Kinetics of the Oxidation of Iodide Ion by Persulfate Ion in the Critical

Article pubs.acs.org/JPCA

Kinetics of the Oxidation of Iodide Ion by Persulfate Ion in the Critical Water/Bis(2-ethylhexyl) Sodium Sulfosuccinate/n‑Decane Microemulsions Handi Yin,† Zhongyu Du,† Jihua Zhao,† and Weiguo Shen*,†,‡ †

Department of Chemistry, Lanzhou University, Lanzhou 730000, P. R. China School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China

‡

ABSTRACT: In this work, we studied the kinetics of the oxidation of iodide ion by persulfate ion in the critical water/bis(2-ethylhexyl) sodium sulfosuccinate (AOT)/n-decane microemulsions with the molar ratios of water to AOT being 35.0 and 40.8 via the microcalorimetry at various temperatures. It was found that the Arrhenius equation was valid for correlating experimental measurements in the noncritical region, but the slowing down effect existed significantly in the near critical region. We determined the values of the critical slowing down exponent and found it to be 0.187 ± 0.023 and 0.193 ± 0.032, respectively, which agreed well with the theoretical value of 0.207 predicted by the Griffiths−Wheeler rule for the singularity of the dimer/monomer droplet equilibrium in the critical AOT/water/ n-decane microemulsions.

1. INTRODUCTION

reaction was widely studied both in normal aqueous solutions and in microemulsions.18,19,24−29 This article is organized as follows. In Theoretical Background, we analyze the reaction mechanism of the oxidation of iodide ion by persulfate ion and suggest possible origins of the critical singularity in the reaction rate, from which we deduce the theoretical values of the critical exponent for comparison with the experiment. The details of our experimental method and results are described in Experimental Section. We discuss our experimental observations and compare with the theoretical prediction in Discussion, and then draw our conclusions in Section 5.

During the last four decades there have been extensive theoretical and experimental studies of critical effects on chemical reactions in critical gas−liquid fluids and critical binary liquid mixtures.1−15 These investigations have considered critical effects in reaction rates1−8 and chemical equilibria.9−15 Some of the experimental results have been reported to be consistent with the predictions made by Griffiths and Wheeler.16 Microemulsions are transparent, isotropic, and thermodynamically stable systems, composed of water, oil, and surfactant(s). The monodisperse droplets can be regarded as super molecules, which when properly mixed with oil molecules, can form a pseudo binary liquid system with a critical composition. The critical behavior of these emulsions has been shown to be consistent with the 3D Ising model.17 The water in oil (w/o) microemulsion droplets can function as microreactors, which have the capability of enhancing or retarding reaction rates.18−21 Properties of the microreactors can be easily adjusted by varying the size of the droplets. The size of droplets is determined by the molar ratio (ω) of water to surfactant,22 and the concentration of the droplets in a microemulsion is usually expressed by the volume fraction (Φ), which was assumed to be Φ = Φw + Φs with Φw and Φs being the volume fractions of water and surfactant, respectively.23 In this work, we extend the studies of the influence of the critical anomaly on the reaction rate and the equilibrium constant by examining microemulsion media using the microcalorimetry. We choose the oxidation of iodide ion by persulfate ion in water/bis(2-ethylhexyl) sodium sulfosuccinate (AOT)/n-decane microemulsions as our system because this © 2014 American Chemical Society

2. THEORETICAL BACKGROUND It was proposed that the oxidation of the iodide ion by the persulfate ion I− + S2 O82 − → I 2 + SO24 −

can be divided into two steps:

(1) 26

k1

step (1): I− + S2 O82 − → S2 O8I3 − k2

step (2): I− + S2 O8I3 − → 2SO24 − + I 2

(2)

where step (1), which produces the intermediate, S2O8I3−ion, is the slow reaction and the rate-determining step and step (2) is the fast reaction and consumes the intermediate S2O8I3− ion Received: September 10, 2014 Revised: October 23, 2014 Published: October 27, 2014 10706

dx.doi.org/10.1021/jp509158p | J. Phys. Chem. A 2014, 118, 10706−10712

The Journal of Physical Chemistry A

Article

quickly. Thus, the steady-state method can be used to derive the observed second-order reaction rate:30

