Definition:First-Order Reaction/Rate Constant

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

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

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


$x$ 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.