Integrated Rate Law

Definition

The integrated rate law expresses the relationship between the concentration of reactants and time, allowing for the determination of reaction rates at any given moment. It is derived from the differential rate laws and varies based on the order of the reaction, providing insight into how reactant concentrations change over time as a reaction proceeds.

5 Must Know Facts For Your Next Test

1. The integrated rate law allows for calculations of reactant concentration at any given time during a chemical reaction.
2. For a zero-order reaction, the integrated rate law is expressed as [A] = [A]₀ - kt, where [A]₀ is the initial concentration, k is the rate constant, and t is time.
3. For a first-order reaction, the integrated rate law takes the form ln[A] = ln[A]₀ - kt, emphasizing an exponential decay in concentration over time.
4. For a second-order reaction, the law can be expressed as 1/[A] = 1/[A]₀ + kt, indicating that the inverse of concentration increases linearly with time.
5. The shape of a plot of concentration versus time can reveal information about the order of the reaction; linear plots indicate zero or first-order reactions, while a curve suggests second-order behavior.

Review Questions

• How does the integrated rate law differ among zero-order, first-order, and second-order reactions?
  • The integrated rate law varies based on the order of the reaction. For zero-order reactions, concentration decreases linearly with time, represented by [A] = [A]₀ - kt. First-order reactions exhibit an exponential decay, shown by ln[A] = ln[A]₀ - kt. In contrast, second-order reactions show that 1/[A] increases linearly over time with 1/[A] = 1/[A]₀ + kt. Understanding these differences helps identify reaction types based on experimental data.
• Explain how you can determine the order of a reaction using integrated rate laws.
  • To determine the order of a reaction using integrated rate laws, you can plot data derived from concentration measurements over time. If a plot of [A] versus time yields a straight line, the reaction is zero-order. A straight line in a plot of ln[A] versus time indicates a first-order reaction. Lastly, if a plot of 1/[A] versus time is linear, it shows that the reaction is second-order. Analyzing these plots allows for clear classification based on their linearity.
• Discuss how understanding integrated rate laws aids in real-world applications such as drug metabolism and environmental science.
  • Understanding integrated rate laws is crucial in fields like drug metabolism and environmental science because it allows scientists to predict how substances break down over time. For instance, in pharmacology, knowing how quickly a drug's concentration decreases helps in determining dosing schedules for optimal therapeutic effects. In environmental science, integrated rate laws can help model how pollutants degrade in ecosystems, guiding cleanup efforts and regulations. This knowledge ultimately impacts health and ecological policies.

Related terms

Differential Rate Law:

An equation that relates the rate of a reaction to the concentration of its reactants, showing how the reaction rate changes as concentrations change.

Reaction Order:

The exponent that indicates the dependency of the reaction rate on the concentration of a particular reactant, which helps classify reactions as zero-order, first-order, or second-order.

Half-life:

The time required for the concentration of a reactant to decrease to half of its initial value, which can vary based on the order of the reaction.