The gas-phase decomposition of hydrogen peroxide can occur by an uncatalyzed path or…

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

The gas-phase decomposition of hydrogen peroxide can occur by an uncatalyzed path or by a chloride-ion-catalyzed path. Overall reaction: 2 H2_2O2_2(g) → 2 H2_2O(g) + O2_2(g) Experimental studies carried out at 600 K in the presence of chloride ion produce the initial-rate data shown.
[H2_2O2_2] / mol L−1^{−1}[Cl−^−] / mol L−1^{−1}Initial rate / mol L−1^{−1} s−1^{−1}
0.0100.0051.4 × 10−5^{−5}
0.0200.0052.8 × 10−5^{−5}
0.0200.0105.6 × 10−5^{−5}
A proposed mechanism for the chloride-catalyzed pathway is: Step 1 Cl−^− + H2_2O2_2 → HOCl + OH−^− (slow) Step 2 HOCl + H2_2O2_2 → Cl−^− + H2_2O + O2_2 (fast) (Neither HOCl nor OH−^− builds up measurably during the reaction.) (a) Determine the empirical rate law (including the value of the rate constant kk with appropriate units) from the data in the table. (b) Based on the proposed mechanism, identify which elementary step is rate-determining. Justify your answer by explicit reference to the empirical rate law you obtained in part (a). (c) The uncatalyzed decomposition of H2_2O2_2 at 600 K is first order in H2_2O2_2 with kuncat=1.0×10−6 s−1k_{\text{uncat}} = 1.0 \times 10^{−6}\,\text{s}^{−1}. Calculate the factor by which chloride ion speeds up the reaction under the conditions of the first experiment in the table.

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