Class 12 Chemistry Chemical Kinetics | Arrhenius equation |

__Arrhenius equation__

- The formula used to calculate the energy of activation and justify the effect of temperature on rate of reaction is called Arrhenius Equation.
- It is given by the formula,

K = A e^{-Ea/RT}

Where,

k = Rate constant

A= Frequency factor

e = mathematical quantity

E_{a}= activation energy

R = gas constant

T = kelvin temperature

ln K = ln A – Ea/(2.303RT)

Equation of a straight line with slope = –*E _{a}* /

- When E
_{a}= 0 , Temperature = Infinity

K = Ae^{0} = A

e^{-Ea/RT }=Boltzmann factor.

- For a chemical reaction the rate constant gets doubled for a rise of 10° temperature. This is because according to Arrhenius Equation,

K = Ae^{-Ea/RT}

Taking log on both sides of the equation

Ln k = ln A – E_{a}/RT

Comparing with the equation of a straight line

y= mx+c,

[m= slope of the line

c= y-intercept]

So we have:

y = ln k

x = 1/T

m = -E_{a} / R

c = ln A

Plotting k Vs (1/*T*)

* PROBLEM*. Find the activation energy (in kJ/mol) of the reaction if the rate constant at 600K is 3.4 M

* SOLUTION*. Ln k = ln A – E

To find E_{a}, subtract ln A from both sides and multiply by -RT.

E_{a} = (ln A - ln k)RT

.