The chemical reactions $ABC$ take place in the liquid phase in an adiabatic ideal CSTR with

mean residence time $.$ The reaction $AB$ obeys first$-$order kinetics with rate constant $k1$ and is

endothermic with enthalpy of reaction $H1=$hkJkmol$-1.$ The second reaction $BC$ obeys first$-$

order kinetics with rate constant $k2$ and is exothermic with enthalpy of reaction $H2=-2$hkJkmol$-$

The heat capacity of all species is $Cp($in kJ kmol$-1$ K$-1).$ The feed temperature is $300K.$ The mean

residence time is $20s.$ The rate constants, in units of $s-1,$ are $k1={10}^{10}$exp$(-\frac{7500}{T})$ and $k2=$

${10}^{10}$exp$(-\frac{8250}{T}).$ The value of $\frac{h}{C}p$ is $75K.$

a$.$ The heat balance below is obeyed at temperature $T=279K,327K$ and $371\mathrm{.}6K.$

$T-T_0=\frac{h}{C_p}(\frac{k_1}{1+k_1})(\frac{2k_2}{1+k_2}-1)$

On the same plot, sketch a graph of

$T-T_{0}vs.T$; and $of$

$\frac{h}{C_p}(\frac{k_1}{1+k_1})(\frac{2k_2}{1+k_2}-1)vs.T$

and thereby explain why the reactor cannot operate stably at one of these temperatures.

b$.$ Calculate the yield of $B$ under both conditions of stable operation.

c$.$ What process conditions should be considered if $B$ is the desired product of the reaction?

Answers:

b$)0\mathrm{.}29$ and $0\mathrm{.}021$ at the lower and higher temperatures respectively