At 30 °C and 85 °C the rate constants of a reaction are 3.75 × 10^-5 and 2.72 × 10^-3 s^-1 respectively. What is the activation energy E_a (kJ mol^-1)?

Question

Quizplus · Accepted Answer

We can use the Arrhenius equation to relate the rate constant (k) to the activation energy (Ea):
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2)
where k1 and k2 are the rate constants at temperatures T1 and T2, respectively, R is the gas constant (8.314 J/mol*K), and Ea is the activation energy.

Substituting the given values, we get:
ln(2.72 × 10^-3/3.75 × 10^-5) = (Ea/8.314)(1/358 - 1/358 + 85)
ln(72.53) = (Ea/8.314)(0.01176)
Ea = (ln(72.53)/0.01176) * 8.314
Ea = 70.31 kJ/mol

Therefore, the answer is C.

At 30 °C and 85 °C the Rate Constants of a Reaction