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Why can a small rise in temperature greatly increase a reaction rate?

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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.

A small rise in temperature significantly increases the rate of a chemical reaction primarily because it increases the number of molecules possessing sufficient energy to overcome the activation energy barrier.1

According to collision theory, a reaction occurs when molecules collide with both the correct orientation and enough kinetic energy to initiate bond breaking and formation. The Maxwell-Boltzmann distribution describes how molecular energies are distributed at a given temperature; as temperature rises, the distribution shifts, resulting in a larger fraction of molecules having kinetic energies that exceed the activation energy required for the reaction to proceed.12

This relationship is mathematically expressed by the Arrhenius equation:
$k = A e^{- E_{a} / R T}$
In this equation, $k$ is the reaction-rate constant, $A$ is the frequency factor, $E_{a}$ is the activation energy, $R$ is the universal gas constant, and $T$ is the absolute temperature. Because temperature appears in the exponent, even a small increase in $T$ leads to a marked, exponential increase in the rate constant $k$ , reflecting the increased probability of successful, high-energy collisions.34