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Elementary and Complex Reactions

In the photoc...

Question

In the photochemical decomposition of acetaldehyde, one photon of absorbed light decomposes one molecule of $C H_{3} C H O$ into $∙ C H_{3} a n d ∙ C H O$ . If $^{'} I_{a b s}^{'}$ is the intensity of light absorbed in the reaction. Write the rate equation for this photochemical decomposition. (Note: the first step in the photochemical reaction is temperature independent)
Calculate $[∙ C H_{3}] a n d \frac{d [C O]}{d t}$ assuming steps (ii) to (iv) given are same and $[∙ C H_{3}], [∙ C H_{3} C O]$ are under steady state.

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Solution

$i) \frac{d [{C H}_{3}]}{d t} = k_{1} [{C H}_{3} C H O] - k_{2} [{C H}_{3} C H O] [{C H}_{3}] + k_{3} [{C H}_{3} C O] - 2 k_{4} {[{C H}_{3}]}_{3}^{2} = 0 i i) \frac{d [{C H}_{3} C O]}{d t} = k_{2} [{C H}_{3} C H O] [{C H}_{3}] - k_{c} [{C H}_{3} C O] = 0 {C H}_{3} C H O + h v \to {C H}_{3} + C H O [{C H}_{3}] = \sqrt \frac{k_{1}}{{2 k}_{4}} {[{C H}_{3} C H O]}_{3}^{1 / 2} = (I_{a b s} / 2 k_{4})^{1 / 2} {[{C H}_{3} C H O]}_{3}^{1 / 2} \frac{d [C O]}{d t} = k_{3} {[{C H}_{3} C H O]}_{3}^{3 / 2} = k_{2} \sqrt \frac{k_{1}}{{2 k}_{4}} {[{C H}_{3} C H O]}_{3}^{3 / 2} = k_{2} (I_{a b s} / 2 k_{4})^{1 / 2} {[{C H}_{3} C H O]}_{3}^{3 / 2}$

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