# Kdroplet =

d[S2 O8I ] = k1[I−][S2 O82 −] − k 2[I−][S2 O8I3 −] = 0 dt

is the dimer/monomer equilibrium constant. As illustrated in eq 6, the concentration of S2O8I3− should be proportional to the concentration of the dimer:

(3)

# [S2 O8I3 −] ∝ Kdroplet [monomer][monomer]

3−

−

(8)

If the content of the dimer in the microemulsion is extremely low then the concentration of the monomer is constant and approximately equals to the number of the droplets in the microemulsion. Thus, according to eq 5, the reaction rate −[(d[I−])/(dt)] can be expressed by

(4)

k [S O2 −] d[I−] = k 2[I−][S2 O8I3 −] = k 2[I−] 1 2 8 dt k2 = k1[I−][S2 O82 −]

(7)

K#droplet

3−

k [I−][S2 O82 −] k [S O2 −] = 1 2 8 [S2 O8I ] = 1 − k 2[I ] k2

[dimer] [monomer][monomer]

(5)

−

When this reaction is carried in a critical pseudo binary microemulsion medium, the concentrations of the reactants and products are totally irrelevant to the critical concentrations of the microemulsion solution. Under these conditions, the Griffiths−Wheeler rule permits only a dynamic reaction rate slowing down effect having a critical exponent of about 0.04.31 However, Menger et al.32 analyzed the hydrolysis of esters in microemulsions and have suggested that the chemical reactions in microemulsions should have their origins in water pools, which merge and separate rapidly, causing the reactants to travel among micelles. They also used fluorescence measurements to confirm the process of droplet collision and instantaneous merging of water pools. These mechanics indicate the existence of dimer droplets in microemulsions which was also evidenced by some other investigations.33−35 The equilibrium of the dimer droplets with the monomer droplets possibly affects the oxidation of iodide ion by persulfate ion in the critical microemulsion system. If the potassium persulfate and potassium iodide exist separately in water pools, the reaction mechanism can be represented as33

d[I−] # [I−][S2 O82 −] ∝ k1Kdroplet dt

(9)

S2O2− 8

In the reaction system, if is largely in excess, the forward reaction becomes a pseudo-first-order reaction: −

d[I−] # ′ Kdroplet [I−] = kobs[I−] = kobs dt

(10)

where kobs is the observed reaction rate constant and k′obs ∝ k1[S2O2− 8 ]. The observed reaction rate constant kobs includes the contribution of K#droplet, therefore the critical singularity of K#droplet may be revealed in kobs. Defining the concentration of the dimer in the chemical equilibrium as ξe, the extent of the reaction in the chemical equilibrium, then # = Kdroplet

ξe ([droplet] − ξe)2

(11)

where [droplet] is the droplet concentration. When the dimer concentration is extremely low, the denominator in eq 11 equals [droplet]2 and is constant in the reaction process for each of the various temperatures. Therefore, K#droplet ∝ [ξe], and ⎛ dK # ⎞ ⎛ dξ ⎞ droplet ⎟ ⎜ ⎟ ∝ ⎜⎜ ⎝ dT ⎠e, P = P ⎝ dT ⎟⎠ c e, P = P

c

(12)

where the subscript “e” refers to the chemical equilibrium, P = Pc represents the pressure which is held constant at the critical value. In accordance with the Griffiths−Wheeler theory,16 the above partial derivatives with only pressure held constant should be strongly divergent as the microemulsion system approaches the critical state:10 ⎛ dK # ⎞ ⎛ dξ ⎞ ⎜ droplet ⎟ ∝⎜ ⎟ ∝ τ −(1 − 1/ δ) ⎜ dT ⎟ ⎝ ⎠e, P = P ⎝ dT ⎠e, P = Pc

where one circle refers to a monomer droplet and the two circles merging together indicates the dimer droplet. If the − concentrations of the S2O2− 8 and I ions are much larger and smaller than that of the microemulsion droplets, respectively, then each of the droplets may be occupied by several S2O2− 8 ions but no more than one I− on average. The excess S2O2− 8 ions, which are not involved in the reaction in the droplets, are for simplicity not indicated in the circles illustrated in eq 6. Equation 6 implies that the reaction only occurs in the dimer droplets, thus the concentration of the dimer also determines the reaction rate in the microemulsion medium. With the assumption that a chemical equilibrium exists between the dimer and monomer droplets:

c

(13)

where τ = |[(T − Tc)/(Tc)]| with Tc being the critical temperature, and δ = 4.82 is the critical exponent.11 Integral of the above formula yields # Kdroplet = I + Cτ1/ δ

