Problem III:

The following liquid phase reaction is carried out in a batch reactor maintained at $54C.$

$2A+BC$

The reaction is first order in each of the two reactant species, and the reaction rate constant at $54C$ is

$0\mathrm{.}006\frac{L}{m}ol-$min. An aqueous feed consisting of both A & B $(C_{A0}=1\frac{\text{m}\text{o}\text{l}}{L}$;$C_{B0}=0\mathrm{.}4\frac{\text{m}\text{o}\text{l}}{L})$ is placed

in the batch reactor $($volume $2000$L$)$ and allowed to react. How long will it take for the concentration of

$C$ in the reaction mixture to reach a value of $0\mathrm{.}3mo\frac{l}{L}?$

a$)$ Solving analytically

b$)$ Using MATLAB