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How is the rate constant used in a chemical rate equation?

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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.

In chemical kinetics, the rate constant (often denoted as k) serves as the proportionality constant in a chemical rate equation. It mathematically defines the relationship between the speed of a reaction and the concentrations of the reacting substances.12

For example, in a second-order reaction involving substances A and B, the rate expression is written as:
$v = k [A] [B]$
In this equation, k accounts for the specific speed at which the reaction proceeds under given conditions. The units of the rate constant vary depending on the overall order of the reaction.1

While the rate constant is used to relate concentration to reaction speed, its value is not fixed; it is highly dependent on temperature. This relationship is described by the Arrhenius equation, which expresses k as a function of activation energy and absolute temperature. By measuring how k changes with temperature, chemists can gain critical insights into the underlying reaction mechanisms and the energy barriers involved in the transformation.13