The following is an Arrhenius plot of a first-order reaction.The rate constant is measured in units of s^-1. Based on this Arrhenius plot,what is the activation energy of the reaction? (R = 8.314 J/K •mol)

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 in Kelvin.

From the graph, we can read off the values of k at two different temperatures, for example at 400 K and 500 K:
ln(k1/k2) = -(Ea/R) (1/T1 - 1/T2)
where k1 and k2 are the rate constants at temperatures T1 and T2, respectively.

Plugging in the values, we get:
ln(2.0/0.5) = -(Ea/8.314) (1/400 - 1/500)
ln(4) = -Ea/8.314 (-0.0025)
Ea = -ln(4) * 8.314 / (-0.0025) = 42 kJ/mol

Therefore, the answer is D, 42 kJ/mol.

The Following Is an Arrhenius Plot of a First-Order Reaction