The activation energy for the reaction CH₃CO $\rarr$ CH₃ + CO is 71 kJ/mol. How many times greater is the rate constant for this reaction at 170^$\circ$C than at 150^$\circ$C

Question

Quizplus · Accepted Answer

According to the Arrhenius equation, the rate constant (k) is directly proportional to the exponential function of the negative of the activation energy divided by the gas constant (R) times the temperature in Kelvin (T).

k = Ae^(-Ea/RT)

Taking the ratio of rate constants at two different temperatures:

k2/k1 = (Ae^(-Ea/RT2))/(Ae^(-Ea/RT1))

k2/k1 = e^(-Ea/R) * (1/T2 - 1/T1)

k2/k1 = e^(-71,000 J/mol / (8.314 J/mol*K)) * (1/(170+273 K) - 1/(150+273 K))

k2/k1 = 2.54

Therefore, the rate constant at 170°C is 2.54 times greater than the rate constant at 150°C, which is closest to 2.5 (choice C).

The Activation Energy for the Reaction CH3CO →\rarr→ CH3 + CO Is 71 KJ/mol

The Activation Energy for the Reaction CH₃CO $\rarr$ CH₃ + CO Is 71 KJ/mol