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GATE 2026 CH – Question 42

Chemical Reaction Engineering · Single and multiple reactions in ideal reactors · 2 marks · Multiple choice

Consider the following homogeneous isothermal liquid-phase parallel reactions carried out in three reactor configurations (having identical volumes and same operating temperatures), as shown in the figure.

$A + B \to D$, rate of formation of D: $r_D = k_1C_AC_B$
$A + B \to U$, rate of formation of U: $r_U = k_2C_A^2C_B$

where D is the desired product and U is the undesired product. The inlet concentrations of A and B are the same in all three configurations ($C_{A0} = C_{B0} = 1$ mol L$^{-1}$). The total molar feed flow rate of A ($F_{A0}$) and that of B ($F_{B0}$) are the same in all three configurations ($F_{A0} = F_{B0} = 10$ mol min$^{-1}$). In configuration I, $F_{A0}$ is equally distributed among all the inlets. Similarly, in configuration III, $F_{B0}$ is equally distributed among all the inlets. Assuming plug flow behavior, at steady state, which one of the following statements is CORRECT?

three plug flow reactors. In configuration I, B enters at the inlet and A is fed in equal parts through side streams along the length. Configuration II is a plain plug flow reactor with A and B both fed at the inlet. In configuration III, A enters at the inlet and B is fed in equal parts through side streams along the length.
  1. Configuration I and Configuration III give the same selectivity of the desired product.
  2. Configuration I gives the highest selectivity of the desired product.
  3. Configuration II gives the highest selectivity of the desired product.
  4. Configuration III gives the highest selectivity of the desired product.

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Correct answer: (B) Configuration I gives the highest selectivity of the desired product.

Explanation

The instantaneous selectivity is $\frac{r_D}{r_U} = \frac{k_1C_AC_B}{k_2C_A^2C_B} = \frac{k_1}{k_2C_A}$. It does not depend on $C_B$ and it is larger when $C_A$ is lower. So the best arrangement keeps the concentration of A as low as possible everywhere in the reactor. Configuration I adds A gradually through the side streams, so $C_A$ stays low all along the reactor. Configuration II has A at its highest at the inlet, and configuration III also starts with all of A at the inlet. Hence configuration I gives the highest selectivity of the desired product.