Sales Toll Free No: 1-855-666-7446

# Activation Energy Calculator

Top
For a reaction to occur, molecules collide and bonds are broken. To break the bond and start a reaction, a minimum energy is required. The minimum energy required is known as activation energy ($E_a$).

The activation energy is calculated by the formula,

$E_a = -RT \ ln$
$\left ( \frac{K}{A} \right )$.
Where,
K = rate constant,
A = frequency factor of the reaction,
R = gas constant = $8.31447215 \ JK^{-1}mol^{-1}$,
T = temperature.

## Steps

Step 1 : Read the given problem and put down the given quantities.

Step 2 : Plug in the given values into the formula given above and find the activation energy.

## Problems

Problems based on activation energy is given below.

### Solved Examples

Question 1: If rate constant of the reaction is $6 \times 10^{-3} \ s^{-1}$ at $25^{\circ}C$. Determine its activation energy with frequency factor as $2.7 \times 10^{9} \ s^{-1}$.
Solution:

Step 1 : Given : K = $6 \times 10^{-3} \ s^{-1}$,
A = $2.7 \times 10^{9} \ s^{-1}$,
R = $8.31447215 \ JK^{-1}mol^{-1}$,
T = $25^{\circ}C$ = 298.15 K,
$E_a$ = ?

Step 2 : Activation energy of the given reaction is,
$E_a$ = $-RT \ ln\left ( \frac{K}{A} \right )$
= $-8.314 \times 298.15 \ ln$ $\left ( \frac{6 \times 10^{-3}}{2.7 \times 10^{9}} \right )$
= $-8.314 \times 298.15 \ ln \ (2.22 \times 10^{-12})$
= $66515.42 \ J/mol$

Therefore, the activation energy of the reaction is $66515.42 \ J/mol$.

Question 2: If rate constant of the reaction is $8 \times 10^{-4} \ s^{-1}$ at $40^{\circ}C$. Determine its activation energy with frequency factor as $3.2 \times 10^{7} \ s^{-1}$.
Solution:

Step 1 : Given : K = $8 \times 10^{-4} \ s^{-1}$,
A = $3.2 \times 10^{7} \ s^{-1}$,
R = $8.31447215 \ JK^{-1}mol^{-1}$,
T = $40^{\circ}C$ = 313.15 K,
$E_a$ = ?

Step 2 : Activation energy of the given reaction is,
$E_a$ = $-RT \ ln\left ( \frac{K}{A} \right )$
= $-8.314 \times 313.15 \ ln$ $\left ( \frac{8 \times 10^{-4}}{3.2 \times 10^{7}} \right )$
= $-8.314 \times 313.15 \ ln \ (2.5 \times 10^{-11})$
= $63557.73 \ J/mol$

Therefore, the activation energy of the reaction is $63557.73 \ J/mol$.