The overall reaction between peroxodisulfate and iodide ions is
S₂O₈²⁻(aq) + 2 I⁻(aq) → 2 SO₄²⁻(aq) + I₂(aq)
A kinetics investigation is conducted at 25 °C under two sets of conditions: (i) no catalyst present and (ii) Fe²⁺ ions present in catalytic amounts. The initial concentrations and corresponding initial rates are summarized below.
Trial 1 (un-catalyzed): [S₂O₈²⁻]_0 = 0.050 M, [I⁻]_0 = 0.060 M, rate₀ = 1.2 × 10⁻⁵ M s⁻¹
Trial 2 (un-catalyzed): [S₂O₈²⁻]_0 = 0.100 M, [I⁻]_0 = 0.060 M, rate₀ = 2.4 × 10⁻⁵ M s⁻¹
Trial 3 (un-catalyzed): [S₂O₈²⁻]_0 = 0.050 M, [I⁻]_0 = 0.120 M, rate₀ = 2.4 × 10⁻⁵ M s⁻¹
Trial 4 (catalyzed): [S₂O₈²⁻]_0 = 0.050 M, [I⁻]_0 = 0.060 M, rate₀ = 1.8 × 10⁻⁴ M s⁻¹
(a) Using only the un-catalyzed data (Trials 1–3), determine the orders m and n with respect to S₂O₈²⁻ and I⁻, respectively, and write the rate law.
(b) Calculate the rate constant k_uncat (with proper units) from one of the un-catalyzed trials.
(c) Using the catalyzed data (Trial 4) and the orders obtained in part (a), calculate the value of k_cat and determine the enhancement factor k_cat ⁄ k_uncat.
(d) Provide a mechanistic argument, based on your results, that explains whether the catalyst changes the reaction orders you found in part (a).