$A+\frac{1}{2}BC$

Given the equation:

$[A]=\frac{k_2}{k_1+k_2}[A{]}_0+\frac{k_1}{k_1+k_2}[A{]}_0{e}^{-(k_1+k_2)t}$

Where:

$-[A]$ is the concentration of reactant $A$

$-[A{]}_0$ is the initial concentration of reactant $A$

$-k_1=0\mathrm{.}010se{c}^{-1}$

$-k_2=0\mathrm{.}004se{c}^{-1}$

$-t$: time $[s]$

The reaction takes place isobarically and isothermally at $1$atm and $26\mathrm{.}85$degC respectively. Initially, there is an equimolar ratio of A and $B$ and no $C$ present in the reactor feed. The reaction takes place in a Plug Flow Reactor with a volume of $80m^3$ and an inlet gas flowrate of $1\mathrm{.}5\frac{m^3}{s}.$ Calculate the initialconcentration of A using this information. Assume ideal gas, and think about using the ideal gas law.