A first$-$order catalytic gas$-$phase reaction

A $$ P $+2$Q

must be carried out in an isothermal packed bed, which is filled with cylindrical

catalyst particles.

The catalyst has a diameter and height of $7\mathrm{.}0$ mm$.$ Reaction kinetic and physical data are given below.

a$)$ What will be the efficiency factor?.

b$)$ The residence time $($space time$)$ of the gas in the bed is $0\mathrm{.}4$s$.$ What will be the turnover ratio of A $?$

Data

k $=1\mathrm{.}0x{10}^{-2}$m$3/($kg s$)$

$\backslash$rho P$=1700$ kg$/m^3($density of the particle$)$

R $3\mathrm{.}5x{10}^{-3}$ m $($particle radius$)$

DA $=1\mathrm{.}5x{10}^{-5}\frac{m^2}{s}$

$\backslash$epsi P$/\backslash$tau P $=0\mathrm{.}25$

$\backslash$rho B$=1200$ kg$/m^3($catalyst bulk density$)$

Biot's number for mass transfer $=20$