In the Laboratory
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Kinetics of Reduction of Toluidine Blue with Sulfite— Kinetic Salt Effect in Elucidation of Mechanism S. B. Jonnalagadda* and N. R. Gollapalli Department of Chemistry, University of Durban–Westville, Private Bag X54001, Durban 4000, South Africa; *
[email protected] An ideal chemical system for study of reaction kinetics in the undergraduate laboratory should be easy to handle, simple in procedure, and suitable to probe into mechanistic details. In these respects, the reduction reaction of toluidine blue (TB+) by sulfite ion is ideal and informative for students in the physical chemistry laboratory to identify the species involved in the rate-limiting step. The pace of decolorization during the reaction gives a qualitative perspective of the velocity of reaction, and kinetics can be followed with relative ease. The reaction is slow enough to allow thermostating of reaction mixtures during the kinetic measurements and fast enough to carry out a kinetic run in about 20 min. The primary kinetic salt effect exhibited by the reaction can be used to understand the nature of the reacting species that form activated complex. The study can be utilized to illustrate different calculation procedures in treating the kinetic data. This laboratory experiment can also be coupled with an extended classroom discussion of concepts in kinetics and salt effects. Theory In aqueous solutions, ionic strength plays an important role in theories of reaction rates. It can be studied by varying the concentration of an inert electrolyte. The Brönsted equation (eq 1) predicts the influence of ionic concentration and charges on the reaction rate in dilute solutions. k = k 0 γ A γB / γ ‡
(1)
where k0 is the limiting value of the rate constant as ionic strength tends to zero and γA, γB, and γ‡ are the activity coefficients for A, B, and activated complex, respectively. The Debye–Hückel limiting law (eq 2) presents the relationship between the ionic strength ( µ) and the activity coefficients ( γ) of the reacting ions in the solution. log γi = A|z i2| µ0.5
(2)
where z is the ionic charge and A is a constant that depends on the dielectric constant and temperature of the solution. By substituting eq 2 in eq 1, we derive a relationship between the rate constant and ionic strength (1) (Appendix). For the reactions in dilute aqueous solutions, the equation may be given as log k = log k0 + 1.02 zAzB µ0.5 (3) Therefore, a plot of log k versus µ0.5 should be linear, with the slope and intercept equal to 1.02 zAzB and log k0, respectively. The slope represents the product of charges on the species involved in the rate-limiting step. If the rate-limiting step is between the species of like charges, a positive slope is expected. When the reaction is between opposite charges, it results in a negative slope. In a kinetic experiment published earlier (2), the effect of ionic strength on the rate constant was investigated, but the kinetic salt effect was not correlated with the nature of 506
species. This laboratory experiment is designed to probe into nature of reacting species in the rate-determining step and to elucidate the reaction mechanism, if such information is not available a priori. Background Reactions of phenothiazine dyes such as toluidine blue (TB+) with different reducing agents are known to exhibit complex kinetics (3). Depending on the reductant, these reactions exhibit varying orders with respect to the reductant and either first-order or fractional-order dependence on TB+. For example, toluidine blue shows fractional-order kinetics in reaction with Sn(II) in acidic solutions (3). During the reaction of TB+ with thiourea, the reaction has first-order dependence on TB+ and the order with respect to thiourea is 1.22. The slightly higher reaction order was interpreted to mean that there existed a major pathway in which one molecule each of reductant and oxidant was involved in the ratedetermining step giving primarily first-order kinetics, but a minor pathway was also present that was second order with respect to thiourea (4). A similar mechanism was proposed for the reaction between thiourea and hexacyanoferrate (III) (5). The TB+–sulfite reaction follows overall second-order kinetics, with first-order dependence on each reactant. During the reaction, TB+ is reduced to toluidine white (TBH), either through two one-electron reduction steps (eq 4) involving formation of semi-toluidine blue as the transient intermediate (3, 6 ) or by a two-electron transfer step (7 ) (eq 5). H3C
N
H2N
S +
+ e–
N(CH3)2
TB+ H3C
N
H2N
S
+ e–
(4) N(CH3)2
TBⴢ H3C
H N
H2N
S
N(CH3)2
TBH
TB+ + SO32 + H2O → TBH + SO42 + H+
(5)
If the rate-limiting step involves one-electron transfer, the order with respect to sulfite will be fractional; and if it involves a two-electron reduction, the order will be unity. Considering first-order dependence of the reaction on both [TB+] and [sulfite], it may be inferred that the title reaction involves a two-electron transfer step. Thus, the TB+–sulfite
Journal of Chemical Education • Vol. 77 No. 4 April 2000 • JChemEd.chem.wisc.edu
In the Laboratory
reaction forms an ideal chemical experiment to be assigned to undergraduate students. Experimental Procedure The experiment is planned for two 3-hour laboratory sessions. This includes time for briefing on the principles and preparation of solutions. It can be divided into four sections: preparation of solutions, kinetic measurements, data analysis, and investigation of kinetic salt effect. In our laboratory, students work in pairs and share the stock solutions but submit their reports individually.
