Integrated rate laws

Definition

Integrated rate laws describe the concentration of reactants as a function of time. They are derived from differential rate laws and are used to determine reaction order and rate constants.

5 Must Know Facts For Your Next Test

1. First-order integrated rate law: $[A](t) = [A]_0 e^{-kt}$, where $[A](t)$ is the concentration at time t, $[A]_0$ is the initial concentration, and k is the rate constant.
2. Second-order integrated rate law: $\frac{1}{[A](t)} = \frac{1}{[A]_0} + kt$, applicable for reactions where the sum of exponents in the rate law equals two.
3. Zero-order integrated rate law: $[A](t) = [A]_0 - kt$, used for reactions with a constant rate independent of reactant concentrations.
4. The units of the rate constant (k) vary depending on the order of the reaction: s⁻¹ for first-order, M⁻¹s⁻¹ for second-order, and M/s for zero-order reactions.
5. Graphical methods can be used to determine reaction order: plotting $ln[A]$ vs. time gives a straight line for first-order reactions, while plotting $\frac{1}{[A]}$ vs. time gives a straight line for second-order reactions.

Review Questions

• What is the form of the integrated rate law for a first-order reaction?
• How can you determine the reaction order using graphical methods?
• What are the units of the rate constant k for a second-order reaction?

Related terms

Differential Rate Law:

An equation that describes how the concentration of reactants changes with respect to time.

Reaction Order:

The sum of powers to which all reactant concentrations appearing in the rate law equation are raised.

$Half-Life (t_{1/2})$: $The time required for half of a reactant to be consumed in a chemical reaction.$