GATE 2023 CH – Question 59

Chemical Reaction Engineering · Single and multiple reactions in ideal reactors · 2 marks · Numerical answer

A unimolecular, irreversible liquid-phase reaction $A \longrightarrow P$ was carried out in an ideal batch reactor at temperature $T$. The rate of the reaction ($-r_A$) measured at different conversions $X_A$ is given in the table below. This reaction is also carried out in an ideal continuous stirred tank reactor (CSTR) at the same temperature $T$ with a feed concentration of 1 mol m$^{-3}$, under steady-state conditions. For a conversion of 0.8, the space time (in s) of the CSTR is __________ (in integer).

$X_A$	0	0.1	0.2	0.4	0.6	0.8
$-r_A$ (mol m$^{-3}$s$^{-1}$)	0.45	0.35	0.31	0.18	0.11	0.05

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 16

Explanation

For a CSTR, $\tau = \frac{C_{A0}X_A}{-r_A}$ evaluated at the exit conversion. At $X_A = 0.8$ the rate is 0.05 mol m⁻³ s⁻¹, so $\tau = \frac{1 \times 0.8}{0.05} = 16$ s.