GATE 2021 CH – Question 59
The following isothermal autocatalytic reaction, $\mathrm{A+B\to2B}$, $(-r_A)=0.1C_AC_B$ (mol L⁻¹ s⁻¹), is carried out in an ideal continuous stirred tank reactor (CSTR) operating at steady state. Pure A at 1 mol/L is fed, and 90% of A is converted in the CSTR. The space time of the CSTR is _____ seconds.
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Correct answer: 100
Explanation
For the intended constant-volume liquid reaction, at 90% conversion $C_A=C_{A0}(1-X)=0.1$ mol/L. Stoichiometry gives $C_B=C_{B0}+C_{A0}X=0+0.9=0.9$ mol/L.
The exit reaction rate is $-r_A=0.1(0.1)(0.9)=0.009$ mol/(L·s). A steady ideal CSTR uses that **exit** rate throughout its volume:
$$\tau=\frac{C_{A0}X}{-r_A}=\frac{1(0.9)}{0.009}=\mathbf{100\ \mathrm s}.$$
The nonzero operating state presupposes that autocatalyst B has been seeded; this does not change the stated steady-state balance.