A certain reaction has a rate constant of 8.8 s^-1 at 298 K and 140 s^-1 at 323 K.What is the activation energy for this reaction?

Question

Quizplus · Accepted Answer

The activation energy can be calculated using the Arrhenius equation:

k = Ae^(-Ea/RT)

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature.

Taking the ratio of the two given rate constants:

k_2/k_1 = (Ae^(-Ea/RT_2))/(Ae^(-Ea/RT_1))
k_2/k_1 = e^((Ea/R)(1/T_1 - 1/T_2))

Taking natural logarithm of both sides:

ln(k_2/k_1) = (Ea/R)(1/T_1 - 1/T_2)

Plugging in the values given:

ln(140/8.8) = (Ea/8.314)(1/298 - 1/323)
ln(15.91) = (Ea/8.314)(0.00335)
Ea = (ln(15.91)/0.00335)*8.314
Ea = 88.6 kJ/mol

Therefore, the best choice is (B), 89 kJ/mol, which is closest to the calculated activation energy.

A Certain Reaction Has a Rate Constant of 8