A gas$-$phase chemical reaction is occurring in the CSTR shown below. The reaction is $0\mathrm{.}5AB$ with

a rate constant of $-r_A=$kCA. The temperature of the reactor is constant, and the feed is pure $A,$ with a

molar flow rate of $q_{Ai}.$ The exit total molar flow rate $($of A and $B)$ is $q_E=(P-P_{\text{a}\text{t}\text{m}}).$

a$)$ Determine an expression for $d\frac{P_A}{?}$ dt$.$ Your answer must be simplified and only contain the terms:

$R,T,V,,q_{Ai},P_A,P_B,P_{\text{a}\text{t}\text{m}},k.$

b$)$ Determine an expression for $d\frac{P_B}{d}t.$ Your answer must be simplified and only contain the terms:

$R,T,V,,q_{Ai},P_A,P_B,P_{\text{a}\text{t}\text{m}},k.$