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How does the Arrhenius equation relate temperature to a reaction-rate constant?

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A graph showing a potential energy curve for a chemical reaction, with the y-axis labeled potential energy and the x-axis labeled progress of reaction. The curve rises from the initial state (reactants) to a peak labeled transition state (activated complex), indicating activation energy, then drops to the final state (products). — chemical kinetics In the Arrhenius equation, the activation energy (E) represents the minimum amount of energy required to transform reactants into products in a chemical reaction. On a potential energy curve, the value of the activation energy is equivalent to the difference in potential energy between particles in an intermediate configuration (known as the activated complex, or transition state) and particles of reactants in their initial state. The activation energy thus can be visualized as a barrier that must be overcome by reactants before products can be formed.

The Arrhenius equation describes how absolute temperature ( $T$ ) influences the reaction-rate constant ( $k$ ). It is expressed as:

$k = A \exp (\frac{- E}{R T})$

In this formula:
* $k$ : The reaction-rate constant.
* $A$ : The pre-exponential factor, representing the frequency of collisions that lead to a reaction.
* $E$ : The activation energy, which is the energy barrier that must be overcome for a reaction to occur.
* $R$ : The ideal gas constant.

The equation predicts that even a small increase in temperature results in a marked increase in the magnitude of the rate constant. This occurs because, according to the Boltzmann principle, the fraction of molecules possessing energy greater than the activation energy increases with temperature, allowing more collisions to be effective. Consequently, plotting the logarithm of the rate constant against the reciprocal of the absolute temperature typically yields a straight line, which allows for the calculation of the kinetic parameters $A$ and $E$ .12