Given the complex reaction in CSTR:

$A+2BC$ with $-r_{1A}=k_{1A}{C}_A{C}_B^2$

$3C+2AD$ with $-r_{2C}=k_{2C}{C}_C^3{C}_A^2$

a$)$ Write the net rate of reaction for each species.

b$)$ The complex liquid phase reactions take place in a CSTR$.$ The feed is equal molar in A and $B$ with $F_{A0}=200mo\frac{l}{m}in,$ the volumetric flow rate is $100d\frac{m^3}{m}in.$ Determine the reactor volume when conversion of the limiting reactant is $70\%.$ What is the concentration of $D,$ selectivity, and yield of C over D for the conversion?

c$)$ The rate constants are:

$k_{1A}=10\frac{(\frac{d{m}^3}{(mol)}{)}^2}{m}in$

$k_{2C}=15\frac{(\frac{d{m}^3}{(mol)}{)}^4}{m}in$

i$.$ Find the concentrations of $A,B,C,$ and $D$ exiting the reactor along with the exiting selectivity.

ii$.$ Plot $F_A,F_B,F_C,F_D$ and $S_{\frac{C}{D}}$ as a function of $V$