Kinetic Study of Methylene Blue in Aqueous Solution (35) P. J. Derrick, A. M. Falick, and A. L. Burlingame, J. Am. Chem. Soc., 95, 437 (1973). The apparently reduced preference for &hydrogen transfer in hexanal as compared to hexanol might be a consequence of the geometries of the transition states. Considering neutral geometries, the distance of closest approach of the P-H to the 0 atom is 0.22 nm in hexanal and 0.19 nm in hexanol. See M. M. Green, R. J. Cook, J. M. Schwab, and R. B. Roy, J. Am. Chem. SOC.,92, 3076 (1970). (36) A. M. Falick, P. J. Derrick, and A. L. Burlingame, Int. J . Mass Spectrom. Ion Phys., 12, 101 (1973).
The Journal of Physlcal Chemistry, Vol. 83,
No. 12, 1979 1573
(37) (a) P. J. Derrick, R. P. Morgan, M. A. Baldwin, and J. T. Hill, Int. J. Mass Spectrom. Ion Phys., 18,393 (1975); (b) M. A. Baldwln, P. J. Derrick, and R. P. Morgan, ibid., 20, 193 (1976). (38) W. G. Brown In “Organic Reactions”, Vol. 6, R. Adams, Ed., Wiiey, New York, 1951, Chapter 10, p 469. (39) 0. Kamm and C. S. Marvel in “Organic Synthesis”, Collect. Vol. 1, H. Gilman and A. H. Blatt, Ed., Wiley, New York, 1964, p 25. (40) E. E. Dreger in ref 39, p 306. (41) L. Caglioto and P. Graselli, Chem. Ind., 153 (1964).
Kinetic Study of the Monomer-Dimer Equilibrium of Methylene Blue in Aqueous Solution Wynetta Spencert and John R. Sutter“ Deparfment of Chemistry, Howard University, Washington, D.C. 20059 (Received August 18, 1978; Revised Manuscript Received December 27, 1978)
The monomer-dimer equilibrium of methylene blue was investigated by utilizing temperature-jump techniques. For the reaction 2MB+ (MB+)z,the extinction coefficient of the monomer (e,) and dimer (€d) and K,, were determined spectrophotometrically at 610 and 660 nm at 20 OC. At 610 nm, em, €d, and Kegwere found to be 3.87 X lo4 M-l cm-’, 9.05 X lo4 M-l cm-l , and 3.97 X lo3 M-l, respectively. No effect of the [H+]on the measured to 6.7 X relaxation times was observed. By using methylene blue concentrations from 1.26 X M at fixed [H+],the measured relaxation times were used to determine forward and reverse rate constants and Keg at five temperatures. The overall AH of the reaction was calculated from a log Keqvs. 1 / T plot and found to be -19.9 f 2.5 kcal/mol. AH was also determined from relaxation amplitude studies at 20 “C which yielded a value of -13.9 f 0.8 kcal/mol. The activation enthalpies in the forward and reverse directions were found to be -11.0 f 1.1and 8.9 f 1.2 kcal/mol, respectively. In light of the activation enthalpy results, a mechanism for the reaction is proposed.
Introduction In order to investigate multielectron transfer reactions using methylene blue (Figure 1) as the oxidant, it is necessary to first examine the monomer-dimer equilibrium of methylene blue in aqueous solution. Like the majority of organic dyes, methylene blue deviates from the Beer-Lambert 1aw.l It has been theorized that this deviation is due to the reversible formation of dye polymers, which are held together by dispersion forces originating from the delocalized 7 electrons of the individual dye molecules.2 In the concentration range from to M, the extent of aggregation of methylene blue is limited to dimerization, which results in absorbances in the visible region at 660 and 610 nm for the respective monomeric and dimeric specie^.^ There has been no kinetic study done on the monomer-dimer equilibrium of methylene blue to elucidate a mechanism for the system or to determine the magnitudes of any associated forward and reverse rate constants. Because dimerization equilibria usually proceed at a rapid rate,4 a kinetic study of the system utilizing temperature-jump techniques was undertaken making possible not only the deduction of reaction mechanisms, but the determination of kinetic activation parameters as well. Experimental Section Methylene blue (Fisher, USP) was purified by using a modification of Tzung’s5 procedure, which involved the continuous extraction of the dye with chloroform. The resulting dried product was then recrystallized three times from ethanol-water and dried over phosphorus pentoxide! Abstracted in part from a dissertation submitted by W. Spencer
to the faculty of Howard University in partial fulfillment of the
requirements for the Ph.D. Degree.
