A liquid$-$phase isomerisation reaction is to be conducted such that $1000$ tonnes of the

desired product are produced per year of operation. Accounting for start$-$up$,$ shutdown

and maintenance periods this can be taken as $8000h$ of reactor operation, regardless

of reactor type. The reaction is operated isothermally at $150C.$ Over the course of

reaction $95\%$ of all of the initial reactant is converted into the desired product. The

following additional parameters are known:

Rate constant: $0\mathrm{.}2h^{-1}$

Density of reactant: $0\mathrm{.}75gc{m}^{-3}$

Density of product: $0\mathrm{.}75gc{m}^{-3}$

Enthalpy of reaction: $-300k\frac{J}{k}g$

Heat capacity of reactant: $2kJk{g}^{-1}{K}^{-1}$

Heat capacity of product: $2kJk{g}^{-1}{K}^{-1}$

$($a$)$ The CSTR is a commonly used model to describe reactors. What does CSTR

stand for and what assumptions underpin this model?

$($b$)$ The design equation for a CSTR can be expressed as:

$r_A=\frac{n_{A0}-n_A}{V}$

Show how this can be derived from an appropriate materials balance.

$($c$)$ If the reaction is to be conducted in a single CSTR$,$ what volume of CSTR is

required?

$($d$)$ If the reaction is to be conducted in two identical CSTRs connected in series,

what volume should each CSTR be$?$