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GATE 2024 Chemical Engineering, Q21 · Reaction Engineering

The correct answer is B, 0.23, 0.12.

Question

Two parallel first-order liquid phase reactions A →(k1)→(k₁) B and A →(k2)→(k₂) C are carried out in a well-mixed isothermal batch reactor. The initial concentration of A in the reactor is 1kmol/m3,1 kmol/m³, while that of B and C is zero. After 2 hours, the concentration of A reduces to half its initial value, and the concentration of B is twice that of C. The rate constants k1k₁ and k2,k₂, in h−1,h⁻¹, are, respectively

  • A. 0.40, 0.20
  • B. 0.23, 0.12
  • C. 0.50, 0.25
  • D. 0.36, 0.18

Official answer: 0.23, 0.12

Why

GATE 2024 official key: (B). CA/CA0=e−(k1+k2)t:0.5=e−2(k1+k2)⇒C_{A}/C_{A0} = e^{−(k1+k2)t}: 0.5 = e^{−2(k1+k2)} \Rightarrow k1+k2 = ln2/2 ≈\approx 0.3466/h. Since CB/CC=C_{B}/C_{C} = k1/k2 = 2, k1 = 2k2 ⇒\Rightarrow 3k2 =0.3466⇒= 0.3466 \Rightarrow k2 ≈0.116,\approx 0.116, k1 ≈0.231,\approx 0.231, matching (0.23, 0.12).

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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