Problem $1$

Consider the following set of multiple reactions: ${?}^{}$

$4A+5B{k}_{1}4C+6D$;$-(r_A{)}_1=k_1{C}_A{C}_B^2$

$4A+3B{k}_{2}2E+6D$;$-(r_A{)}_2=k_2{C}_A{C}_B$

$B+2C{k}_{3}2F$;$-(r_B{)}_3=k_3{C}_B{C}_C^2$

$4A+6C{k}_{4}5E+6D$;$-(r_C{)}_4=k_4{C}_A^{\frac{2}{3}}{C}_C$

Give expressions for the rates of reaction of components $A,B$ and $C($i$.$e$.r_A,r_B,r_C)$ in terms

of the rate constants $($i$.$e$.k_1,$cdots,$k_4)$ and the concentrations.