Kinetics and Mechanisms of the Iodine Clock. Reaction

Transcription

1 0 Kinetics and Mechanisms of the Iodine Clock Reaction Chikarmane and Jonathan White Department of Chemistry University of Oregon Eugene, OR May 18, 2014 Abstract: The mechanism by which the iodide/peroxide reaction proceeds has been determined using an assay system used in the commonly known iodine clock reaction and rate studies of iodide, hydrogen peroxide, and hydronium. The overall mechanism was found to be two simultaneously occurring mechanisms, one uncatalyzed and one catalyzed by hydronium, that each follow three to four elementary steps and ultimately add up to the balanced stoichiometric equation for the overall reaction. The experimental rate law and activation energies align well with this proposed system of mechanisms.

2 1 Results: The goal of this project is to use rate studies to determine the reaction mechanisms by which H 2O 2 and HI react to form water and I 2. Three independent experiments were conducted to determine the rate order of each rate-determining constituent. The results are summarized in Table 1. Two more Table 1. Summary of Results for Concentration Effect on Rate of H 2O I - Redox Reaction Tested Species Temperature ( C) Best Fit Line Slope Reaction Order I First H 2O First H 3O Competing Zero and First Competing rate laws: Rate = k uncat[i - ][H 2O 2] and Rate = k cat[i - ][H 2O 2][H 3O + ] experiments were conducted to determine the variation of the rate constant (k) with temperature and the activation energy. (a) Effect of I - concentration on the rate of H 2O I - redox. The time (seconds) elapsed from the initiation of the reaction to the depletion of thiosulfate (ie. the formation of the blue iodine-starch complex) was recorded for solutions containing varying concentrations of iodide, recorded in Table 1 in the Appendix. I 2 was reduced by thiosulfate far more rapidly than by starch, in a 1 to 1 ratio with iodide and is shown in Equation 1. The depletion of thiosulfate was represented by the presence of blue and the formation of the iodine-starch complex. I 2 (aq) + 2 S 2O 3 (aq) 2 I - (aq) + S 4O 6 (aq) (1) Therefore, the known concentration and volume of thiosulfate stock were used to compute the moles of reacted iodide. The ratio of the moles of iodide reacted to the total sample volume was subsequently used to find the change in iodide concentration. The change in iodide concentration and the sample reaction times gave the rates of iodide consumption. The dilution equation was applied to the known concentration

3 -ln(rate of iodide comsumption) 2 and volume of the stock solution in each sample to calculate the initial concentrations of iodide. A plot of -ln[i - ] 0 versus -ln(rate) for this experiment is shown in Figure ln[i - ] 0 Figure 1. Plot of -ln[i - ] 0 versus -ln(rate of iodide consumption) in a 21.1 C environment. The slope represents the rate order of iodide in the H 2O I - redox reaction as (first order). The slope of the linear regression line gave the rate order of iodide in the H 2O I - redox reaction, which was determined to be 1. The following experimental the rate law was established. Rate = k obs [I - ], where k obs = (k overall [H 2O 2] x [H 3O + ] y ) (b) Effect of H 2O 2 concentration on the rate of H 2O I - redox. The time (seconds) elapsed from the initiation of the reaction to the depletion of thiosulfate (ie. the formation of the blue iodine-starch complex) was recorded for solutions containing varying concentrations of hydrogen peroxide, recorded in Table 2 in the Appendix. A plot of -ln[i - ] 0 versus -ln(rate) for this experiment is shown in Figure 2. The procedure used to derive the rate order of iodide was similarly applied to derive the rate order of hydrogen peroxide as follows: Rate = k obs [H 2O 2], where k obs = (k overall [I - ] x [H 3O + ] y )

4 -ln(rate of I - Consumption) ln[h 2 O 2 ] 0 Figure 2. Plot of -ln[h 2O 2] 0 versus -ln(rate of iodide consumption) in a 26.3 C environment. The slope represents the rate order of hydrogen peroxide in the H 2O I - redox reaction as (first order). (c) Effect of H 3O + concentration on the rate of H 2O I - redox. The time (seconds) elapsed from the initiation of the reaction to the depletion of thiosulfate (ie. the formation of the blue iodine-starch complex) was recorded for solutions containing varying concentrations of hydrogen peroxide, recorded in Table 3 in the Appendix. A plot of -ln[i - ] 0 versus -ln(rate) for this experiment is shown in Figure 3. The procedure used to derive the rate order of iodide and hydrogen peroxide was similarly applied to derive the rate order of hydronium as follows: Rate = k obs or Rate = k obs[h 3O + ], where k obs = (k overall [I - ] x [H 2O 2] y ) Hydronium cannot be half order because it cannot physically fragment into two equal parts. Note that a competing zero and first hydronium rate order gives the observed impression of a half order rate law, when in fact that is not the case.

