Q$4)$ 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 ${0\mathrm{.}3}^{m^3}$ at $130C.$

kgcat.min

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

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.