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# Arrhenius Equation Calculator

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Arrhenius equation shows the dependence of rate constant at various temperature of a chemical reaction and activation energy. The probability is high if the two molecules collide at high temperature. The higher the collision rate, higher will be the kinetic energy and which effects the activation energy.

Arrhenius equation is given by,
$k = Ae^{\frac{-E_{a}}{(RT)}}$

where,
k = rate constant,
A = frequency factor in $sec{-1}$,
$E_{a}$ = activation energy in $kJ mol_{-1}$,
R = universal gas constant = $8.314 \times 10^{-3} kJ mol^{-1}K^{-1}$
T = temperature in K.

Plug in the all the values of parameter given into this online Arrhenius equation calculator to calculate the rate constant.

## Steps

Step 1: Observe the parameter values given in the problem.

Step 2: Substitute those values into the arrhenius equation to get the rate constant of the reaction.

$k = Ae^{\frac{-E_{a}}{(RT)}}$

## Problems

Here are some of the problems shown related to arrhenius equation.

### Solved Examples

Question 1: Determine the rate constant if activation energy is 210 kJ/mol and frequency factor is 10 $M_{-1}s_{-1}$ at temperature 289K.
Solution:

Step 1: Given :
Activation energy $E_{a}$ = 210 kJ/mol,
Frequency factor A = 10 $M^{-1}s^{-1}$,
Temperature T = 289K.

Step 2: Rate constant k is,
$k = Ae^{\frac{-E_{a}}{(RT)}}$

$k = (10 M^{-1}s^{-1}) \times$ $e^{\frac{-210 kJ/mol}{(8.314 \times 10^{-3} kJ mol^{-1}K^{-1} \times 289K)}}$

$k = 1.10322 \times 10^{-37} M^{-1}s^{-1}$

Rate constant of this constant is $1.10322 \times 10^{-37} M^{-1}s^{-1}$.

Question 2: If activation energy is 600 kJ/mol and frequency factor is 15 $M_{-1}s_{-1}$ at temperature 353K, calculate its rate constant.
Solution:

Step 1: Given :
Activation energy $E_{a}$ = 600 kJ/mol,
Frequency factor A = 15 $M_{-1}s_{-1}$,
Temperature T = 353K.

Step 2: Rate constant k is,
$k = Ae^{\frac{-E_{a}}{(RT)}}$

$k = (15 M^{-1}s^{-1}) \times$ $e^{\frac{-600 kJ/mol}{(8.314 \times 10^{-3} kJ mol^{-1}K^{-1} \times 353K)}}$

$k = 2.44790 \times 10^{-88} M^{-1}s^{-1}$

Rate constant of this constant is $2.44790 \times 10^{-88} M^{-1}s^{-1}$.