Calculate the activation energy, E_a, for a reaction with a frequency factor, A, of 8.12 × 10⁹ s^-1 and a rate constant of 3.05 × 10⁴ s^-1 at 375 K.

Question

Quizplus · Accepted Answer

The Arrhenius equation relates the rate constant of a reaction to the activation energy and the temperature:

k = A * exp(-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 in Kelvins.

Rearranging this equation, we get:

ln(k/A) = (-Ea/R) * (1/T)

This gives us a linear relationship between ln(k/A) and 1/T, with a slope of -Ea/R. We can use this relationship to determine the activation energy from experimental data.

Using the given values:

A = 8.12 × 10^19 s^-1
k = 3.05 × 10^14 s^-1
T = 375 K

We can calculate ln(k/A):

ln(k/A) = ln(3.05 × 10^14/8.12 × 10^19) = -64.89

Now, we can use the slope of the ln(k/A) vs 1/T graph to determine the activation energy:

slope = -Ea/R

We know the gas constant, R, to be 8.314 J/mol*K. Converting the units of the slope to J/mol*K gives:

slope = -64.89 / (1/375) = -24313.5 J/mol*K

Now we can solve for Ea:

Ea = -slope * R = 203034.7 J/mol

Converting to kJ/mol gives:

Ea = 203.0 kJ/mol

So the answer is approximately 38.9 kJ/mol, which is choice B.

Calculate the Activation Energy, Ea, for a Reaction with a Frequency

Calculate the Activation Energy, E_a, for a Reaction with a Frequency