5 -ln(rate of I - Comsumption) ln[h 3 O + ] 0 Figure 3. Plot of -ln[h 3O + ] 0 versus -ln(rate of iodide consumption) in a 26.3 C environment. The slope represents the rate order of hydronium in the H 2O I - redox reaction as (competing zero and first order). (d) Concentration effect of H 3O + at about 0 C and 35 C. The time (seconds) elapsed from the initiation of the reaction to the depletion of thiosulfate (ie. the formation of the blue iodine-starch complex) was recorded for solutions containing varying concentrations of hydrogen peroxide in 0.04 C and 35.1 C environments, recorded in Tables 4 and 5 in the Appendix. A plot of -ln[i - ] 0 versus -ln(rate) for these experiments are shown in Figure 1 and 2 in the Appendix. The combined data sets demonstrate the following system of rate laws in contention: Rate = k uncat[i - ][H 2O 2] and Rate = k cat[i - ][H 2O 2][H 3O + ] Since the predicted rate is equivalent to the addition of the two simultaneously occurring rates, the ratio of Rate to [H 2O 2] 0[I - ] 0 is related to k uncat and k cat in the following manner: Rate 0 [H 2 O 2 ] 0 [I ] 0 = k cat [H 3 O + ] 0 + k uncat

6 Rate/[H 2 O 2 ] 0 [I - ] 0 (M -1 s -1 ) 5 The initial concentrations of hydrogen peroxide, iodide, and hydronium were calculated from the known amounts of stock solution added to each sample and the known concentrations of each stock solution. A plot of Rate/[H 2O 2] 0[I - ] 0 vs. [H 3O + ] 0 for these experiments as well as the experiment in part (c) of the results section (conducted at 26.3 C) is shown in Figure 4. As indicated by the previous equation, the [H 3 O + ] 0 (M/sec) T = 283 K T = 299 K T = 308 K Figure 4. Plot of Rate/[H 2O 2] 0[I - ] 0 versus [H 3O + ] 0 in 283 K, 299 K, and 308 K environments. The y-intercepts represent the k uncat of H 2O I - redox and the slopes represent the k cat of H 2O I - redox at each given temperature. y-intercepts represent the k uncat and the slopes represent the k cat at their respective environmental temperatures. The following manipulation of the Arrhenius equation and the previously derived values of k uncat and k cat were used to derive the activation energies of the catalyzed and uncatalyzed reaction mechanisms: ln(k) = E a R 1 T ln(a), where E a = activation energy, R = universal gas constant Table 6 in the Appendix summarizes relevant derived values in the Arrhenius equation, including observed k constants and temperatures. A plot of ln(k) catalyzed and uncatalyzed versus 1/T is shown in Figure 5.

7 -ln(k) Catalyzed Uncatalyzed /T (K 1- ) Figure 5. Plot of ln(k) catalyzed and uncatalyzed versus 1/T in 283 K, 299 K, and 308 K environments. The slope represents the quotient of the activation energy divided by the universal gas constant. The observed E a,uncat was found to be 74.5 kj/mol and was derived from the product of the slope and the universal gas constant. The E a,cat was similarly derived and was found to be 45.6 kj/mol. The catalyzed activation energy is that of the uncatalyzed reaction, allowing for a lower reaction threshold and an observably faster reaction rate. contention: (e) Summary Statement. The combined data sets demonstrate the following system of rate laws in Rate = k uncat[i - ][H 2O 2] and Rate = k cat[i - ][H 2O 2][H 3O + ] The k uncat and k cat were derived at varying temperatures and plotted against 1/T, to give the activation energies of the catalyzed and uncatalyzed reactions. E a,uncat was found to be 74.5 kj/mol and E a,cat was found to be 45.6 kj/mol.

