Definition:First-Order Reaction/Rate Constant

Definition

Let $S$ be a substance which decomposes spontaneously in a first-order reaction.

By First-Order Reaction, this is governed by the equation:

$x = x_0 e^{-k t}$

where:

$x$ is the quantity of $S$ at time $t$

$x_0$ is the quantity of $S$ at time $t = 0$

$k$ is a positive number.

The number $k$ is called the rate constant.

$k$ is constant for a particular substance, and different substances, in general, have different rate constants.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 4$: Growth, Decay and Chemical Reactions