If the activation energy Ea = 42 kJ/mol and temperature rises from 298 K to 348 K, estimate the factor by which k increases (use k2/k1 ≈ exp[-Ea/R(1/T2 - 1/T1)]).

• A. About 2
• B. About 5
• C. About 11
• D. About 50

Answer: (C)

Temperature controls reaction rate through the Arrhenius relation: k = A e^{-Ea/(RT)}. When temperature rises, the exponential factor becomes less negative, so k increases.

Compute k2/k1 = exp[-Ea/R (1/T2 - 1/T1)] with Ea = 42 kJ/mol, T1 = 298 K, T2 = 348 K, R = 8.314 J/mol·K.

1/T2 − 1/T1 = 1/348 − 1/298 ≈ 0.0028736 − 0.0033557 ≈ −0.0004821 K⁻¹.

Ea/R ≈ 42000 J/mol ÷ 8.314 J/mol·K ≈ 5.054×10^3 K.

So the exponent is −Ea/R × (1/T2 − 1/T1) ≈ −5054 × (−0.0004821) ≈ 2.43.

Thus k2/k1 ≈ e^{2.43} ≈ 11.

The rate increases by about elevenfold when the temperature goes from 298 K to 348 K.