The elementary reversible gas phase decomposition reaction.

Aharr$2D$

is being carried out in a CSTR at constant temperature and pressure of $67C$ and $202\mathrm{.}6$kPa respectively. The leed consists of pure A and the concentration equilibrium constant, $Kc,$ at $67C$ is $0\mathrm{.}1$ mol. $L^{-1}.$ The rate constant for the forward reaction $(Ka)$ is $0\mathrm{.}5s^{-1}$ and the wolumetric flowrate to the reactor is $42\mathrm{.}0L^{-1}.$

$($a$)$ Select appropriate equation from the formula sheet and write the concentration equations of the reactant and product $(C_A$ and $C_D)$ in terms of their initial concentrations, conversion and expansion factors.

$[5$ marks$]$

$($b$)$ Calculate the equilibrium conversion with respect to the reactant $\text{'}$A:

$[14$ marks$]$

$($c$)$ Calculate the rate of the overall reaction $(ra).$

$[8$ marks$]$

$($d$)$ Determine the required CSTR volume to achieve $80\%$ of the equilibrium conversion.

$[3$ marks$]$