(14)

Combining with eq 10, we have kobs = I ′ + C′τ1/ δ

(15)

where C, C′, I, I′ are constants. Equation 15 characterizes the critical singularity of kobs. As we suggested in our previous publication,31,36 kobs may be expressed by kobs = kbϕ(τ), where 10707


The Journal of Physical Chemistry A ⎧ ⎪1(far from the critical point) φ (τ ) = ⎨ ⎪ 1/ δ ⎩ I ″ + C″τ (near the critical point)

Article

the water/AOT/n-decane microemulsions. However, the critical temperatures of the microemulsions containing K2S2O8 with the ratios ω = 35.0 and ω = 40.8 turned to be 313.445 ± 0.100 K and 311.647 ± 0.100 K, respectively, increasing about 0.2 K as compared with that of the water/AOT/n-decane microemulsions, which may be attributed to the salt effect. We initiated the reactions by adding 25 μL solution (2) into 2.7 mL solution (1) for both microemulsion media with ω being 35.0 and 40.8 and determined the critical concentrations and the critical temperatures of the reaction systems after the chemical reaction reached equilibrium. No changes of the critical compositions were detected, and the critical temperatures were found to be 313.515 ± 0.100 K and 311.738 ± 0.100 K, respectively. Comparing the critical temperatures of the microemulsions containing K2S2O8 and the uncertainties in measurement of the critical temperatures, we concluded that addition of a small amount of KI and formation of the products of the reaction had no significant impact on the critical composition or the critical temperature. 3.4. Kinetics Measurement. The kinetic measurements of the reaction were conducted by using an isothermal titration microcalorimeter (TAM 2277-201, Thermometric AB, Sweden). This calorimeter was equipped with two 4 mL cells, one was a sample cell and the other was a reference cell. The temperature in the cells was controlled to within ±1 × 10−3 K. Before the reaction was initiated, 2.7 mL solution (1) was added into the sample cell, while 3.0 mL water/AOT/n-decane microemulsion was added into the reference cell to reduce the instrument noise in the measurements. A certain amount of solution (2) was filled in a Hamilton syringe. After thermal equilibration, 25 μL solution (2) was injected into sample cell by the Hamilton syringe, and the calorimetric signal for the reaction at various reaction times at a fixed temperature was recorded automatically. This procedure was repeated for various temperatures from the noncritical region to the critical region. The content of the droplets were estimated by the aggregation number of the droplets, and it was found that each of the droplets was occupied by about 10 ions of S2O2− 8 and 0.1 ions of I− in average, which ensured the reaction being a pseudo-firstorder one and in the case described in Theoretical Background. The heats of mixing 2.7 mL of solution (1) and 25 μL of solution (2) without KI and mixing 2.7 mL of solution (1) without K2S2O8 and 25 μL of solution (2) were determined and found to be about 0.8% of the heat of the reaction, which could be neglected. As an example, a typical plot of the calorimetric signal against time at 313.321 K for the reaction I− + S2O2− 8 in a water/AOT/ n-decane microemulsion with ω = 35.0 is shown in Figure 1. 3.5. Data Analysis. Defining a dimensionless reduced extent (Ψ) of the reaction as a ratio of the reaction extent ξ at time t to the reaction extent ξe at the equilibrium:22

(16)

Thus, in the near-critical region: kobs − I ″ = C″τ1/ δ kb

(17)

When kobs/kb ≫ I″, eq 17 can be written as

kobs = C″τ1/ δ kb

(18)

The natural logarithm of both sides in eq 18 gives ln

kobs 1 = ln τ + ln C″ δ kb

(19)

Consequently, a slowing down effect of the reaction predicted by eqs 17 or 19 with 1/δ = 0.207 may be expected to be experimentally observed.

