The following reversible gas$-$phase reaction is carried out isothermally in a constant$-$pressure batch reactor $).$

$A2B$

This is an elementary reaction and the forward reaction rate constant $(k_A)$ at $400K$ is ${10}^{-2}(e^{-1}).$ The equilibrium constant $(K_C)$ at $400K$ is $100\frac{\text{m}\text{o}\text{l}}{m^3}.$ The initial concentration of A and $B$ is $10\mathrm{.}0\frac{\text{m}\text{o}\text{l}}{m^3}$ and $5\mathrm{.}0\frac{\text{m}\text{o}\text{l}}{m^3},$ respectively. The other chemical species, if they are present in a reactor, can be considered to be inert. The equation of state for the ideal gas can be applied. $($The gas constant $(R)=8\mathrm{.}314\frac{J}{\text{m}\text{o}\text{l}*K})$

Calculate the equilibrium conversion of $A$