The rate constant for a reaction at 40.0°C is exactly 5 times that at 20.0°C.Calculate the Arrhenius energy of activation for the reaction.

Question

Quizplus · Accepted Answer

The Arrhenius equation is given by:

k = A * exp(-Ea/RT)

where:
k = rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant (8.314 J/mol/K)
T = temperature in Kelvin

Let's call the rate constant at 20°C k1 and the rate constant at 40°C k2. According to the problem, we have:

k2 = 5 * k1

We can use the Arrhenius equation at both temperatures and divide the equations to eliminate A:

k2/k1 = exp[(Ea/R) * (1/T1 - 1/T2)]

5 = exp[(Ea/8.314) * (1/293 - 1/313)]
5 = exp[(Ea/8.314) * (-0.0068)]
ln(5) = -0.0068(Ea/8.314)
Ea = -ln(5) * 8.314 / 0.0068
Ea ≈ 61.4 kJ/mol

Therefore, the answer is C.

The Rate Constant for a Reaction at 40