Chemistry

Chemistry

Problem

Nitrosyl bromide, NOBr(g)\mathrm{NOBr(g)}, decomposes according to 2 NOBr→2 NO+Br22\,\mathrm{NOBr} \to 2\,\mathrm{NO} + \mathrm{Br_{2}}. Experimental studies yield the rate law rate=k[NOBr]2\text{rate} = k[\mathrm{NOBr}]^2. Two different mechanisms have been suggested: Mechanism I Step 1 NOBr⇌NO+Br\mathrm{NOBr} \rightleftharpoons \mathrm{NO} + \mathrm{Br} (fast) Step 2 NOBr+Br→NO+Br2\mathrm{NOBr} + \mathrm{Br} \to \mathrm{NO} + \mathrm{Br_{2}} (slow) Mechanism II Step 1 2 NOBr⇌N2O2Br22\,\mathrm{NOBr} \rightleftharpoons \mathrm{N_{2}O_{2}Br_{2}} (fast) Step 2 N2O2Br2→2 NO+Br2\mathrm{N_{2}O_{2}Br_{2}} \to 2\,\mathrm{NO} + \mathrm{Br_{2}} (slow) Using principles of chemical kinetics, evaluate the two mechanisms. (a) For each mechanism, list the species that are present in the reaction vessel immediately before the slow step begins. (b) For each mechanism, state the reaction order predicted with respect to NOBr\mathrm{NOBr}, based solely on the concentrations of the species present just before the slow step starts. (c) Indicate which mechanism is consistent with the experimentally determined rate law. Provide a concise justification that explicitly connects the predicted reaction order to the observed one. (d) For the mechanism you selected in part (c), explain why Br2\mathrm{Br_{2}} does not appear in the rate law even though it is produced in the overall reaction.
Intuitive explanation

The key to evaluating mechanisms is checking whether each one predicts the observed rate law and produces the correct overall reaction. For the rate law, only the slow (rate-determining) step and any fast pre-equilibria matter: use equilibrium expressions from fast steps to eliminate intermediate concentrations. Both mechanisms must also sum to give 2 NOBr→2 NO+Br22\,\mathrm{NOBr} \to 2\,\mathrm{NO} + \mathrm{Br_{2}} with no net intermediates. Work through the algebra for each mechanism to see which one yields rate=k[NOBr]2\text{rate} = k[\mathrm{NOBr}]^2.

Intuitive explanation

The key to evaluating mechanisms is checking whether each one predicts the observed rate law and produces the correct overall reaction. For the rate law, only the slow (rate-determining) step and any fast pre-equilibria matter: use equilibrium expressions from fast steps to eliminate intermediate concentrations. Both mechanisms must also sum to give 2 NOBr→2 NO+Br22\,\mathrm{NOBr} \to 2\,\mathrm{NO} + \mathrm{Br_{2}} with no net intermediates. Work through the algebra for each mechanism to see which one yields rate=k[NOBr]2\text{rate} = k[\mathrm{NOBr}]^2.

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