3. EXPERIMENTAL SECTION 3.1. Materials. The AOT (≥99% mass fraction) was purchased from Sigma-Aldrich and dried in a vacuum desiccator over P2O5 for 2 weeks before use. The n-decane (>99% mass fraction) was purchased from Alfa Aesar. KI (>99% mass fraction) and K2S2O8 (>99% mass fraction) were purchased from Beijing chemical reagent factory. The doubly distilled water was used throughout the study. 3.2. Sample Preparation. Both KI and K2S2O8 aqueous solutions with the concentrations being 0.015 mol L−1 were prepared, which were used to further prepare the AOT microemulsion containing KI or K2S2O8 separately. During preparation of any of these microemulsions, proper quantities of AOT, n-decane, and the KI (or K2S2O8) aqueous solutions were weighed into a sealable glass tube according to a required molar ratio ω of water to AOT and a required concentration of AOT. The microemulsion with the reactant KI or K2S2O8 was denoted as solution (1) or solution (2), respectively. The reaction started when solutions (1) and (2) were mixed. Particular attention was paid to ensure that the two microemulsions had the same value of ω and the same concentration of AOT, which avoided the heat of mixing as the two microemulsions were mixed. A water/AOT/n-decane microemulsion with required value of ω and the concentration of AOT but without the reactant was also prepared as the reference in calorimetric measurements. 3.3. Determination of the Critical Compositions and the Critical Temperatures of the Reaction Systems. The critical compositions and the critical temperatures of the water/ AOT/n-decane microemulsions and the K2S2O8 aqueous solution/AOT/n-decane microemulsions with ω being 35.0 or 40.8 were determined by the method of “equal volume”: adjusting the droplet concentration to achieve identical volumes of two separating liquid phases at the phase separation temperature, and these concentrations and phase separation temperatures were taken to be the critical ones.31,36 The critical volume fractions (Φc) of the water/AOT/n-decane microemulsions with the ratios ω = 35.0 and ω = 40.8 were found to be 0.099 and 0.098, respectively, and the corresponding critical temperatures were 313.248 ± 0.100 K and 311.449 ± 0.100 K, respectively. The critical concentrations for microemulsions containing K2S2O8 were found to be no different from that of

Ψ=

ξ ξe

(20)

where ξ is proportional to the total heat (Q) produced in the reaction before time t for a chemical reaction, thus Ψ=

Q ξ = ξe Qe

(21)

where Q is the heat produced in the reaction before time t and Qe is the total heat produced in the whole reaction. 10708



Article

Table 1. Observed Rate Constants kobs at Various Temperatures T for the reaction I− + S2O2− 8 in Critical Water/AOT/n-Decane Microemulsions (ω = 35.0) T (K) 305.078 306.117 307.118 308.122 309.245 310.123 311.124 312.125 312.315 312.555 312.736 312.923 313.112

Figure 1. Typical plot of calorimetric signal P vs t of the reaction I− + S2O2− 8 in the water/AOT/n-decane microemulsion (ω = 35.0, T = 313.321 K).

T (K)

± ± ± ± ± ± ± ± ± ± ± ± ±

313.224 313.246 313.263 313.279 313.298 313.321 313.343 313.355 313.386 313.403 313.449 313.466 313.480

2.25 2.41 2.56 2.84 3.00 3.16 3.44 3.75 3.60 3.46 3.46 3.31 3.01

0.09 0.10 0.11 0.11 0.12 0.13 0.14 0.15 0.25 0.24 0.24 0.23 0.21

104kobs (s−1) 3.29 3.28 3.16 2.85 3.01 2.99 2.85 2.71 2.85 2.72 2.58 2.42 2.08

± ± ± ± ± ± ± ± ± ± ± ± ±

0.23 0.23 0.22 0.20 0.21 0.21 0.20 0.18 0.20 0.19 0.18 0.17 0.15

Table 2. Observed Rate Constants kobs at Various Temperatures T for the Reaction I− + S2O2− 8 in Critical Water/AOT/n-Decane Microemulsions (ω = 40.8)

For a first-order or a pseudo-first-order reaction, the reduced extent (Ψ) of the reaction could be expressed by ln(1 − Ψ) = −kobst

104 kobs (s−1)

T (K)

(22)

302.125 303.635 305.135 306.585 308.085 310.024 310.271 310.562 310.886 311.206 311.221 311.242 311.263

Therefore, a plot of ln(1 − Ψ) against t should yield a straight line, and the slope is −kobs. Such a plot for the reaction in the microemulsion medium with ω = 35.0 and at T = 313.321 is shown in Figure 2 as an example. The values of kobs

104 kobs (s−1)

