GATE 2022 BT – Question 59

Fundamentals of Biological Engineering · Bioreaction Engineering: Ideal reactors (batch, mixed flow, plug flow), enzyme immobilization, Thiele modulus, effectiveness factor, Damkohler number · 2 marks · Numerical answer

An enzyme converts A to B with $-r_A=C_A/(5+C_A)$ mol/(L min). Feed containing 10 mol/L A enters an ideal MFR at 10 L/min. Volume for 50% conversion is ___________ L.

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Correct answer: 100

Explanation

For an ideal **mixed flow reactor (MFR/CSTR)** the design equation for the volume is
$$V=\frac{F_{A0}\,X_A}{-r_A}=\frac{v_0\,(C_{A0}-C_A)}{-r_A},$$
with the rate evaluated at the **exit** concentration.

**Step 1: exit concentration.** For 50% conversion of the 10 mol/L feed, $C_A=5$ mol/L.

**Step 2: rate at the exit.**
$$-r_A=\frac{C_A}{5+C_A}=\frac{5}{5+5}=0.5\text{ mol L}^{-1}\text{min}^{-1}.$$

**Step 3: volume.**
$$V=\frac{10\ \text{L/min}\times(10-5)\ \text{mol/L}}{0.5\ \text{mol L}^{-1}\text{min}^{-1}}=\frac{50}{0.5}=\mathbf{100\ L}.$$