Rate and mechanism

Exercise 2

    

The reaction (r) $2NOCl(g)$ $\longrightarrow$ $ 2NO_2(g)$ $+$ $Cl_2(g)$ is first order with respect to $NOCl(g)$. Submit two elementary processes!

(a) $NO_2Cl$ $+$ $Cl_2$ $\longrightarrow$ $NO_2$ $+$ $Cl\cdot$ $v_a=k_a[NO_2Cl][Cl_2]$ (slow) (b) $Cl\cdot$ $+$ $NO_2Cl$ $\longrightarrow$ $NO_2$ $+$ $Cl_2$ $v_b=k_b[NO_2][Cl.]$ (fast) $v_r=v_a$