T (K)

± ± ± ± ± ± ± ± ± ± ± ± ±

311.451 311.476 311.505 311.528 311.539 311.558 311.577 311.591 311.613 311.633 311.653 311.673 311.678

1.49 1.81 1.97 2.25 2.57 2.90 3.02 3.18 3.01 2.98 2.72 2.85 2.71

0.06 0.07 0.08 0.09 0.10 0.12 0.12 0.13 0.21 0.21 0.19 0.20 0.19

104 kobs (s−1) 3.16 3.00 2.67 2.56 2.70 2.56 2.54 2.69 2.40 2.54 2.55 2.39 2.11

± ± ± ± ± ± ± ± ± ± ± ± ±

0.22 0.21 0.19 0.18 0.19 0.18 0.18 0.19 0.17 0.18 0.18 0.17 0.15

and 40.8. The critical temperature decreases about 1.80 K as the value of ω increases from 35.0 to 40.8. It was well-known that a decrease of the critical temperature for a pseudo binary microemulsion solution with a low critical solution point results in the reduction of the stability of the system, which was attributed to the fact that the microemulsion droplets with larger size have stronger net interaction between them, hence more conducive to droplet aggregation and further to the phases separation.37,38 Therefore, the value of dimer/monomer equilibrium constant K#droplet in eq 7 and hence the observed reaction rate constant, according to eq 10, should be larger for the microemulsion system with ω = 40.8 than that with ω = 35.0. However, this prediction could not be observed in Tables 1 and 2. It is not surprising because it was evidenced that the oxidation of iodide ion by persulfate ion was significantly accelerated in water/AOT/n-decane microemulsion media as compared in the aqueous solutions, and the reaction rate increases with decreases of ω due to variation of the water activity and the salt effect in the water core of the microemulsion droplet,39 which is dominant over the dimer/monomer effect. The plots of ln kobs versus 103/T for the microemulsions with ω being 35.0 and 40.8 are shown in Figures 3 and 4, respectively. The Arrhenius equation is expressed by

Figure 2. Typical plot of ln(1 − Ψ) vs t for the reaction I− + S2O2− 8 in the water/AOT/n-decane microemulsions (ω = 35.0, T = 313.321). ■ represents the experimental result; the line represents the result of the fit with eq 22.

at various temperatures for the two different microemulsions with the ratios ω being 35.0 and 40.8 were obtained by the least-squares fits of the experimental data of ln(1 − Ψ) at various t, which are listed in Tables 1 and 2, respectively. The uncertainties in determinations of kobs were estimated to be about 4% and 7% of the values for the noncritical and the near critical regions, respectively.

4. DISCUSSION As was shown in Determination of the Critical Compositions and the Critical Temperatures of the Reaction Systems, the critical temperatures are 313.248 and 311.449 K for the water/ AOT/n-decane microemulsion systems with ω being 35.0 and 40.8 and 313.445 and 311.647 K for the K2S2O8 aqueous solution/AOT/n-decane microemulsions with ω being 35.0

ln k b = −Ea /RT + B 10709

(23)



Article

corresponding temperature were obtained through eq 23 with known values of the activation energies (Ea) and the intercepts (B). The calculated values of kobs/kb at various temperatures in the near critical regions then were fitted to eq 17 to obtain the values of I″, C″, and 1/δ, which are listed in Table 3. The values Table 3. Results of Fits with eq 17 at ω = 35.0 and 40.8. ω

I″

C″

1/δ

35.0 40.8

0.017 ± 0.008 0.015 ± 0.005

2.882 ± 0.945 3.099 ± 0.878

0.189 ± 0.034 0.195 ± 0.028

of 1/δ were found to be 0.189 ± 0.034 and 0.195 ± 0.028 for the microemulsions with ω being 35.0 and 40.8, respectively, showing a universal characteristic independent of the size of the microemulsion droplet in the experimental uncertainties. It was found that kobs/kb > 0.45 and I″ was about 0.015, indicating kobs/kb ≫ I″, therefore, eq 19 is valid and the plot of ln(kobs/kb) against ln τ should yield a straight line. These linear relations for the microemulsions with ω being 35.0 and 40.8 are shown in Figures 5 and 6. The critical exponents were redetermined by

Figure 3. Plot of ln kobs vs 103/T for the reaction I− + S2O2− 8 in the critical water/AOT/n-decane microemulsion (ω = 35.0). ■ represents the experimental results; the line represents the result of the fit with eq 23.

