1.87 X IO3, 26.4, 1.05 X lo5,and 1.36 X lo6. At low hydrogen ion, K,, is linear in H+ with slope equal to K"Kl,K2,&f,tf,2/ f&2K,2. A h e a r least-squares program yielded M-I. A linear fit was used rather a value of K" = 1.45 X than fitting all the data to a nonlinear equation so as to avoid using one of the ionic strength dependent constants, K2, in evaluating the equilibrium constant. Further, by using Rock's value9 of +0.3704 V for the standard electrode potential of the ferricyanide/ferrocyanide couple one obtains +0.20 V for the standard potential of B+ H+ 2e = H W . The Relaxation Kinetics and Mechanism. The following series of mechanistic steps was examined by using Castellan's method to develop the relaxation equations."
+
CHART I: Diagram Showing Relations between the Thermodynamically Dependent Reactions 11-16 and the Independent Ones" (11)
KlK2(H+)212/[l + KI,H+
+
Sutter and Spencer
~ - I ~ ( H B ' ) ( F , ) ( H +(16) ) (7) Nikol'skii, B. P.; Zakhar'evskii, M. S.;Pal'chevskii, V. V. Uch. Zap. Leningr. Gos. Univ. im A . A . Zhdanova, Ser. Khim. Nauk. 1957, 15, 26 [Chem. Abstr. 1958, 52, 98121. (8) Nancollas, G. H. Inreracrions in EIectrolyte SoIufions;Elsevier: New York, 1966; p 15. (9) Rock, P. A. J . Phys. Chem. 1966, 70, 576.
where ra is the rate of the 0th reaction, (1)-( 16), with forward rate equal to reverse rate for each step of the mechanism. Examples of these rates are given above in the listing of the steps. The gabterms are defined by the equation gab = ~u,,u,b/c,, with gab = g,. The u's are the stoichiometric coefficients, negative for reactants and positive for products, c, is the concentration of the ith chemical species, and the summation is over all species in the reaction pair. Some examples are g8.8 = 1/B+ I/HB. + l/F3, g8,9 = I/F3, &,IO = - l / H B ' + 1/F3, and g4,7 = &,IO etc. = 0. Species held at high concentration, buffered, are not included in the gab matrix elements and if an a b reaction pair contains no species in common, that element is zero. The H + and the total concentration of ferrocyanide are some 100 times larger, in all the kinetic experiments, than any of the other species and hence the ferrocyanide species, F, HF, and H 2 F as well as H + are buffered and constant and do not appear in the gab terms. The A's are the reciprocal relaxation times and 6,b is the Kronecker delta. Not all of the above reactions are thermodynamically independent; see Chart I. Steps 11-16 were arbitrarily chosen as the dependent reactions and may be written in terms of the others; e.g., for step 11, 11 - 8 4 -2 = 0. The elements of column 11 are now replaced by using this relation as follows: g , , , , ,= +1, g8,lI = -1, g4,,,= + I , g2,,,= -1, with all other ga,,,= 0. N o rate terms or A's appear in this column. Each of the reactions 11-16 is treated in this way such that when incorporated into the columns of the secular equation, according to the Castellan formalism, allows one to reduce it to a nine by nine. This is done by simply adding/subtracting the rows in order to replace all the 1's with zeros in columns 11-16 except those lying on the principal diagonal. Since the temperature jump runs showed only one relaxation under all experimental conditions, the secular determinant had to be tailored in its reduction so as to produce a final equation consistent with the experimental observation of a single relaxation.
+
+
(10) Castellan, G. W . Ber. Bunsen-Ges. Phys. Chem. 1963, 67, 898
Methylene Blue-Ferrocyanide Reaction This was done by considering the following. Reaction 1 is included only for the sake of the completeness in writing the reaction scheme, for at concentrations less than M, methylene blue exists exclusively as the monomer, with the dimer neither participating in the reaction scheme nor necessary for the advancing of any of the sequence of steps4 The rates of the protonation reactions, (2)-(7), are taken to be infinitely fast. These rates are eliminated from their respective rows by dividing each term in the ath row by its rate, ro, and allowing the rate to go to infinity. The large protonation constants for the methylene whites allow only the species H3W to be present even at the lowest acidity used in this study. The radical intermediate B' (or HB') is present in vanishingly small steady-state concentrations and may be eliminated by judicious addition and subtraction of the columns in which it appears. Only a single protonated species, HB', of this intermediate is considered, for further protonation would necessitate placing the proton on the already positive center of an amine nitrogen. The reaction B+ H 2 F = HB' F3 H+ is included even though its back step is termolecular and should be unimportant. The alternative of involving a protonated ferricyanide species is no better. Nevertheless, the diprotonated ferrocyanide would be expected to reduce methylene blue at perhaps a slower rate than the unprotonated species. Reaction I O also presents a problem in that it involves the apparent transfer of several protons. There is no really better alternative way to include this step. Our earlier study of the methylene blue monomer/dimer equilibrium revealed that its relaxation was independent of H+ and that the absorbances of the two species were also not affected by changes in H+ as was evident from the fit of the Beer's law data.4 Thus, protonation equilibria involving the monomer were excluded from the mechanism. Incorporating these procedures reduces the secular equation to one of a single relaxation, X = 1 / ~ .
