Questions: What is an integrated rate law?

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An integrated rate law is a mathematical expression that relates the concentration of a reactant to time. It is derived from the differential rate law, which describes how the rate of reaction depends on the concentration of reactants. The integrated rate law provides a way to calculate the concentration of a reactant at any given time during the reaction.

The purpose of the integrated rate law is to allow chemists to predict the concentration of reactants over time, which is useful for understanding the kinetics of a reaction and for determining reaction order and rate constants.

For a first-order reaction, the integrated rate law is: \[ [A] = [A]_0 e^{-kt} \] where:

• \([A]\) is the concentration of the reactant at time \(t\),
• \([A]_0\) is the initial concentration of the reactant,
• \(k\) is the rate constant,
• \(t\) is the time.

For a second-order reaction, the integrated rate law is: \[ \frac{1}{[A]} = \frac{1}{[A]_0} + kt \]

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