# Activation Energy Equation

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To start any chemical reaction we need some energy.  Molecules require some minimum energy to react. Reaction involves formation and breaking of bonds which also require some minimum amount of energy.

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

Example: If the rate constant is 13M^-1s^-1 at 345K and the frequency factor is 23s^-1 calculate the activation energy.

Solution

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

Example: A second-order reaction was observed. The reaction rate constant at 3 °C was found to be 8.9 x 10^-3 L/mol at 35 °C. If the frequency factor is 6.4 x 10^6 s^-1 what is the activation energy of this reaction?

Solution:

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