Calculation of Activation Energy

Calculation of the activation energy can often be thought of as the energy required for a reaction to occur. The following example is edited from Fogler's Elements of Chemical Reaction Engineering.

Find the activation energy for the decomposition of benzene diazonium chloride into chlorobenzene and nitrogen, given the fact that the rate constant is 0.00043 s^-1 at 313.0 K, and 0.00717 s^-1 at 333.0 K. The ideal gas constant is 8.3145 J/mol K.

Solution

First, take the natural log of both sides of Arrhenius' equation to get:

ln(k) = ln(A)-E/(RT)

Since we are given two data points, we can call them k₁, k₂, T₁, and T₂, where:

k₁ = 0.00043 s^-1
k₂ = 0.00717 s^-1
T₁ = 313.0 K
T₂ = 333.0 K

If we use both of these data points in the above equation, we get:

ln(k₁) = ln(A) - E/(RT₁)
ln(k₂) = ln(A) - E/(RT₂)

Subtracting the two equations gives:

ln(k₂/k₁) = -E/(R(1/T₂-1/T₁))

We can rearrange this equation to:

E = -R*ln(k₂/k₁)/(1/T₂-1/T₁)

where:

ln(k₂/k₁) = ln(0.00717/0.00043) = 2.8139

So therefore:

E = -8.3145*2.8139/(1/333-1/313) = 120 kJ/mol

This can be otherwise thought of as the energy required from molecular collisions to react a mole of reactant.

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This project was funded in part by the National Science Foundation and is advised by Dr. Masel and Dr. Blowers at the University of Illinois.