Definition:First-Order Reaction
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Definition
Suppose a body has a tendency to decompose spontaneously into smaller bodies at a rate independent of the presence of other bodies.
Then the number of bodies that decompose in a single unit of time is proportional to the total number present.
Such a reaction is called a 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.
Also see
Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 4$: Growth, Decay and Chemical Reactions