Preparation of Solutions Toluidine blue (TB+Cl) is recrystallized by adding 150 mL of ethanol to 100 mL of 5% aqueous solution of toluidine blue and cooling the mixture to about 5 °C (6 ). Students need to prepare 100 mL of stock solutions of TB+ = 2.0 × 104 M, Na2SO3 = 0.20 M, and NaCl = 0.60 M. Since aqueous sulfite solution undergoes photochemical oxidation, it is advisable to prepare this solution by adding trace amounts of benzyl alcohol (0.03 mL in 100 mL of solution) (8) to avoid photochemical oxidation.
method gives good results even if toluidine blue is used without further purification. Under pseudo-first-order conditions, a linear plot of log A or log ∆A vs time indicates the first-order dependence of rate on TB+ and the slope of the log [sulfite] vs log k′ plot will be equal to the order of reaction with respect to sulfite.
Investigation of Kinetic Salt Effect The primary kinetic salt effect can be studied by experiments with varying initial concentrations of sodium chloride at fixed concentrations of TB+ and sulfite. The ionic strength can be varied between 0.06 and 0.12 M by adding appropriate volumes of NaCl solution. A plot of log k′ vs µ0.5 is linear, with a slope 1.02 zAzB (eq 3). The sign of the slope indicates whether the species involved in the rate-determining step have like or unlike charges, and the magnitude gives the product of charges on the species.
Kinetic Measurements Initially, the spectrum of the reaction mixture containing 4.0 mL of TB+, 4.0 mL of sodium sulfite solutions, and 12.0 mL of water was scanned repetitively at 2-min intervals. Repetitive scanning is useful to determine the absorption maximum, to assess the approximate speed of reaction, and to detect the peak shifts, if any. TB+ has an absorbance peak at a wavelength of 596 nm ( λmax), with molar extinction coefficient ε = 24,000 M1 cm1. Kinetic runs are pursued by measuring absorbance of a mixture of thermostated solutions as a function of time at regular 20- or 30-s intervals up to 20 min. The requisite ionic strength of the medium is maintained by adding appropriate volumes of 0.60 M NaCl solution. The reaction is initiated by adding sulfite solution. In a typical kinetic run, the reaction mixture contains 4.0 mL of TB+, 4.0 mL of NaCl, 4.0 mL water, and 8.0 mL of sodium sulfite. The total volume of the reaction mixture is always kept at 20.00 mL. Plans for the student experiments are given in the supplemental material online.W
Results and Discussion The honors and undergraduate students in the chemistry department, UDW, have been using this experiment as a physical chemistry laboratory exercise. As a case study, the results of six undergraduate students are discussed here. The students undertook kinetic experiments in pairs, using the same stock solutions, thermostated at 25.0 ± 0.1 °C. They used Cary 1E Varian and NovaspecII UV–vis spectrophotometers. In the presence of excess sulfite (0.10 M) and low TB+ (2.0 × 105 M), in a typical kinetic run, the plot of log A vs time was linear (Fig. 1, curve a) for more than two half-lives. The data were also analyzed using the Guggenheim method (Fig. 2). The pseudo-first-order rate coefficients obtained by these two methods are 3.85 × 103 s-1 and 4.01 × 103 s-1, respectively. Since ionic strength influences the reaction rate between charged species significantly, µ was maintained constant during the variation of [sulfite]. Table 1 summarizes the rate constants for various concentrations of sulfite. The plot of log [sulfite] vs log k′ was linear with a slope equal to unity, suggesting a first-order dependence with respect to sulfite. The mean second-order rate constant was (3.6 ± 0.4) × 102 mol1 s1. Then ionic strength was varied between 0.06 and 0.12 M at fixed concentrations of TB+ and sulfite. The concentrations
Data Analysis According to the Beer–Lambert law (eq 6), the absorbance (A) of a dilute solution is proportional to its concentration, c, and path length, ᐉ: A = ε cᐉ (6) Under the experimental conditions, the TB+ concentration obeys the Beer–Lambert law. In the presence of excess sulfite and low [TB+] (pseudo-first-order conditions), the reaction is first order with respect to TB+. For a pseudo-first-order reaction, a plot of log [TB+] vs time or log A vs time should be linear (eq 7), with a slope k′/2.303. Here k′ a is pseudofirst-order rate constant. Thus, rate constants can be calculated from the gradient of the plot. log A = (k′/2.303) t + C (7) Alternatively, the Guggenheim method (9, 10) can be used to calculate rate constants. In this method, the slope of a plot of the log of the difference between consecutive absorbance values (log ∆A) vs time equals to k′/2.303. This
Figure 1. Plot of log A versus time for the toluidine blue–sulfite reaction. Curve a: experimental curve; curve b: regression line. [Sulfite] = 10.00 × 102 M and [TB+] = 2.0 × 105 M.
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Figure 2. Plot of log A versus time by the Guggenheim method. Conditions same as in Fig. 1.
Figure 3. Variation of log k ′ with ionic strength (µ0.5). [Sulfite] = 2.00 × 102 M and [TB+] = 2.0 × 105 M.
are in the range where the Debye–Hückel limiting law is obeyed. Therefore, activity coefficients of the ions are assumed near to unity and activities are equal to the concentrations of the charged species. Figure 3 illustrates a linear plot of log k′ vs µ0.5 whose slope is approximately 2.