Figure 4. Plot of ln kobs vs 103/T for the reaction I− + S2O2− 8 in the critical water/AOT/n-decane microemulsion (ω = 40.8). ■ represents the experimental results; the line represents the results of the fit with eq 23.

Figure 5. Plot of ln(kobs/kb) vs ln τ for the reaction I− + S2O2− 8 in the critical water/AOT/n-decane microemulsion (ω = 35.0) near the critical point.

where Ea is activation energy, R is gas constant, kb = kobs when the temperature ranges far away from critical temperature. Figures 3 and 4 present good linear relations between ln kobs and 103/T in the temperature range (Tc − T) > 1.3 K. The values of the activation energies (Ea) and the intercept B in eq 23 for the two microemulsions with ω being 35.0 and 40.8 were obtained from the linear least-squares fits, which were 56.90 ± 1.89 and 65.02 ± 1.93 kJ mol−1 for Ea and 14.02 ± 0.74 and 17.10 ± 0.76 for B, respectively. The values of the observed reaction rate constants in the two media at 298 K were calculated to be 0.0087 mol−1 s−1 L and 0.0071 mol−1 s−1 L for the microemulsions with ω being 35.0 and 40.8, respectively, and well-agreed with that reported by Izquierdo et al. for the same reaction system.18 These linear relations served as the “background” for determining the critical effect. It can be observed in Figures 3 and 4 that the rate constants of the pseudo-first-order reaction deviate from the “background” significantly in the near critical region, showing obvious slowing down effects. We calculated the values of kobs/kb at various temperatures in the near critical regions for microemulsions with ω being 35.0 and 40.8. During the calculations, the values of kb at each

Figure 6. Plot of ln(kobs/kb) vs ln τ for the reaction I− + S2O2− 8 in the critical water/AOT/n-decane microemulsion (ω = 40.8) near the critical point.

linear least-squares fits and found to be 0.187 ± 0.023 and 0.193 ± 0.032. These values are significantly larger than 0.04 predicted for a dynamic slow-down effect but agree well with 10710



