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°C than at 150°C?

Question

Quizplus · Accepted Answer

The rate constant (k) is given by the Arrhenius equation:

$k = A \cdot e^{-E_a/RT}$

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

To compare the rate constants at 170°C and 150°C, we need to calculate the ratio of the rate constants (k2/k1):

$k_2/k_1 = (A \cdot e^{-E_a/RT_2})/(A \cdot e^{-E_a/RT_1}) = e^{-E_a/R} \cdot (1/T_2 - 1/T_1)$

Substituting the given values, we get:

$k_2/k_1 = e^{-71000/(8.314 \cdot 170)} \cdot (1/443 - 1/423) \approx 2.5$

Therefore, the rate constant at 170°C is about 2.5 times greater than at 150°C. The answer is (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