$1mo\frac{l}{s}$ of a species $A$ is fed into a continuous gas phase reactor. The following two fast

equilibrium reactions take place in the reactor, which operates at $298K$ and a pressure $P$ :

R$1$: $,AB+C+D,K_{a,R1}=0\mathrm{.}375at{m}^2$

R$2$: $,A+BE+C,K_{a,R2}=3$

The output of the reactor is assumed to be at equilibrium. The selectivity of the desired product

$D$ with respect to the undesired product $E(SDE)$ is $2$:$1.$

Organize

$($a$)$ Draw a process flow diagram and label all stream and system variables. $(4$ pts$)$

$($b$)$ Write down three auxiliary equations in terms of the variables you wrote down in

your process flow diagram only. $(6$ pts$)$

Analyze

$($c$)$ Count the DOF using the table on the right,

or using the definition $($# unknowns $-$ # independent equations$).$

If you use the definition, give an account for the unknowns and

equations by writing down their names $($e$.$g$.,$ nA$\mathrm{.}2,$ MB of A$)$

$(3$ pts$)$

Solve

$($d$)$ Write down all material balances, including the total material

balance. $(12$ pts$)$

$($e$)$ Solve to determine the fractional selectivity for the formation of

$D$ from $A(3$ pts$)$

Hint: express the total output flow rates and all mole fractions in terms of one of the extent of

reaction variables using one of the

AUX eqns and all balances. Then substitute into another AUX eqn which does not involve

the unknown pressure $P$ to solve for the extent of reaction variable. Then solve for all other

unknowns.

$($f$)$ Determine the reactor pressure $P(2$ pts$)$

As an alternative way to answering $($e$)$ and $($f$),$ you can write a Matlab code calling fsolve to

solve for the reactor pressure $P$ and calculate the fractional selectivity for the formation of $D$

from A$.$