Question $2[30$ marks $]$

$($a$)$ The following equation can be derived for the kinetics associated with $1^{st}-$order reaction in a

plug$-$flow reactor:

$ln(\frac{[A{]}_o}{[A{]}_i})=-k(\frac{V}{v})$

Define all of the terms in this equation.

$[5$ marks$]$

$($b$)$ Peracetic acid vapour at $2\%$ by volume in nitrogen carrier gas at a total pressure of $101$kPa

and $490K$ flows through a $1\mathrm{.}4mm$ radius teflon tubing and is sampled $1\mathrm{.}2m$ downstream

with the following results:

Show that reaction follows first order kinetics and calculate the rate constant, $k.$

$[15$ marks$]$

$($c$)$ A rate constant has the value of $1\mathrm{.}78{10}^{-4}d{m}^{3}mo{l}^{-1}{s}^{-1}$ at a temperature of $19C(292K)$

and of $1\mathrm{.}38{10}^{-3}d{m}^{3}mo{l}^{-1}{s}^{-1}$ at $37C(310K).$ Draw a suitable graph to determine the

activation energy of the reaction.

$[10$ marks$]$