The gas phase reaction Longleftrightarrow$3B$ occurs in a tubular reactor at $127C$ and $2$ atm. Equilibrium is completely toward $B$ at these conditions. A disk of catalyst is placed at the end of a tube $20cm$ long, $2\mathrm{.}5cm$ in diameter; the opposite end of the tube is exposed to pure A at $2$atm,$127C.$ The catalyst is so active that the concentration of A is zero adjacent to the disk. The binary gas diffusivity under these conditions is $0\mathrm{.}325c\frac{m^2}{s}.$ The molecular weight of $A$ is $26$ and that of $B$ is $17.$

$($a$)$ Determine the initial concentration of the gaseous system in $k\frac{g}{m^3}$ assuming ideal gas behavior.

$($b$)$ Find the molar flux of A along the diffusion path at steady state.