Integrated Rate Law

Definition

The integrated rate law is a mathematical expression that describes the relationship between the concentration of a reactant and the time elapsed during a chemical reaction. It allows for the determination of the order of a reaction and the rate constant, providing a quantitative understanding of the reaction kinetics.

5 Must Know Facts For Your Next Test

1. The integrated rate law is derived from the differential rate law, which describes the instantaneous rate of a reaction.
2. The integrated rate law can be used to determine the order of a reaction and the rate constant by analyzing the relationship between the reactant concentration and time.
3. For a zero-order reaction, the integrated rate law is a linear function of time, with the concentration of the reactant decreasing linearly with time.
4. For a first-order reaction, the integrated rate law is an exponential function of time, with the concentration of the reactant decreasing exponentially with time.
5. For a second-order reaction, the integrated rate law is a hyperbolic function of time, with the concentration of the reactant decreasing more rapidly than in a first-order reaction.

Review Questions

• Explain how the integrated rate law is derived from the differential rate law and the significance of this relationship.
  • The integrated rate law is derived by integrating the differential rate law, which describes the instantaneous rate of a reaction. This relationship is significant because the integrated rate law provides a quantitative description of how the concentration of a reactant changes over time, allowing for the determination of the reaction order and the rate constant. By analyzing the mathematical form of the integrated rate law, researchers can gain insights into the underlying mechanisms and kinetics of the chemical reaction.
• Describe the differences in the mathematical forms of the integrated rate law for zero-order, first-order, and second-order reactions, and explain how these differences reflect the underlying reaction kinetics.
  • The integrated rate law for a zero-order reaction is a linear function of time, indicating that the concentration of the reactant decreases at a constant rate. For a first-order reaction, the integrated rate law is an exponential function of time, reflecting the fact that the rate of the reaction is proportional to the concentration of the reactant. In the case of a second-order reaction, the integrated rate law is a hyperbolic function of time, suggesting that the rate of the reaction is proportional to the square of the reactant concentration. These differences in the mathematical forms of the integrated rate law provide valuable insights into the underlying reaction kinetics and the order of the reaction.
• Discuss how the integrated rate law can be used to determine the order of a reaction and the rate constant, and explain the significance of these parameters in understanding the reaction mechanism.
  • The integrated rate law can be used to determine the order of a reaction and the rate constant by analyzing the relationship between the concentration of the reactant and the elapsed time. The order of the reaction is indicated by the mathematical form of the integrated rate law, as described in the previous question. The rate constant, on the other hand, is a proportionality factor that represents the intrinsic reactivity of the chemical system. By determining the order of the reaction and the rate constant, researchers can gain insights into the underlying reaction mechanism, including the frequency of successful collisions between reactant molecules and the factors that influence the rate of the reaction. These parameters are crucial for understanding the kinetics and dynamics of chemical processes, which is essential for the optimization of chemical reactions and the development of new materials and technologies.

Related terms

Reaction Order:

The exponent to which the concentration of a reactant is raised in the rate law expression, indicating the dependence of the reaction rate on the concentration of that reactant.

Rate Constant:

A proportionality constant that represents the intrinsic reactivity of a chemical system, indicating the frequency of successful collisions between reactant molecules.

Reaction Kinetics:

The study of the rates of chemical reactions and the factors that influence them, including the mechanisms by which the reactions occur.