Problem #$6(10$ points$)$

Consider the Lindemann mechanism for the following association reactions:

$k_a$

$A+B>C^{**}$

$k_d$

$C^{**}+M{k}_{s}C+M$

where

$\frac{d[C]}{dt}=k_{\text{a}\text{s}\text{s}\text{o}\text{c}}[A][B]$

Derive the association rate constant, $k_a,$ in the low and high$-$pressure limits by using the steadystate assumption for $C^{**}.$