According to the Arrhenius equation, with Ea = 75 kJ/mol, near 300 K, increasing temperature by 10 K changes k by about what factor?

• A. About 1.1
• B. About 2–3 (approximately 2.7)
• C. About 5
• D. About 10

Answer: (B)

The factor by which the rate constant changes with temperature is controlled by the Arrhenius exponential, k(T2)/k(T1) = exp[-Ea/R (1/T2 − 1/T1)]. With Ea = 75 kJ/mol and R = 8.314 J/mol·K, take T1 ≈ 300 K and T2 ≈ 310 K. Compute 1/310 − 1/300 ≈ −1.075×10^-4 K^-1. Multiply by −Ea/R ≈ −75000/8.314 ≈ −9026, giving an exponent of about 0.97. Exponentiating, k(310 K)/k(300 K) ≈ e^{0.97} ≈ 2.6–2.7. So the rate increases by about a factor of 2–3, roughly 2.7.