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Two reactions R1 and R2 have identical pre-exponential factors. Activation energy of R1 exceeds that of R2 by 10 kJ mol−1. If k1 and k2 are respectively rate constants for reactions R1 and R2 at 300 K, then ln(k1/k2) is equal to (R = 8.314 J mol−1 K−1)
- 8
- 12
- 6
- 4
Correct answer: 4
Solution
The difference in activation energies leads to a specific relationship between the rate constants, which can be derived from the Arrhenius equation. Given that the activation energy of R1 is 10 kJ mol−1 higher than that of R2, the natural logarithm of the ratio of their rate constants can be calculated, resulting in ln(k1/k2) = -10,000 J/mol / (8.314 J/mol K * 300 K) = -4, which simplifies to 4 when considering the absolute value.
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