0022-3654/79/2083-1573$0 1 .OO/O
Stock solutions of methylene blue were prepared by weight with distilled water, The ionic strengths of the solutions were maintained at 0.5 or 1.0 M for all temperatures with potassium nitrate (Mallinckrodt, Analytical Reagent). No change in relaxation times was observed at 14 “C when the ionic strength was changed from 0.5 to 1.0 M ( I = 0.5 M, 1 / =~1.75 f 0.13 X lo5 s-l I = 1.0 M, 1 / ~ = 1.73 f 0.08 X lo5 s-’), Hydrochloric acid (Baker and Adamson, ACS Reagent), used without further purification, was standardized against sodium carbonate. The spectrophotometric determinations of em, Ed, and KA were performed on a Beckman DK ratio recording spectrophotometer with a thermostated cell holder. The temperature-jump apparatus used for kinetic runs is described el~ewhere.~ All relaxation times for the kinetic study of the monomer-dimer equilibrium were measured a t 610 nm. Relaxation spectra of a solution 1.2 X lov5M in methylene blue, [Ht] = 0.1 M, obtained a t 610 and 660 nm had the same amplitudes and relaxation times but “relaxed” in opposite direction. The thermostated cell holder maintained the solutions at a temperature such that, after perturbation, the final temperatures are those given in the text. A jump of 4 or 8 “C was obtained depending on the cell and/or the capacitor used. Results and Discussion
Absorbances at 660 and 610 nm were obtained at 20 “C from the variation of the total methylene blue concentration from 8.39 X lo-@to 2.09 X M for the determination of em, €& and Kegof dimerization. The plots of absorbance vs. concentration at both wavelengths exhibited the expected deviation from linearity necessitating the derivation of expressions for the absorbance in terms of the total concentrations and the 0 1979 American Chemical Society
1574
The Journal of Physical Chemistry, Vol. 83, No. 12, 1979
W. Spencer and J. R. Sutter
TABLE 11: Rate Constants for Methylene Blue
T. C 9
10 14 20 30 Flgure 1. Methylene blue.
a
k f X lo-' M-I s - l
kc X
10.93 t 0.41 10.43 i 0.52 6.16 i 0.70 5.09 r 0.60 3.02 ?r 0.9
K , x 10-3
h-I a
s-'
6.49 i 0.20 6.57 t 0.20 11.20 t 0.56 13.27 i 0.39 21.2 i 0.05
16.83 15.88 5.49 3.84 1.42
K,, was determined from the ratio of kflk,.
TABLE I: Thermodynamic Parameters for Methylene Blue
/
x 10-4 T,K
ref 3 8 9
300
10 11
303
12 13 14 15 16
298 293 298 303 300 293
this work a
K e a , M-' 3.57 X l o 3
2.59 X l o 3 4.65 X l o 3 5.88 X l o 3 2.0 X l o 3 2.5 X l o 3 3 . 9 7 ~l o 3 a
(h,
x 10-4
nm)
4.0(656.5) 8.4(660) 8.0(660) 5.83(667) 6.2(665) 9.0(668) 9.5(664) 7.8(665) 8.5(662) 3.88(610) 7.18(660)
/ /
( A , nm)
1.02(656.5) /
3 9.
4.42(605)
/
9.0(615) 9,06(610) 1.54(660)
K,, was determined spectrophotometrically. /
unknown parameters E,, Ed, and K,,. For two monomers in equilibrium with a dimer 2MB+ e (MB+)z Keq
I
(1)
= kf/kr = [(MBf)~l/[MBf12
the absorbance may be expressed as A = EmCm + EdCd (2) where Cm and Cd are the respective monomer and dimer concentrations. Representing the total concentration of methylene blue as [MB+IT= Cm 2Cd, the absorbance is written as
+
l i Tx
cd[MBt 1T (3) 2 where eq 1 and 2 have been utilized. The non-linear least-squares computer analysis of the data fitted to eq 3 gave the following values for the parameters at 610 nm (eq 4a) and at 660 nm (eq 4b). E , = 3.88 f 0.1 X lo4 M-l cm-' Ed = 9.06 f 0.28 X io4 M-l Cm-' (44 K , ~= 3.97 f 0.47 x 103 M-1 E,
= 7.18 f 0.1 X lo4 M-l cm-l lo3 M-' cm-l K,, = 4.67 f 0.52 X lo3 M-l = 1.54 f 3.05 X
(4b)
The values of Keqat 20 "C and the extinction coefficient for the monomer at 660 nm compare favorably with prc iriously determined values in the literature"16 (Table I). By assuming that the mechanism for the monomerdimer equilibrium of methylene blue is the simple, one-step reaction in eq 1,an expression for the reciprocal relaxation time, 117, may be derived by using the method of Castellanl' 1 /= ~ 4kf[MB+]+ k, (5)
36
103
Flgure 2. Plot of log K,, vs. l I T ( K ) for methylene blue: 0 ,ref 3; A, ref 12; 0,ref 13; 0 , ref 14; H, ref 15; A, ref 16; 0, this work.