Article

(7) Wang, J.; Chen, Y.; Shi, B.; Xie, Y.; Cao, Y.; Liu, Y.; Zhang, S. Kintetics of SN1 Reaction in Triethylamine + D2O near the Consolute Point. J. Mol. Liq. 2013, 177, 313−316. (8) Wang, J.; Shi, B.; Shi, Z.; Cao, Y.; Liu, Y.; Zhang, S. Saponification of Ethyl Acetate in 2,6-Lutidine + Water near its Critical Point. Phys. Chem. Liq. 2013, 51, 338−348. (9) Gitterman, M. Singularity in the Degree of Dissociation near a Critical Point. Phys. Rev. A 1983, 28, 358−360. (10) Wheeler, J. C. Singularity in the Degree of Dissociation of Isobutyric Acid, Water Solutions at the Critical Solution Point. Phys. Rev. A 1984, 30, 648−649. (11) Anderson, E. M.; Greer, S. C. Chemical Reactions near Critical Points: The Dissociation of Weak Acids. Phys. Rev. A 1984, 30, 3129− 3135. (12) Procaccia, I.; Gitterman, M. Anomalies in Chemical Equilibria near Critical Points. Phys. Rev. A 1983, 27, 555−557. (13) Wheeler, J. C.; Petschek, R. G. Anomalies in Chemical Equilibria near Critical Points of Dilute Solutions. Phys. Rev. A 1983, 28, 2442− 2448. (14) Tveekrem, J. L.; Cohn, R. H.; Greer, S. C. The Effect of Critical Fluctuations on Chemical Equilibrium. J. Chem. Phys. 1987, 86, 3602− 3606. (15) Hu, B.; Baird, J. K.; Richey, R. D.; Reddy, R. G. A Chemical Test of the Principle of Critical Point Universality: The Solubility of Nickel (II) Oxide in Isobutyric Acid + Water near the Consolute Point. J. Chem. Phys. 2011, 134, 154505. (16) Griffiths, R. B.; Wheeler, J. C. Critical Points in Multicomponent Systems. Phys. Rev. A 1970, 2, 1047−1064. (17) An, X. Q.; Feng, J.; Shen, W. G. Critical Behavior of a Pseudobinary System for a Three-Component Microemulsion. J. Phys. Chem. 1996, 100, 16674−16677. (18) Izquierdo, C.; Casado, J.; Rodriguez, A.; Moyá, M. L. Microemulsions as a Medium in Chemical Kinetics, II. The I− + S2O4= and Crystal Violet + OH− Reactions in Different Surfactant/ Oil/Water Microemulsions. Int. J. Chem. Kinet. 1992, 24, 19−30. (19) Valaulikar, B. S. Reactions in Microemulsion Formed by Sodium Dodecyl Sulfate, Water, and Hexanol. J. Colloid Interface Sci. 1993, 161, 268−269. (20) Holmberg, K. Organic Reactions in Microemulsions. Eur. J. Org. Chem. 2007, 5, 731−742. (21) Chen, Z. Y.; Zhao, J. H.; He, W.; An, X. Q.; Shen, W. G. Study of Association Thermodynamics between Crystal Violet and Sodium Bis(2-Ethylhexyl)- Sulfosuccinate and Kinetics of Basic Fading of Crystal Violet in Microemulsions. Int. J. Chem. Kinet. 2008, 40, 294− 300. (22) Du, Z. Y.; An, X. Q.; Fan, D. S.; Shen, W. G. Calorimetric Investigation of Reaction Ca(NO3)2 + Na3PO4 in Water and Microemulsions Saturated with CO2. Int. J. Chem. Kinet. 2011, 43, 322−330. (23) Lee, C. T., Jr.; Johnston, K. P.; Dai, H. J.; Cochran, H. D.; Melnichenko, Y. B.; Wignall, G. D. Droplet Interactions in Water-inCarbon Dioxide Microemulsions Near the Critical Point: A SmallAngle Neutron Scattering Study. J. Phys. Chem. B 2001, 105, 3540− 3548. (24) Moyá, M. L.; Izquierdo, C.; Casado, J. Microemulsions as a Medium in Chemical Kinetics: The Persulfate-Iodide Reaction. J. Phys. Chem. 1991, 95, 6001−6004. (25) Muñoz, E.; Gómez-Herrera, C.; del Mar Graciani, M.; Moyá, M. L.; Sánchez, F. Kinetics of the Oxidation of Iodide by Persulphate in AOT-Oil-Water Microemulsions. J. Chem. Soc., Faraday Trans. 1991, 87, 129−132. (26) Brönsted, J. N. Zur Theorie der Chemischen Reaktionsgeschwindigkeit. Z. Phys. Chem. 1922, 102, 169−207. (27) Jette, E.; King, C. V. The Oxidation of Iodide Ion by Persulfate Ion. I. The Effect of Tri-Iodide Ion Formation on the Reaction Velocity. J. Am. Chem. Soc. 1929, 51, 1034−1047. (28) King, C. V.; Jacobs, M. B. The Oxidation of Iodide Ion by Persulfate Ion. IV. Kinetics of the Reaction in Highly Dilute Aqueous Solution. J. Am. Chem. Soc. 1931, 53, 1704−1714.

1/δ = 0.207, predicted for the singularity of thermodynamic equilibrium by the Griffiths−Wheeler rule, which indicates that the critical singularity of the dimer/monomer equilibrium of the microemulsion droplets in the critical region possibly dominates the temperature-dependent reaction rate and results in a critical slowing down of the reaction.

5. CONCLUSIONS We extended the studies of the universality of the critical phenomena in chemical reactions to more complicated microemulsion media. The observed reaction rate constants for the oxidation of iodide ion by persulfate ion in water/AOT/ n-decane microemulsions with the molar ratios of water to AOT ω being 35.0 and 40.8 at various temperatures were determined via the microcalorimetry, and the slowing down of the reaction in the near critical region was detected. It showed good linear relations between ln kobs and 1/T in the noncritical region described by the Arrhenius equation for the two microemulsion systems. With these linear relationships as the “background”, we determined the values of the critical slowingdown exponent 1/δ to be 0.187 ± 0.023 and 0.193 ± 0.032, respectively, by a simple crossover model and a rational approximation. This slowing down was evidenced to be the result from the singularity of the dimer/monomer equilibrium in the critical water/AOT/n-decane microemulsions, characterized by a slowing-down exponent with the theoretical value of 1/δ = 0.207 predicted by the Griffiths−Wheeler rule. This study suggests the universal critical behavior in chemical reactions in microemulsions and added to the current interest in microemulsion systems functioning as media for chemical reactions.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86−21−64250804. Fax: +86-21-64252510. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 20973061, 21173080, 21373085, and 21303055).

