$($a$)$ Sterilisation of liquids by heat is a first$-$order process,

$r_m=k_s{C}_m$

where, $C_m$ is the concentration of live microbes, $-r_m$ is the rate of microbe death. For a typical micro$-$organism, $k_s$ is $0\mathrm{.}03s^{-1}$ at $100C.$ The liquid initially contains ${10}^5$ live microbes per $ml.$ Make use of the appropriate equation in the formula sheet and calculate the time required to bring the concentration $($microbe population$)$ down to ${10}^{-3}$ live microbes per $ml.$

$[10$ marks$]$

$($b$)$ An adiabatic autocatalytic liquid phase exothermic reaction is to be carried out in a $25d{m}^3$ CSTR$.$ The entering molar flow rate of species $\text{'}$A$\text{'}$ times the reciprocal of the rate of reaction is shown in the figure below as a function of conversion. $$

Calculate the conversion exiting the CSTR$.$

$[13$ marks$]$

$($c$)$ Write the steps involved in a heterogeneous catalytic reaction system in bullet points.

$[7$ marks$]$