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In the equation \[k = ZAB{\text{ }}\dfrac{{{e^{ - Ea}}\;}}{{RT}},\] what does \[\dfrac{{{e^{ - Ea}}\;}}{{RT}}\] represent?

Last updated date: 19th Jul 2024
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Hint: The given equation represents the rate equation proposed by Arrhenius in chemical kinetics. It is called the Arrhenius equation, and is associated with the collision theory.

Complete answer:
\[k = ZAB{\text{ }}\dfrac{{{e^{ - Ea}}\;}}{{RT}}\] is the Arrhenius equation. It is the formula which depicts the relation between temperature and reaction rates.
Let us consider a reaction:
$A + B \to \,AB$
The rate of the corresponding reaction is:
\[k = ZAB{\text{ }}\dfrac{{{e^{ - Ea}}\;}}{{RT}}\]
- k is the rate constant, which indirectly represents the number of active collisions taking place in the reaction
- ZAB is a term which depicts the frequency of collisions taking place in a reaction. It is in accordance with the collision theory.
-${E_a}$ is the activation energy for the reaction $\left( {{\text{in}}\,Jmo{l^{ - 1}}} \right)$
- R is the universal gas constant $\left( {R = 8.314J{K^{ - 1}}mo{l^{ - 1}}} \right)$
- T is the absolute temperature (in Kelvin)
The term \[\dfrac{{{e^{ - Ea}}\;}}{{RT}}\] represents the fraction of collisions that take place in a reaction which have enough energy to overcome the activation barrier at temperature T. The activation barrier is interpreted as the energy equal to the activation energy or greater than the activation energy, in possession of which the barrier can be overcome and the reaction can take place.

According to collision theory, the rate of a reaction can be predicted by taking into consideration the number of effective collisions between the reactant molecules. For effective collision to take place between reactant molecules, two factors must be satisfied: the reactant molecules must collide in a state of minimum energy and they must collide with proper orientation