The following nonelementary gas phase esterification reaction, where butanoic

acid $(C_3{H}_{7}C{O}_{2}H)$ reacts with ethanol $(C_2{H}_{5}OH)$ to produce ethyl butanoate

$(C_3{H}_{7}C{O}_2{C}_2{H}_5)$ and water is carried out in a packed bed reactor. The reaction is

carried out using equal molar feed rate of butanoic acid and ethanol at

temperature of $130C.$

The reaction is first order in ethanol and pseudo$-$zero order in butanoic acid the

specific reaction rate rate is $0\mathrm{.}3\frac{m^3}{\text{k}\text{g}\text{c}\text{a}\text{t}\text{.}\text{m}\text{i}\text{n}}$ at $130C.$

$C_3{H}_{7}C{O}_{2}H(g)+C_2{H}_{5}OH(g)C_3{H}_{7}C{O}_2{C}_2{H}_5(g)+H_{2}O(g)$

The total molar feed rate is $2$kmo$\frac{l}{m}in.$ The reaction is studied using $12kg$

microporous resin as a catalyst. The inlet pressure is $10$ atm.

a$)$ Calculate the conversion

i$.$ Neglecting pressure drop

ii$.$ Accounting for pressure drop $($Pressure Drop Parameter, $=0\mathrm{.}035k{g}^{-1})$

b$)$ Calculate the error in conversion when pressure drop is neglected.

Formulae

$R=0\mathrm{.}082\frac{m^3(atm)}{\text{k}\text{m}\text{o}\text{l}\text{e}\text{K}}$

Pressure Ratio for $=0$:$,\frac{P}{P_0}=(1-W{)}^{0\mathrm{.}5}$