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How does a first-order reaction depend on reactant concentration?

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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 a first-order reaction, the reaction rate is directly proportional to the concentration of a single reacting substance.12

This relationship is expressed by the kinetic equation:
$v = k [A]$

In this equation:
* v represents the reaction rate.1
* k is the rate constant.1
* [A] represents the concentration of the reactant.1

Because the rate depends on the concentration of only one species raised to the first power, the reaction is classified as first-order. A notable characteristic of these reactions is that the half-life remains constant and does not depend on the initial concentration of the reactant.1