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So we can define that the minimum energy which is required to start the chemical reaction is called the activation energy. The equation for activation energy can be written as:

K = A e^-Ea/RT

Or, ln K = ln A – Ea/RT

Or, log K = log A – Ea/2.303RT

Where, Ea = Activation energy

K = rate constant

A = Frequency factor

R = rate constant

T = Absolute temperature

Rate constant, K = 13M^-1s^-1

Frequency factor, A = 23s^-1

Temperature, T = 345

Now, we can use the equation to calculate the activation energy,

log K = log A – Ea/2.303RT

Log(13) = log(23) – Ea/2.303(8.314)(345)

Ea = [Log (23) – Log (13)]*2.303(8.314)(345)

Ea = 1637 Jmole^-1 = 1.6 KJmole^-1

Rate constant, K = 8.9 x 10^-3 L/mol

Frequency factor, A = 6.4 x 10^6 s^-1

Temperature = 3 + 273 = 300 k

Now, we can use the equation to calculate the activation energy,

log K = log A – Ea/2.303RT

Log(8.9 x 10^-3) = Log(6.4 x 10^6) – Ea/2.303(8.314)(300)

So, Ea = 61746 J mole^-1 = 62 KJ mole^-1