Example

Reactant A decomposes by three simultaneous reactions to form three products, one that is

desired $B,$ and two that are undesired $x$ and $Y.$ These gas$-$phase reactions along with the

appropriate rate laws are called the trambouze reactions.

$Ax,-r_{1A}=r_x=k_1=0\mathrm{.}0001$mol.$d{m}^{-3}*s^{-1}$

$AB,-r_{2A}=r_B=k_2{C}_A=(0\mathrm{.}0015s^{-1})C_A$

$AY,r_{3A}=r_Y=k_3{C}_A^2=0\mathrm{.}008$mol.$d{m}^{-3}.(mol.s{)}^{-1}{C}_A^2$

The specific reaction rates are given at $300K$ and the activation energies for reactions are

$E1=10,000$kca$\frac{l}{m}ol,E2=15,000$kca$\frac{l}{m}ol,$ and $E3=20,000$kca$\frac{l}{m}ol.$

How and under what conditions $($e$.$g$.$ reactor type, temperature, concentration$)$ should the

reaction be carried out to maximize the selectivity of $B$ for an entering concentration of $A$ of

$0\mathrm{.}4M$ and a volumetric flow rate of $2d\frac{m^{-3}}{s}?$