The liquid phase reaction $A+BC$ follows an elementary rate law and is carried out isothermally in a batch reactor

a$)$ Calculate the specific rate constant $($k$)$ for the above reaction at $77C$ if the kinetic rate constant $(k)$ at $27C$ is $0\mathrm{.}07d\frac{m^3}{m}$olminandE$=20$kca$\frac{l}{m}ol.$

b$)$ Calculate time taken to achieve $90\%$ conversion in a $200dm3$ batch reactor with $C_{A0}=C_{B0}=1mo\frac{l}{d}m3$ at a temperature of $27C.$ Additional information: $R=1\mathrm{.}987ca\frac{l}{m}$olK