The rate constant for a reaction at 40.0°C is exactly 3 times that at 20.0°C.Calculate the Arrhenius energy of activation for the reaction.

Question

Quizplus · Accepted Answer

The Arrhenius equation is:

k = Ae^(-Ea/RT)

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

If we take the ratio of the rate constants at 40.0°C and 20.0°C, we get:

k(40)/k(20) = e^(-Ea/R * (1/40 - 1/20))

3 = e^(-Ea/R * (1/40 - 1/20))

Taking the natural logarithm of both sides, we get:

ln(3) = -Ea/R * (1/40 - 1/20)

Solving for Ea, we get:

Ea = (-R * ln(3))/(1/40 - 1/20)

Ea ≈ 41.9 kJ/mol

Therefore, the answer is C.

The Rate Constant for a Reaction at 40