What is the value of the rate constant at 425 K for a reaction wi...

Question

What is the value of the rate constant at 425 K for a reaction with rate constants of 0.0117/s at 400.0 K and 0.689/s at 450.0 K?

Accepted Answer

Identify that the problem involves calculating the rate constant at a specific temperature using the Arrhenius equation.. Recall the Arrhenius equation: $ k = A e^{-\frac{E_a}{RT}} $, where $ k $ is the rate constant, $ A $ is the pre-exponential factor, $ E_a $ is the activation energy, $ R $ is the gas constant, and $ T $ is the temperature in Kelvin.. Use the two given rate constants and temperatures to set up two equations based on the Arrhenius equation: $ \ln(k_1) = \ln(A) - \frac{E_a}{R} \cdot \frac{1}{T_1} $ and $ \ln(k_2) = \ln(A) - \frac{E_a}{R} \cdot \frac{1}{T_2} $.. Subtract the first equation from the second to eliminate $ \ln(A) $ and solve for $ E_a $: $ \ln(k_2) - \ln(k_1) = -\frac{E_a}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) $.. Once $ E_a $ is found, use it in the Arrhenius equation to solve for the rate constant $ k $ at 425 K: $ \ln(k) = \ln(A) - \frac{E_a}{R} \cdot \frac{1}{425} $.