$M+Hx+Me,x+HT+Me$

Where, $M=$ mesitylene, $x-m-$xylene, $T=$ toluene, $Me=$ methane, $H=$ hydrogen

Mole balance on gives the following:

$-\frac{d{C}_H}{d}=k_1{C}_H^{\frac{1}{2}}{C}_M+k_2{C}_x{C}_H^{\frac{1}{2}}$

$-\frac{d{C}_M}{d}=k_1{C}_M{C}_H^{\frac{1}{2}}$

$-\frac{d{C}_x}{d}=-k_1{C}_M{C}_H^{\frac{1}{2}}+k_2{C}_x{C}_H^{\frac{1}{2}}$

$C_H(0)=0\mathrm{.}021$

$C_M(0)=0\mathrm{.}0105$

Where,

$C_x(0)=0$

$k_1=55\mathrm{.}2$

$k_2=30\mathrm{.}2$

$($a$)$ Solve the given three $0.,v_0=476$

NIN MAT $=0$ to $=0\mathrm{.}5.$

line, respectively. Determine

$F_H=v_0{C}_H,F_M=v_0{C}_M,F_x=v_0{C}_x,F_{Me}=f_0$ rates $of$ enecies from concentrations $as$ follows:

$F_T=v_0(0\mathrm{.}0105-C_M-C_x)$

$F_{M_e}=v_0(0\mathrm{.}021-{?}^2)$