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

Ea= activation energy

R = gas constant

T = kelvin temperature

ln K = ln A – Ea/(2.303RT)

Equation of a straight line with slope = –Ea /R.

• When Ea = 0 , Temperature = Infinity

K = Ae0 = 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 – Ea/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 = -Ea / 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-1 s-1 and 31.0 at 750K.

SOLUTION.   Ln k = ln A – Ea/RT

To find Ea, subtract ln A from both sides and multiply by -RT.

Ea = (ln A - ln k)RT

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