Using the Arrhenius equation, calculate k for A = 1.0×10^13 s^-1, Ea = 50 kJ/mol, T = 298 K. (R = 8.314 J/mol·K)

• A. About 1.7×10^-9 s^-1
• B. 1.7×10^-3 s^-1
• C. 1.7×10^-15 s^-1
• D. 1.7×10^-6 s^-1

Answer: (A)

The Arrhenius equation shows how the rate constant depends on temperature and activation energy: k = A exp(-Ea/(R T)). Here A is 1.0×10^13 s^-1, Ea is 50 kJ/mol, T is 298 K, and R is 8.314 J/mol·K.

Compute Ea/(R T) = 50,000 / (8.314 × 298) ≈ 20.19. The exponential factor is exp(-20.19) ≈ 1.7×10^-9. Multiply by A: k ≈ (1.0×10^13) × (1.7×10^-9) ≈ 1.7×10^4 s^-1.

So the rate constant is about 1.7×10^4 s^-1. The options given do not match this result, suggesting a possible misprint or mismatch in the choices. The key takeaway is how the large Ea relative to RT drives the exponential term down, but a large A can still yield a sizable k.