Answer:
53.7kJ/mol
Explanation:
Using Arrhenius equation
Given
T1 = 12°C = 273 + 12 = 285K
T2 = 21°C = 273 + 21 = 294K
k = A exp(-Ea/RT)
Where k = Rate constant
A = the pre-exponential factor
Ea = the activation energy
R = the Universal Gas Constant = 8.314J/kmol
T = the temperature
Taking logarithms of both sides of the Arrhenius Equation.
ln(k) = ln(A) - Ea/RT
If there are the rates at two different temperatures, we can derive the expression to be;
ln(k2/k1) = Ea/R(1/T1 - 1/T2)
The reaction doubles the rate constant
So, k2/k1 = 2 (Given)
Then we have
ln(2) = Ea/8.314(1/285 - 1/294)
ln(2) * 8.314 = Ea*(1/285 - 1/294)
6.9314E-1 * 8.314 = Ea*(1/285 - 1/294)
5.7628 = Ea*(1/285 - 1/294)
5.7628 = Ea*1.0741E-4
Ea = 5.7628 / 1.074E-4
Ea = 53657.35567970204J
Ea = 53.7kJ/mol
