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GATE 2024 CH – Question 45

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

A first-order liquid phase reaction $A \to B$ is carried out in two isothermal plug flow reactors (PFRs) of volume 1 m$^3$ each, connected in series. The feed flow rate and concentration of $A$ to the first reactor are 10 m$^3$ h$^{-1}$ and 1 kmol m$^{-3}$, respectively. At steady-state, the concentration of $A$ at the exit of the second reactor is 0.2 kmol m$^{-3}$. If the two PFRs are replaced by two equal-volume continuously stirred tank reactors (CSTRs) to achieve the same overall steady-state conversion, the volume of each CSTR, in m$^3$, is

  1. 1.54
  2. 3.84
  3. 7.28
  4. 1.98

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Correct answer: (A) 1.54

Explanation

For the PFRs in series, $\ln\frac{C_0}{C} = k\tau$ with $\tau = \frac{2}{10} = 0.2$ h: $k = \frac{\ln 5}{0.2} = 8.047$ h⁻¹. For two equal CSTRs in series, $\frac{C_0}{C} = (1 + k\tau_1)^2 = 5$, so $1 + k\tau_1 = 2.236$ and $\tau_1 = 0.1536$ h. The volume of each is $0.1536 \times 10 = 1.54$ m³.