+
+ +
+ l / H 3 W + 4/F3)/(Rl + R2) where R , = r9 + r l 0+ r I 2+ rl3 + rl4 + rI5,R 2 = rs + r l l + rI6, X = RIR2(1/B+
and, for example, rIowould be written as rl0= k-,,(H,W)(F,) so that HB', which has already been assumed to be present only in vanishingly small steady-state concentrations, would not appear. Since the methylene white species W, HW, and H2W are present in such extremely small concentrations, the rate terms r,, rI2, rl3, r14, and r I 5should not participate to any extent in the mechanism and are removed. The final working equation takes the form
+ 1 / H 3 W + 4/F3)(H,W)(F3)/X
= l/k-,O + (H,W)(F,)[I + KI(H+) + KlK2(H+)*1/(B+)(Fe")[k, + ksK1(H+) + kl&1K2(H')21
( 1 /B+
A simplified, skeleton mechanism would consist of forward steps 8, 1 1 , and 16 and the reverse of step IO. As a starting point in the determination of the four rate constants, it was assumed that ks = k , , = k16 = k p This makes the equation linear, so that it can be plotted as well as easily handled by computer. The results were somewhat surprising. All of the data fit on the same straight line, with some scatter, but suggesting nothing but a linear plot. The rate constants are kf = (9.15 f 0.1 1 ) X I O 2 and klo= (2.75 f 0.24) X lo5, in units of M-l s-I, with the errors being quite reasonable for relaxation experiments. This result suggests that the extent of the protonation of ferrocyanide has no effect on the rate, all three species being equally effective in reducing methylene blue. One would expect that k l , would be the largest rate constant, controlling the reduction of the positive methylene blue with the' Fe" species of largest negative charge, and that increasing the
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 4119 H+ should make the rate constants smaller as the charge on the ferrocyanide is decreased through the formation of more H F and H2F. While this may be true, certain experimental difficulties come into play. Much below 0.02 M H+, it was not possible to gather useful relaxation data. At 0.02 M H+, the concentration of unprotonated ferrocyanide is less than the other Fe" species by over a factor of IO, so that only at our lowest H + is k , , contributing to the observed relaxation. A computer fit of the data is possible, however. The calculated rate constants are klo= (2.2 f 0.2) X lo5, k I 6= (9.0 f 0.1) X IO2, ks = (9.3 f 0.2) X IO2, and k , , = ( I . f 0.7) X IO4, with k l l clearly quite uncertain. This is presumably the upper limit to k , , . With the exception of the addition of the k , , term, these values differ little from those calculated by assuming equal rate constants and, in addition, the variance of these results is only slightly improved. This may simply mean that, for this reaction between oppositely charged species, the expected decrease in rate constants due to the charge reduction by protonation is unimportant. The effect of rate enhancement due to the protonation of ferrocyanide on an oxidizing agent of like charge has been reported by Diebler' and in our earlier study of the permanganate ferrocyanide reaction." In order to test further the H+ dependence, a series of runs was made using stopped flow procedures. The reactions were run under pseudo-first-order conditions with a fixed initial B+ concentration M. At an initial concentration of 8.1 X M of 3.2 X ferrocyanide and H + concentrations from 0.02 to 0.2 M, a pseudo-first-order rate constant of 2.69 f 0.08 s-I was obtained, whereas, with the ferrocyanide concentration at 5.2 X M and H+ concentrations from 0.001 to 0.26 M the observed pseudofirst-order rate constant was 51.0 f5 s-'. That is, there is no observed H+ dependence. This independent result further supports the view that the degree of protonation of ferrocyanide has little effect on the redox properties for this system. That is, the relaxation results suggesting that the rate constants for the forward steps are the same are probably closest to the truth, and attempting to computer fit an equation whose parameters are quite close together usually presents a problem. A few stopped flow runs were made with fixed H+ and varying total Fe". As expected, a very complicated dependence resulted. Since the reaction was proceeding to equilibrium and the concentrations of all the species involved could not be adequately accounted for, no serious attempt was made to formulate a conventional rate law. The equilibrium constant may be written in terms of the experimentally determined rate constants, as Since, only the rate constants ks and Llowere experimentally obtained, and K2 is known, it was not possible to verify the equilibrium constant in this way. On accepting the experimental was value of the equilibrium constant, a value of 3.2 X calculated for the ratio of kI0/k+ Although this is an interesting result, little more may be said. The two reactions of HB' are with different species and the result that HB' is oxidized much more rapidly than reduced should not be generalized to include all reactions of this radical intermediate. What would have been interesting is the determination of the values of both k8,k-8 and/or kll,k-ll. With these, the redox potentials for the reduction of B+ to B' or to HB' could have been estimated, giving valuable information on the behavior of protonated or unprotonated radical intermediates. Unfortunately, this was not meant to be; too few relaxations were observed. Other, less complicated systems are planned with the hope of gaining such information. Registry No. B+, 61-73-4; B', 613-1 1-6; W, 126296-37-5; Na,Fe(CN)6, 13601- 19-9; Na,Fe(CN),, 14217-21-1. (11) Rawoof, M. A,; Sutter, J . R.J . Phys. Chem. 1967, 71, 2767.
