$(30$P$)3.($a$)$ Consider the following first order decomposition reactions.

$A_T\frac{k_1}{(k_2{)}_{k_2}}R{?}^{k_3}S\frac{k_5}{(k_4{)}_U}M$

Write down the following rates;

$r_A=$

$r_R=$

$r_S=$

$r_T=$

$r_U=$

$r_M=$

$($b$)B$ is desired product for following parallel reaction

$AB,$;$,r_B=\frac{2C_A}{1+2C_A}mo\frac{l}{t}ts$

$AC,$;$,r_C=1\mathrm{.}2C_A$

Initial concentration of $A$ is $4M.$ The conversion of $A$ at the outlet is