Hello,

The activation energy can be calculated using the Arrhenius Equation which is:

Ln(k2/k1) = - (Ea/R) * ((1/t2) – (1/t1)) (Equation 1)

where   k2 = rate constant at temperature t2

k1 = rate constant at temperature t1

Ea = activation energy in J/mol

R = gas constant = 8.314 J/mol-K

t1 = reaction temperature 1 in Kelvin

t2 = reaction temperature 2 in Kelvin

Now, temperature coefficient = 2 (given)

We know that temperature coefficient = ratio of rate of the reaction

Therefore, k2/k1 = 2

Also, T1 = 25C = 298.15 K (given)

and T2 = 35C = 308.15 K (given)

Now substituting the values of k2/k1, R, t1 and t2 in equation 1, we get

ln(2) = - (Ea/8.314) * ((1/308.15) - (1/298.15))

Rearranging and solving the above equation, we get Ea = 5.29 * 10^4 J/mol (Answer)