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Problem $1$ The dehydrogenation of a compound $($elementary kinetics$)$ is taking place in a selective membrane reactor under isothermal conditions.

AlongrightarrowB$+\frac{1}{2}C$

The reaction is reversible and $Kc$ is the equilibrium constant. The manner in which $Kc($ the mass transfer coefficient at volumetric flow rate $v_0)$ increases with flow rate depends upon the flow geometry and the mass transfer dependence on velocity is given by

$Kc=k_{co}(\frac{v}{v_o}{)}^{\frac{1}{2}}$

And the membrane transport of $C$ is given by $k_c{C}_c$ when permeate concentration of $C$ is low.

The following parameter values apply,

$k=0\mathrm{.}5d\frac{m^3}{k}g*min,vo=50d\frac{m^3}{m}in,K_c=0\mathrm{.}5((kg)-mo\frac{l}{d}{m}^3{)}^{\frac{1}{2}}$

$Po=10$atm,FAo$=10kg-mo\frac{l}{m}in$;$=0\mathrm{.}002at\frac{m}{k}g$

Kco$=0\mathrm{.}1d\frac{m}{m}$inW$=200kg$

Compare the calculated output valued of FB$,$ the molar flow rate of B for no pressure drop.