GATE 2026 CH – Question 56
A first-order homogeneous liquid-phase reaction (A→B) occurs in a non-ideal isothermal reactor operating at steady state. The variance ($\sigma^2$) of residence time distribution (RTD) from a pulse tracer experiment is 4 min$^2$. The volumetric flow rate of the feed is 5 L min$^{-1}$ and volume of the reactor is 25 L. The reaction rate constant is 0.4 min$^{-1}$. Based on the tanks-in-series model, the conversion (in %) is _______ (rounded off to one decimal place).
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Correct answer: 81.99 to 82.81
Explanation
The mean residence time is $\tau = \frac{25}{5} = 5$ min. In the tanks-in-series model the number of tanks is $N = \frac{\tau^2}{\sigma^2} = \frac{25}{4} = 6.25$. For first order kinetics, $\frac{C_A}{C_{A0}} = \frac{1}{(1 + k\tau/N)^N} = \frac{1}{(1 + 0.32)^{6.25}} = 0.1764$. The conversion is $1 - 0.1764 = 0.8236$, that is 82.4 %.