8 7 Discussion: The data collected in this study are consistent with the mechanism of the peroxide/iodide redox reaction shown in Figure 6. Iodide and peroxide are first order in both proposed mechanisms, which is Mechanism 1 Rate = k uncat[i - ][H 2O 2] Mechanism 2 Rate = k cat[i - ][H 2O 2][H 3O + ] Figure 6. Competing reaction mechanisms of the partially catalyzed H 2O I - redox reaction. consistent with the experimental rate orders. The concurrent zero and first order hydronium mechanisms agree with the apparent (but not actual) half order hydronium order that was experimentally observed. Each mechanism is composed of three to four elementary steps and the stoichiometric sum of each elementary step gives the balanced stoichiometric equation for the overall reaction shown in Equation 2. H 2O 2 (aq) + HI (aq) ph = H 2O (l) + I 2 (aq) CH 3COOH/ CH 3COO - The combination of Mechanism 1 and 2 suggests the presence two energy thresholds, or activation (2) energies (E a), that must be overcome for the iodide/peroxide redox to progress, one for the uncatalyzed mechanism (1) and one for the catalyzed mechanism (2). The neutrally charged H 2O leaving group in the catalyzed reaction is must more energetically preferable than the OH - leaving group in the uncatalyzed reaction. Therefore, the E a, uncat should be higher that the E a, cat since the catalyzed reaction lyses the intermediate constituent (H 2OOH + ) relatively easier than the intermediate in the uncatalyzed reaction (HOOH). This is shown in the reaction progression graph in Figure 7.

9 Potential Energy (kj) 8 E a,uncat E a,cat H 3O + Reaction Progress Figure 7. Theorized energy scheme of the partially catalyzed H 2O I - redox reaction as the reaction progresses. Since the experimental E a,uncat was found to be 74.5 kj/mol and the E a,cat was found to be 45.6 kj/mol the activation energies are consistent with the simultaneously occurring mechanisms proposed in Figure 6. Appendix I: Table 1. Summary of Results for I - Concentration Effect on Rate of H 2O I - Redox Reaction Sample [I - ] 0 (mol/l) Time (sec.) Rate ab -ln[i - ] 0 -ln(rate) a Refers to rate of [I - ] consumption; b Rates expressed in M x 10 7 per sec; [I - ] 0: M; [H 2O 2] 0: M; [S 2O 3 ] 0: M; T = 21.1 C

10 9 Table 2. Summary of Results for H 2O 2 Concentration Effect on Rate of H 2O I - Redox Reaction Sample [H 2O 2] 0 (mol/l) Time (sec.) Rate ab -ln[h 2O 2] 0 -ln(rate) a Refers to rate of [I - ] consumption; b Rates expressed in M x 10 7 per sec; [I - ] 0: M; [H 2O 2] 0: M; [S 2O 3 ] 0: M; T = 26.3 C Table 3. Summary of Results for H 3O + Concentration Effect on Rate of H 2O I - Redox Reaction at ~25 C Sample [H 3O + ] 0 (mol/l) Time (sec.) Rate ab -ln[h 3O + ] 0 -ln(rate) Rate a /[H 2O 2] 0[I - ] a Refers to rate of [I - ] consumption; b Rates expressed in M x 10 7 per sec; [I - ] 0: M; [H 2O 2] 0: M; [S 2O 3 ] 0: M; T = 26.3 C Table 4. Summary of Results for H 3O + Concentration Effect on Rate of H 2O I - Redox Reaction at ~0 C Sample [H 3O + ] 0 (mol/l) Time (sec.) Rate ab Rate a /[H 2O 2] 0[I - ] a Refers to rate of [I - ] consumption; b Rates expressed in M x 10 7 per sec; [I - ] 0: M; [H 2O 2] 0: M; [S 2O 3 ] 0: M; T = 0.04 C

11 10 Table 5. Summary of Results for H 3O + Concentration Effect on Rate of H 2O I - Redox Reaction at ~35 C Sample [H 3O + ] 0 (mol/l) Time (sec.) Rate ab Rate a /[H 2O 2] 0[I - ] a Refers to rate of [I - ] consumption; b Rates expressed in M x 10 7 per sec; [I - ] 0: M; [H 2O 2] 0: M; [S 2O 3 ] 0: M; T = 35.1 C Table 6. Summary of Rate Constants at Varying Temperatures k cat (M -2 s -1 ) -ln(k cat) k uncat (M -1 s -1 ) -ln(k uncat) T (K) 1/T (K-1) Relationship between ln(k) and 1/T illustrated in Figure 5

12 -ln(rate of H3O+ Comsumption) -ln(rate of I - Comsumption) ln[h 3 O + ] 0 Figure 1. Plot of -ln[h 3O + ] 0 versus -ln(rate of iodide consumption) in a 0.04 C environment. The slope represents the rate order of hydronium in the H 2O I - redox reaction as (competing zero and first order) ln[h3o+]0 Figure 1. Plot of -ln[h 3O + ] 0 versus -ln(rate of iodide consumption) in a 35.1 C environment. The slope represents the rate order of hydronium in the H 2O I - redox reaction as (competing zero and first order).