Substance A was slowly and continuously fed into the water reactor for $0\mathrm{.}5($hr$)$

hours. Substance A rapidly dissolves and decomposes into R $(0$th order reaction$),$

and the generated $R$ slowly decomposes into $S(1$st order reaction$)$

The volume of liquid in the reactor is kept constant at $3m^3,$ and if the

decomposition reaction of $R$ to $S$ does not occur, the concentration of $R$ in the

reactor is $100mo\frac{l}{m^3}$ after adding A for $0\mathrm{.}5($hr$)$ hours. However, at the beginning

$(t=0)C_A=C_{A0},C_{R0}=C_0=0,$ all reactions are basic reactions.

Write the reaction rate equation $(-r_A,r_R).$

Find the reaction rate constant $k_1.$

Derive the equation $C_R($must be expressed using $k_1,k_{2}t)$ while A exists in the

reactor and find the maximum concentration of $R(C_{R,\text{m}\text{a}\text{x}}).$