where hf and k, are the forward and reverse rate constants for the reaction. By expressing the monomer concentration in terms of the total methylene blue concentration, the reciprocal relaxation time may be written as 1 / 7 = 8kflz,[MB+],
c
td
34
32
+ 12:
(6)
Initially, the methylene blue concentration was fixed at 1.26 X M, I = 0.5 and [H'] was varied from 7.94 X lo-' to 0.41 M. The relaxation times measured a t 14 "C were not affected over the wide [H+]range. At [H+] = 7.94 X loT7,1.82 X 0.13, 0.25, and 0.41 M the reciprocal relaxation times were 1.61, 1.40, 1.61, 1.51, and 1.66 X lo6 s-l, respectively. The concentration of methylene blue was then varied from 1.26 X 10" to 6.7 X M at a fixed [H+] of 0.1 M and the relaxation times measured a t 9, 10, 14, 20, and 30 "C. Values of kf, k,, and K,, = kf/k, were evaluated at each temperature by a linear least-squares fit of the data to eq 6 (Table 11). K,, calculated a t 20 "C compared favorably with the K,, evaluated from absorbance measurements at 20 "C. The overall enthalpy of dimerization, AH, was determined from the slope of the line defined by plotting the log K vs. 1/T. The resulting value, -19.9 f 2.5 kcal/mol, as we? as the values of Kegmay be compared with those reported by a variety of investigators (Figure 2). AH was also determined from relaxation amplitude studies at 20 OC. For the monomer-dimer equilibrium of methylene blue, the derived expression for the relaxation amplitude is the linear equation18
where AE =
td
-
2t, and 1 is the temperature-jump cell
'i
monomer units into a sandwich structure with the principal axes parallel and the bridging nitrogen of one monomer unit opposite the sulfur atom of the sec0nd.1~ The above mechanism leads to the expression for the reciprocal relaxation time
H
8 m
.
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The Journal of Physical Chemistry, Vol. 83, No. 12, 1979
Kinetic Study of Methylene Blue in Aqueous Solution
1'
c\l
b-4
72
4kf,obsd[MB+l + kr,obsd (lo) L
1
2
4
3
L
Flgure 3. Plot of d1/2.3031vs. [(4/[MB+]) OP.
+ (l/[(MB+)2])]-1 at 20
u.
after assuming the steady-state approximation for the complex. The equilibrium constant is obtained from the ratio of the observed forward and reverse rate constants as it must. The steady-state approximation for the complex leads to a relaxation amplitude expression for mechanism I that is identical with the solution for the one-step mechanism.ls If, for example, mechanism I had been treated as a system with two well-separated relaxation times with only the slower one observed, the ratio of the forward and reverse rate constants would not have yielded K , and, hence, must be discarded. ?'he forward and reverse rate constants, eq 10, will yield the observed negative AH; provided kl >> k-zKeq,then AH,' = AH AH-z' and AH,' = A X 2 * with , AH,' being negative because AH is exothermic to the extent of 19 kcal/mol. The reciprocal relaxation time is then given by
+
+
+ k-z
klk2
1,'. = 4k-zKeq[MB+] k-2 = 4-[MB+] k-1
(11)
By assuming that the first step of mechanism I is diffusion controlled, the rate constants kl and k-l may be determined ignoring the effect of high ionic strength on the calculation, from the relationship^'^ 3
kl =
l / T x 10
(-)(
Figure 4. Plots of log [ k , l T ( K ) ] and log [ k , I T ( K ) ] vs. l I T ( K ) .
