For a gaseous reaction, $2\,\mathrm{NO(g)}+\mathrm{Cl_2(g)} \rightarrow$ Non-linear T.S. $\rightarrow 2\,\mathrm{NOCl}$, the pre-exponential factor in the rate constant is proportional to
(a)$T^{1/2}$
(b)$T^{-1/2}$
(c)$T^{-5/2}$
(d)$T^{-7/2}$
Answer
Answer: D ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
Transition-state theory: A ∝ (kT/h)·q‡/(q_NO² q_Cl₂). Translation: T^{3/2}/T^{9/2} = T⁻³; rotation: non-linear TS T^{3/2} over three linear reactants T³ = T^{−3/2}; with the kT/h factor: T^{1−3−3/2} = T^{−7/2}.