For the first-order parallel reactions: A → B (K1 = 8 min^-1) and A → C (K2 = 2 min^-1) at 300 K. If the activation energies for the formation of B and C are 20 and 28.314 kJ/mol, respectively, find t

Question

For the first-order parallel reactions: A → B (K1 = 8 min^-1) and A → C (K2 = 2 min^-1) at 300 K. If the activation energies for the formation of B and C are 20 and 28.314 kJ/mol, respectively, find the temperature at which B and C will be obtained in 2:1 mole ratio.

Prashant Kotian · Accepted Answer

Correct answer: C. Ratio is K1/K2. At 300 K, K1/K2 = 4. We want K1/K2 = 2. ln((K1/K2)_T / (K1/K2)_300) = -(Ea1 - Ea2)/R [1/T - 1/300]. ln(0.5) = -(-8.314 × 10^3) / 8.314 [1/T - 1/300] => -0.693 = 1000 [1/T - 1/300]. 1/T = 1/300 - 0.000693 ≈ 0.00264. T = 1/0.00264 ≈ 378.8 K, matching 379.75 K. Therefore, correct answer is C.

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