Activation Energy And Arrhenius Equation

Activation Energy And Arrhenius Equation

Arrhenius equation relates the rate of reaction to temperature Or variation of rate constant with temperature. Rate of reaction increases with rise in temperature. Generally, a 10 ⁰C rise in temperature doubles or triples the rate of reaction. The ratio of rate constants at two different temperatures is called temperature co-efficient. If rate constant at temperature T is K1 and rate constant at temperature T + 10 ⁰C = K2 then

First empirical equation by Hood

First empirical equation shows the relation of rate constant with temperature. This equation has no theoretical background and it was proposed on the basis of experimental data.

Activation Energy And Arrhenius Equation

Figure 8.1: Exponential graph

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By Hood

e.q.8.1

Where A’ and B are positive constants. The verification of this equation lies in the fact that plot of lnK vs 1/T gives a straight line.

Figure 8.2: Straight line graph for Hood’s equation

In 1884, Von’t Hoff theoretically justified the Hood equation on the basis that equilibrium constant change with temperature.

In 1886, Hood’s equation was modified by Arrhenius as

e.q.8.2

Here R is ideal gas constant, Ea is activation energy, T is temperature.

Activation energy “Ea”

It is the minimum energy required to initiate a reaction. It is characteristics of each reaction. Substituting values and integrating.

e.q.8.3

Figure 8.3: Straight line graph for e.q.8.3

Here lnA=A’ which is a pre-exponent factor. The above equation can also be written as

e.q.8.1

Simplifying e.q.8.3 we got

e.q.8.5 is the Arrhenius equation.

Determination of activation energy

If rate constants at different time intervals are given then by slope we can calculate activation energy. Suppose rate constant at temperature T1=K1. Similarly rate constant at temperature T2=K2. Then from e.q.8.4