Final answer:
To calculate the activation energy for the reaction at 57°C, use the Arrhenius equation by substituting the given values and rearranging the equation to solve for Ea.
Step-by-step explanation:
To calculate the activation energy for a reaction, we can use the Arrhenius equation: ln(k) = -Ea/(R*T) + ln(A), where k is the rate constant, Ea is the activation energy, R is the gas constant, T is the temperature in Kelvin, and A is the frequency factor. We need to convert the temperature from Celsius to Kelvin by adding 273.15. Rearranging the equation to solve for Ea, we have: Ea = -(ln(k) - ln(A)) * (R*T).
Given that the rate constant is 0.224 s'-1 and the frequency factor is 7.30 x 1011, we can substitute these values into the equation along with the temperature in Kelvin (330.15 K) and the gas constant (8.314 J/(mol*K)).
Calculating the activation energy using the given values, we get:
Ea = -(ln(0.224) - ln(7.30 x 1011)) * (8.314 J/(mol*K) * 330.15 K)
Ea ≈ 64.715 kJ/mol
Learn more about activation energy