A reaction has a rate constant of 0.0117 s⁻¹ at 400.0 K and 0.689 s⁻¹ at 450.0 K. Using the Arrhenius equation, what is the value of the rate constant at 425 K?

• A. 0.500 s⁻¹
• B. 0.150 s⁻¹
• C. 0.300 s⁻¹
• D. 0.350 s⁻¹

Answer: (D)

Verified step by step guidance

1. Identify the given data: rate constants k1 = 0.0117 s⁻¹ at T1 = 400.0 K and k2 = 0.689 s⁻¹ at T2 = 450.0 K. We need to find the rate constant k3 at T3 = 425 K.
2. Use the Arrhenius equation in its logarithmic form: ln(k2/k1) = (Ea/R) * (1/T1 - 1/T2), where Ea is the activation energy and R is the gas constant (8.314 J/mol·K).
3. Rearrange the equation to solve for Ea: Ea = (ln(k2/k1) * R) / (1/T1 - 1/T2). Substitute the known values to calculate Ea.
4. Once Ea is determined, use the Arrhenius equation again to find k3: ln(k3/k1) = (Ea/R) * (1/T1 - 1/T3).
5. Rearrange to solve for k3: k3 = k1 * exp((Ea/R) * (1/T1 - 1/T3)). Substitute the known values to calculate k3 at 425 K.