In laboratory studies of the dimerization of ethanoyl radicals

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

Problem

In laboratory studies of the dimerization of ethanoyl radicals, the overall stoichiometric reaction can be written 2 CH3CO → (CH3CO)2 (products follow in subsequent very fast steps that do not affect the rate law). Kinetic data suggest the mechanism below: Step 1 CH3CO ⇌ (CH3CO)2 fast equilibrium Kc=1.4×104K_c = 1.4 \times 10^4 Step 2 (CH3CO)2 → products slow k2=3.2×10−3 s−1k_2 = 3.2 \times 10^{-3}\, \text{s}^{-1} At 298 K298\,\text{K} the initial concentration of CH3CO radicals in a photochemical experiment is 2.5×10−5 mol L−12.5 \times 10^{-5}\, \text{mol L}^{-1}. (a) Write the rate law for the overall reaction in terms of the concentration of the intermediate (CH3CO)2 and the elementary-step rate constant k2k_2. (b) Using the equilibrium information from Step 1, express the concentration of the intermediate in terms of the concentration of CH3CO radicals. (c) Combine your results from parts (a) and (b) to obtain the overall rate law in terms of the measurable concentration [CH3CO]. Identify the observed rate constant kobsk_{\text{obs}}. (d) Calculate the numerical value of kobsk_{\text{obs}} (include appropriate units). (e) Determine the initial rate (in mol L−1 s−1\text{mol L}^{-1}\, \text{s}^{-1}) for the experiment described.

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