# How do you find A and Ea using the Arrhenius equation?

Mar 18, 2018

The Arrhenius equation is given by $K = A {e}^{-} \left({E}_{a} / \left(R T\right)\right)$
Use this equation to find out the desired quantity.

#### Explanation:

The Arrhenius equation is given by $K = A {e}^{-} \left({E}_{a} / \left(R T\right)\right)$
where:
1. ${E}_{a}$ is Activation energy
2. A is pre-exponential factor
3. R is Universal Gas Constant
4. T is Temperature
5. K is Rate Constant

Before starting of I would like to invoke the old rule of mathematics which states "In order to find the value of all variable the number of equations is equal to the no. of unknowns."

I am also assuming you know about Chemical Kinetics.
The pre-exponential factor and ${E}_{a}$ are different for different reacting species under different conditions.

So suppose you don't know one of the equations say The ${E}_{a}$, assume it's value is x and substitute in the equation.

All the quantities other than R and ${E}_{a}$ will be given.
Chose the appropriate value of R based on the table in the link.

Solving for ${E}_{a}$:

$K = A {e}^{-} \left(\frac{x}{R T}\right)$

taking log on either side:
$\log \left(K\right) = \log \left(A\right) - {E}_{a} / \left(R T\right)$

${E}_{a} = R T \left[\log \left(\frac{A}{k}\right)\right]$

Remeber that this log is the natural log i.e. the log with base e.
In terms of log with base ten the eqaution becomes:

${E}_{a} = \frac{1}{2.303} R T \left[\log \left(\frac{A}{k}\right)\right]$

Regards