\begin{definition}[Definition:First-Order Reaction/Rate Constant]
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'''.
\end{definition}