Calculate the temperature if a reaction has a rate constant, k, of 841 s^-1, a frequency factor, A, of 6.0 × 10¹² s^-1, and an activation energy, E_a, of 62 kJ mol^-1.

Question

Quizplus · Accepted Answer

The Arrhenius equation relates temperature and rate constant through the following equation:

k = A * e^(-Ea/RT)

Where R is the gas constant and T is temperature in Kelvin.

R = 8.314 J mol^-1 K^-1
k = 841 s^-1
A = 6.0 × 10^12 s^-1
Ea = 62 kJ mol^-1

We need to solve for T.

Taking natural logarithm of both sides, we get:

ln k = ln A - (Ea/RT)

Solving for T:

T = Ea/(R * slope) + intercept

where
slope = -R
intercept = Ea / (R * ln A)
R = 8.314 J mol^-1 K^-1
k = 841 s^-1
A = 6.0 × 10^12 s^-1
Ea = 62 kJ mol^-1

Plugging in the values, we get:

T = 330 K

Therefore, the answer is D.

Calculate the Temperature If a Reaction Has a Rate Constant