The second-order rate constant is calculated by dividing the pseudo-first order constant by the sulfite concentration. Although the species in the rate-limiting step and the reactants are identical in this system, it is not a necessary situation in all reactions. Equation 10 is consistent with the experimentally obtained reaction orders. The agreement with the experimental results supports the proposed mechanism as the probable mechanism. Thus, the TB+–sulfite reaction can best illustrate the application of the kinetic salt effect in predicting the species involved in the rate-determining step and in elucidating reaction mechanism.
Rate Law and Reaction Mechanism The rate law expresses the relationship of the reaction rate to the rate coefficient and the concentrations of the reactants raised to some power—that is, the order of reaction with respect to respective reactants. The kinetic salt effect indicates possible species involved in the slowest step of the reaction scheme. Thus, the proposed mechanism should agree with the experimentally observed reaction orders with respect to the reactants. A first-order dependence of the reaction rate on the reactants and the observed negative kinetic salt effect suggests that the rate-limiting step involves one ion each of SO32 and TB+. Thus, the rate-limiting step of the reaction is a nucleophilic attack of sulfite ion on TB+ (eq 8). The activated complex subsequently hydrolyses to TBH and sulfate (eq 9). k
TB + SO3 → [TB–SO3] 2
+
(slow)
[TB–SO3] + H2O → TBH + SO4 + H
2
+
(8) (fast)
(9)
Based on eqs 8 and 9, the rate law can be written as r = k [SO32][TB+]
Here, k is the second-order rate constant. In excess [SO32], eq 10 reduces to eq 11. (11)
where k′ = k [SO32]. Table 1. Pseudo-First-Order and SecondOrder Rate Constants for Variation of Sulfite [Sulfite]/M
k ′/s 1
2.00 × 102
0.61 × 103
3.04 × 102
4.00 × 10
1.30 × 10
3.25 × 102
6.00 × 10
2.27 × 10
3.78 × 102
8.00 × 10
3
3.10 × 10
3.88 × 102
10.00 × 102
3.95 × 103
3.95 × 102
2 2 2
508
k /M1 s 1 3 3
Acknowledgments We thank the University of Durban–Westville, Durban, and Foundation for Research Development, Republic of South Africa, for funding these studies and O. Rajnund and other students for running the laboratory experiments. W
(10)
r = k′[TB+]
Post-Laboratory Discussion In post-laboratory questions, students can be questioned about concepts learned through this experiment, such as pseudo-first-order reaction, rate-determining step, ionic strength, kinetic salt effect and elucidation of the reaction mechanism.
Supplemental Material
Supplemental material for this article is available in this issue of JCE Online. Literature Cited 1. Laidler, K. J. Reaction Kinetics, Vol. 2, Reactions in Solution; Pergamon: Oxford, 1963; p 18. 2. Watkins, K. W.; Olson, J. A. J. Chem. Educ. 1980, 57, 158–159. 3. Jonnalagadda, S. B.; Dumba, M. Int. J. Chem. Kinet. 1993, 25, 745–753. 4. Jonnalagadda, S. B.; Tshabalala, D. Int. J. Chem. Kinet. 1992, 24, 999–1007. 5. Lilani, M. D.; Sharma, G. K.; Shankar, R. Ind. J. Chem. 1986, 25A, 370–374. 6. Mahadevan, J.; Guha, S. N.; Kishore, K.; Moorthy, P. N. Proc. Ind. Acad. Sci. 1989, 101, 43–48. 7. Hay, D. W.; Martin, S. A.; Ray, S.; Lichtin, N. N. J. Phys. Chem. 1981, 85, 1474–1479.
Journal of Chemical Education • Vol. 77 No. 4 April 2000 • JChemEd.chem.wisc.edu
In the Laboratory 8. Nilsson, G.; Rengemo, T.; Sillen, L. G. Acta Chem. Scand. 1958, 12, 868–875. 9. Espenson, J. H. Chemical Kinetics and Reaction Mechanisms, 2nd ed.; McGraw Hill: New York, 1995. 10. Hemalatha, M. R. K; Batcha, I. N. J. Chem. Educ. 1997, 74, 972– 994.
Appendix
log k = log k 0 – A {zA2 + z B2 – z‡2} µ0.5
Since the total charge on the activated complex is the sum of the charges on the reacting species log k = log k 0 – A {zA2 + z B2 – (zA + z B)2} µ0.5 Since
a2
log k = log k 0 + log γA + log γB - log γ‡ Substituting eq 2 in eq A1, we get
(A1)
(A3)
+ b2 – (a + b)2 = 2ab, eq A3 becomes log k = log k 0 + 2AzA z B µ0.5
If logarithms are taken on both sides of eq 1,
(A2)
(A4)
The value of A is approximately 0.51 for aqueous solution at 25 °C (1). Hence, eq A4 may be written as log k = log k0 + 1.02 zA z B µ0.5
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