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

$($a$)$ Determine the initial concentration of the gaseous system in kg$/$m$3$assuming ideal gas behavior.

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

$($c$)$ What is the production rate of B at steady state? This is a problem in mass transfer, not reaction engineering or heat so solve it accordingly.