$($b$)$ For a reaction carried out in a batch reactor $($initial concentration $C_{AO}),$ its $C_A$ varies according to $(\frac{1}{C_A})-(\frac{1}{C_{A_0}})=kt$; where $\text{'}t\text{'}$ is time and $\text{'}k\text{'}$ is kinetic constant. Derive an expression for the rate of reaction.