pathlength. The linear least-squares fit of the dI/2.3031 vs. [(4/[MB+]) (l/[(MB+)z])]-lplot as suggested by eq 7 (Figure 3) yielded AH = -13.9 f 0.8 kcal/mol. The transition-state equation was used to calculate the activation enthalpies and entropies for the forward and reverse directions at 9, 10, 14, 20, and 30 "C by plotting log ( k f , , / T )vs. 1 / T (Figure 4): AH,' = -11.0 f 1.1kcal/ mol; AS$ = -56 f 4 cal/mol K, A",' = 8.9 f 1.2 kcal/mol; AS,* = 4.7 f 4 cal/mol K; AH = AH,' - AHr' = -19.9 kcal/mol; and A S = AS,' - AS: = -60.7 eu. In view of the negative AH: obtained, it is unlikely that the mechanism for the monomer-dimer equilibrium of methylene blue is represented by the one-step reaction in eq 1. It is necessary, therefore, to propose one or more mechanisms that are consistent with all of the kinetic data and provide an explanation for the negative activation enthalpy in the forward direction. One such mechanism involves the formation of a complex from the diffusion-controlled interaction of two monomers, followed by the transformation of the complex into the dimer:
+
mechanism I
2MB+ * C
C
F!
(MB+)z
hi, h-1
(8)
kz, h-z
(9)
Step 9 of mechanism I is governed by one of two kinetically indistinguishable processes; the ejection of a water molecule by the complex to form the dimer, or the geometrical rearrangement of the complex to the most stable dimer configuration. The latter process is the stacking of the
k-l =
[
4raDNo 1000
-][exp[ 6DZ2e2 a3dkbT
"')[
exp[
E'hbTa
"1
]
-1
dhbTa
E] - I] E'kbTa
exp[
"1
C'hbTa (12)
KD = k i / k - i where e is the electronic charge, e' is the dielectric constant of the medium, 80.18 at 20 " C ,2 is the ionic charge, +1 in this case, and D is the diffusion coefficient of the monomer, determined by Vetter and Bardelebeni2 to have a value of 7.6 X lo4 cmz/s. Rabinowitch and Epstein have calculated 3.12 A as the equilibrium separation of the monomers in the dimera3 By using this value plus the diameter of a water molecule, 2.8 A, for a, the distance of closest approach, one calculates hl = 1.76 X lo9 M-' s-l and kl = 2.23 X 1O1O s-l. By assigning h, = k2and by using Keaand KD, a value of 6.74 X lo9 s-l is calculated for kz. This value is somewhat faster than that expected for a water exchange step and suggests that this step is involved with the reorganization and stacking of the ions. Compare this to the water exchange rate constant of 5.9 X lo9 s-l for Cs+, also a large positive ion.20 kl is seen to be about 3.5 times faster than k-,K, which would just meet the requirement necessary to reduce the relaxation equation to the form of eq 11 and account for the negative A",'. A larger guess for a would better satisfy the requirement. The reaction thus consists of a diffusion-controlled equilibrium followed by an organizational step for the forward process with a reverse process being governed entirely by k-z.
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The Journal of Physical Chemistty, Vol. 83, No. 12, 7979
The diffusion-controlled approach and separation of these two large ions would normally be expected to be accompanied by only a small change in entropy, that entropy associated with the formation of the pairs and the release or partial release of solvent molecules. The AS; obtained, then, results principally from AS; and not ASD and would suggest that the stacking process of these ions occurs in step k2. On the other hand, while the large negative value of AH makes the A“,‘ reasonable, an alternative formulation of AH: must be examined; AH“ = AHD+ AH;. Since AH2’ must be positive, AHDmust be responsible for the observed exothermic activation enthalpy, and suggests that the dipole-dipole and/or iondipole interactions between the ions are already coming into play in this diffusion-controlled step. These interactions could, of course, result in the loss of internal degrees of freedom, which would result in a further loss in entropy not considered above. Two very interesting papers have appeared in the recent literature on the kinetics of the dimerization of thionine.21v22 The solvent effects discussed by Turner are consistent with our findings except that k-2 alone must bear the responsibility for the increase in k , on changing from water to ethanol-water mixtures rather than a decrease in both k 2 and k-l. By considering the monomeric methylene blue more strongly solvated than the intermediate, C, with the dimer the least solvated is consistent with the data. That is, solvent molecules seem to be lost in both steps of the mechanism. It would be of interest to determine the activation parameters in the mixed solvents to further examine the mechanism.
Acknowledgment. W.S. thanks the Biomedical Inter-
Masaaki Ishikawa disciplinary Project sponsored by the N.I.H. for a fellowship.
