Graduate students preparing for qualifying exams in physical chemistry find the solutions manual invaluable for practice. Many exam problems are variations of textbook problems.
From ( d[CH_3CO]/dt = 0 ), we get ( k_3[CH_3CO] = k_2[CH_3][CH_3CHO] ). Substitute into ( d[CH_3]/dt ) equation. The ( k_2 ) and ( k_3 ) terms cancel, leaving ( k_1[CH_3CHO] = 2k_4[CH_3]^2 ), so ( [CH_3] = \sqrt{ \frac{k_1}{2k_4} [CH_3CHO]^{1/2} } ).
For :
The gas-phase decomposition of acetaldehyde, ( CH_3CHO \rightarrow CH_4 + CO ), follows the rate law ( -d[CH_3CHO]/dt = k [CH_3CHO]^{3/2} ). Derive a mechanism consistent with this rate law, using the steady-state approximation for free radicals ( CH_3 ) and ( CHO ).