Activation energy equation

$$k = A e^{-E_a / (RT)}$$

Where:

• $k$ is the rate constant
• $A$ is the pre-exponential factor or frequency factor
• $E_a$ is the activation energy
• $R$ is the universal gas constant ($8.314 \text{ J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$)
• $T$ is the absolute temperature in Kelvin

The activation energy ($E_a$) can be isolated from this equation:

$$E_a = -RT \ln\left(\frac{k}{A}\right)$$

Or, more commonly, by comparing rate constants at two different temperatures:

$$\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$

This equation allows for the calculation of the activation energy if the rate constants at two different temperatures are known.