Supplementary Material Available: Tables of thermodynamic and’kinetic data for methylene blue (3 pages). Ordering information is available on any current masthead page. References and Notes (1) S.Sheppard and A. Geddes, J. Am. Chem. Soc., 66, 1995,2003 (1944). (2) S. E. Sheppard, Rev. Mod. Phys., 14, 303 (1942). (3) E. Rabinowitch and L. Epstein, J. Am. Chem. SOC.,63, 69 (1941). (4) M. Eigen and L. DeMaeyer, “Techniques of Organic Chemistry”, 2nd ed, Vol. VIII, Part 2,A. Weissberger, Ed., Wiiey-Interscience, New York, 1963,p 895. (5) C.-Y. Tzung, Anal. Chem., 39, 391 (1967). (6) R. Wopschall and I. Shain, Anal. Chem., 39, 1527 (1967). (7) R. M. Reich and J. Sutter, Anal. Chem., 49, 1081 (1977). (8) G. Lewls and J. Bigeleisen, J . Am. Chem. Soc., 65, 1144 (1943). (9) L. Michaelis and S. Granick, J . Am. Chem. Soc., 67, 1212 (1945). (10) D. Lemin and T. Vickerstaff, Trans. Faraday Soc., 43, 491 (1947). (11) M. Schubert and A. Levine, J . Am. Chem. Soc., 77, 4197 (1955). (12) K. Vetter and J. Bardeleben, Z. Elektrochem., 61, 135 (1957). (13) H. Dunken and D. Schmidt, Z. Chem., 11, 349 (1962). (14) K. Bergmann and C. O’Konski, J. Phys. Chem., 67, 2169 (1963). (15) E. Brasweil, Z. Phys. Chem., 94, 161 (1975). (16) A. K. Ghosh, Z. Phys. Chem., 94, 161 (1975). (17) G. Casteilan, Z. Phys. Chem., 67, 898 (1963). (18) D. Thusius, J. Am. Chem. SOC., 94, 356 (1972). (19) I. Amdur and G. Hammes, “Chemical Kinetics; Principles and Selected Topics”, “Series in Advanced Chemlstry”, McGraw-Hili, New York, 1966,p 62. (20)G. Fiynn and N. Sutin, “Chemical and Biochemical Applications of Lasers”, C. Bradley Moore, Ed., Academic Press, New York, 1974, I) 328. (21) W. Inaoka, S. Harada, and T. Yasunaga, Bull. Chem. SOC.Jpn., 51, 1701 (1978). (22) T. G. Dewey, P. Wilson, and D. Turner, J . Am. Chem. SOC.,100, 4550 (1978).
Polyion Effect on Ionic Reactions. 2. Reactions between m and n Valent Ions Masaaki Ishikawa Department of Polymer Chemistry, Kyoto University, Kyoto, Japan (Received October 18, 1978)
The acceleration factor for reactions between m and n valent ions in the presence of polyions was calculated by using the numerical solutions of the Poisson-Boltzmann equation applied to a rodlike polyelectrolyte solution. A comparison between theory and experiment for the dependence of the acceleration factor on polyion concentration was carried out for four types of reactions. The agreement between the calculated and experimental results is generally satisfactory. In the reaction between divalent counterions, however, a parameter for competition of the reactants for the polyion domain was introduced to give better agreement. Moreover, the aspects of the polyion effect, that is, the product inhibition phenomenon, and also the dependence of acceleration factor on the valencies of reactants, the radius of polyion, the charge spacing of polyion, etc. were discussed. It is concluded that the theory based on the Poisson-Boltzmann equation can well explain the polyion effect on ionic reactions.
Introduction There have been a great number of experimental studies of the polyion effect on interionic reactions. Ise and c o - w ~ r k e r s interpreted l~~~~ the polyion effect in terms of an activated complex in analogy to the Bronsted theory by using Manning’s treatment of polyelectrolyte solution. The agreement between theoretical and experimental values for the acceleration factor was satisfactory in some ionic reactions between oppositely charged ~ p e c i e s . ~ Because of the limitation of Manning’s theory, however, their theory is applicable neither to reactions between
similarly charged species, nor to reactions between oppositely charged species when one of the reactants completely condenses on the polyion. Morawetz and c o - w ~ r k e r s ~interpreted -~ the polyion effect in terms of local concentrations of reactants and expressed the acceleration factor for the reaction between A and B as
where k z is the rate constant in the presence of polyion,
0022-3654/79/2083-1576$01.00/00 1979 American Chemical Society
