The rate constant for a first-order reaction is 2.4 × 10^-4L/(mol·s)at 600 K and 6.2 × 10^-4L/(mol · s)at 900 K.Calculate the activation energy.(R = 8.31 J/(mol · K))

Question

Quizplus · Accepted Answer

We can use the Arrhenius equation:

k = A * exp(-Ea/RT)

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

Taking the natural logarithm of both sides, we get:

ln k = ln A - Ea/RT

We can then use the given rate constants to set up two equations with two unknowns (ln A and Ea):

ln k1 = ln A - Ea/(R * 600 K)
ln k2 = ln A - Ea/(R * 900 K)

where k1 and k2 are the rate constants at 600 K and 900 K, respectively.

Solving for ln A and Ea using these equations, we get:

ln A = (ln k2 * 600 K - ln k1 * 900 K) / (600 K - 900 K) = 27.11
Ea/R = (ln k1/k2)/(1/T2 - 1/T1) = (ln 2.4 × 10^-4/6.2 × 10^-4)/(1/900 K - 1/600 K) 
Ea/R = 1.42 × 10^4 K
Ea = 1.42 × 10^4 K * 8.31 J/(mol · K) = 1.18 × 10^5 J/mol
Ea ≈ 1.42 × 10^5 J/mol or 1.42 × 10^4 kJ/mol

Therefore, the closest answer choice is C, 1.42 × 10^4 J/mol.

The Rate Constant for a First-Order Reaction Is 2