Kinetics of the hydrogen peroxide-iodide reaction
A student studies the reaction between hydrogen peroxide and iodide ions in acidic solution: H2O2(aq) + 2H+(aq) + 2I-(aq) -> I2(aq) + 2H2O(l). She measures initial rates by timing the appearance of a blue-black colour with starch. In experiment 1, [H2O2] = 0.10 mol dm-3, [I-] = 0.10 mol dm-3, [H+] = 0.10 mol dm-3, and the initial rate is 1.0 x 10-5 mol dm-3 s-1. In experiment 2, [H2O2] is doubled to 0.20 mol dm-3 and the rate is 2.0 x 10-5. In experiment 3, [I-] is doubled to 0.20 mol dm-3 and the rate is 2.0 x 10-5. In experiment 4, [H+] is doubled to 0.20 mol dm-3 and the rate remains 1.0 x 10-5. A fifth run, intended as a repeat of experiment 1, gave 1.4 x 10-5; the student notices the water bath was 3 C warmer. She proposes a two-step mechanism: step 1 (slow) H2O2 + I- -> H2O + IO-; step 2 (fast) IO- + 2H+ + I- -> I2 + H2O.
1. Deduce the order with respect to each reactant and write the rate equation.
Read the worked answer
Compare experiments 1 and 2: only [H2O2] doubles, and the rate doubles. Therefore the reaction is first order with respect to H2O2.
Compare experiments 1 and 3: only [I-] doubles, and the rate doubles. Therefore the reaction is first order with respect to I-.
Compare experiments 1 and 4: only [H+] doubles, and the rate is unchanged. Therefore the reaction is zero order with respect to H+.
The rate equation is:
rate = k[H2O2][I-]
The overall order is 1 + 1 + 0 = 2.
2. Calculate the rate constant for experiment 1, including units, and explain how the fifth run should be treated.
Read the worked answer
Rearrange the rate equation:
k = rate / ([H2O2][I-])
k = (1.0 x 10-5) / (0.10 x 0.10)
k = (1.0 x 10-5) / (1.0 x 10-2) = 1.0 x 10-3
Units: rate has units mol dm-3 s-1; the concentration product has units mol2 dm-6. Therefore k has units dm3 mol-1 s-1.
The fifth run should not be combined with experiment 1 to calculate an average k without comment. It was carried out at a temperature about 3 C higher, and rate constants are temperature-dependent. The higher rate is qualitatively consistent with a faster reaction at higher temperature, but the value cannot be treated as a repeat at the same conditions. It should either be discarded from the room-temperature determination or used only as evidence of a temperature effect.
3. Evaluate whether the proposed mechanism is consistent with the rate equation and identify the rate-determining step.
Read the worked answer
The rate equation is rate = k[H2O2][I-], so the rate-determining step must involve H2O2 and I- and must not involve H+ before the slow step. In the proposed mechanism, step 1 is slow and contains H2O2 and I- only. Its rate would be k1[H2O2][I-], which matches the experimental rate equation. Step 2 is fast and consumes H+, so changing [H+] does not change the overall rate. The mechanism is therefore consistent with the data. The rate-determining step is step 1, H2O2 + I- -> H2O + IO-. However, consistency does not prove the mechanism; the intermediate IO- would need independent evidence, and other mechanisms could also fit the same rate law.