■

REFERENCES

(1) Snyder, R. B.; Eckert, C. A. Chemical Kinetics at a Critical Point. AlChE J. 1973, 19, 1126−1133. (2) Baumann, C.; Becker, F. Thermokinetics of Reactions with Liquid-Liquid Phase Separation. Berichte der Bunsengesellschaft fur Physikalische Chemie 1996, 100, 1335−1340. (3) Kim, Y. W.; Baird, J. K. Effect of the Consolute Point of Isobutyric Acid + Water on the Rate of an SN1 Hydrolysis Reaction. Int. J. Thermophys. 2001, 22, 1449−1461. (4) Kim, Y. W.; Baird, J. K. Kinetics of SN1 Reactions in Binary Liquid Mixtures near the Critical Point of Solution. J. Phys. Chem. A 2003, 107, 8435−8443. (5) Kim, Y. W.; Baird, J. K. Reaction Kinetics and Critical Phenomena: Rates of Some First Order Gas Evolution Reactions in Binary Solvents with a Consolute Point. J. Phys. Chem. A 2005, 109, 4750−4757. (6) Hu, B.; Baird, J. K. Reaction Kinetics and Critical Phenomena: Iodination of Acetone in Isobutyric Acid + Water near the Consolute Point. J. Phys. Chem. A 2010, 114, 355−359. 10711



Article

(29) Vučina-Vujović, A. J.; Janković, I. A.; Milonjić, S. K.; Nedeljković, J. M. Influence of AlOOH Nanoparticles on the Oxidation of Iodide by Persulphate. Colloids Surf., A 2003, 223, 295−300. (30) Steady state (stationary state). http://goldbook.iupac.org/ S05962.html (accessed Feb 24, 2014). (31) Du, Z. Y.; Mao, S. Y.; Chen, Z. Y.; Shen, W. G. Kinetics of the Reaction of Crystal Violet with Hydroxide Ion in the Critical Solution of 2-Butoxyethanol + Water. J. Phys. Chem. A 2013, 117, 283−290. (32) Menger, F. M.; Donohue, J. A.; Williams, R. F. Catalysis in Water Pools. J. Am. Chem. Soc. 1973, 95, 286−288. (33) Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. The Kinetics of Solubilisate Exchange between Water Droplets of a Water-in-Oil Microemulsion. J. Chem. Soc., Faraday Trans. 1 1987, 83, 985−1006. (34) Moulik, S. P.; Paul, B. K. Structure, Dynamics and Transport Properties of Microemulsions. Adv. Colloid Interface Sci. 1998, 78, 99− 195. (35) Eicke, H. R.; Shepard, J. C.; Steinemann, A. Exchange of Solubilized Water and Aqueous Electrolyte Solutions between Micelles in Apolar Media. J. Colloid Interface Sci. 1976, 56, 168−176. (36) Du, Z. Y.; Yin, H. D.; Hao, Z. G.; Zheng, P. Z.; Shen, W. G. Critical Anomalies of Alkaline Fading of Phenolphthalein in the Critical Solution of 2-Butoxyethanol + Water. J. Chem. Phys. 2013, 139, 224501. (37) Huang, J. S.; Safran, S. A.; Kim, M. W.; Grest, G. S.; Kotlarchyk, M.; Quirke, N. Attractive Interactions in Micelles and Microemulsions. Phys. Rev. Lett. 1984, 53, 592−595. (38) Li, P.; An, X. Q.; Shen, W. G. Density, Turbidity and Microscopic Structure of AOT/H2O/Oil Microemulsions. Acta Physicochimica Sinica 2001, 17, 144−149. (39) An, X. Q.; Wang, T.; Shen, W. G. Study on the Persulfate-Iodide Reaction in Microemulsions. Acta Chim. Sin. 2002, 60, 980−984.

10712


Kinetics of the Oxidation of Iodide Ion by Persulfate Ion in the Critical

Recommend Documents