The reaction $A+BP$ is carried out in a solution at $50C,$ where the initial concentrations of A and $B$ are $0\mathrm{.}11mold{m}^{-3}$ and $0\mathrm{.}06mold{m}^{-3},$ respectively. The reaction is found to be first order in both A and B$.$ If the frequency factor of the reaction is $2\mathrm{.}42{10}^{11}d{m}^{3}mo{l}^{-1}{s}^{-1}$ and that of activation energy is $78000J*mo{l}^{-1},$

a$)$ what is the rate constant of the reaction?

b$)$ what is the concentration of each reactant $($ A and $B)$ after $5$min $?($Hint: use the integrated rate law$).$

c$)$ what is the half life of each reactant and $B?$

Hint: $ln(u)=vu=e^v$