First-Order

Definition

First-order is a kinetic term that describes a reaction where the rate of the reaction is directly proportional to the concentration of a single reactant. In other words, the rate of the reaction only depends on the concentration of one of the reactants.

5 Must Know Facts For Your Next Test

1. In a first-order reaction, the rate of the reaction is directly proportional to the concentration of the reactant, meaning the rate doubles when the concentration doubles.
2. The rate law for a first-order reaction has the form rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.
3. The half-life of a first-order reaction is constant and independent of the initial concentration of the reactant.
4. First-order kinetics are commonly observed in many chemical and biological processes, such as radioactive decay, enzyme-catalyzed reactions, and the decomposition of certain drugs.
5. The integrated rate law for a first-order reaction is ln[A] = -kt + ln[A]₀, where [A]₀ is the initial concentration of the reactant.

Review Questions

• Explain how the rate of a first-order reaction is related to the concentration of the reactant.
  • In a first-order reaction, the rate of the reaction is directly proportional to the concentration of the reactant. This means that if the concentration of the reactant is doubled, the rate of the reaction will also double. The rate law for a first-order reaction has the form rate = k[A], where k is the rate constant and [A] is the concentration of the reactant. This linear relationship between the rate and the concentration of the reactant is a defining characteristic of first-order kinetics.
• Describe the significance of the half-life in the context of a first-order reaction.
  • The half-life of a first-order reaction is the time it takes for the concentration of the reactant to decrease to half of its initial value. The half-life is inversely proportional to the rate constant, k, of the reaction. This means that the larger the rate constant, the shorter the half-life. The half-life is an important parameter in first-order reactions because it allows for the determination of the rate constant and the prediction of how the concentration of the reactant will change over time, which is crucial in many chemical and biological processes.
• Analyze how the integrated rate law for a first-order reaction can be used to determine the rate constant and the initial concentration of the reactant.
  • The integrated rate law for a first-order reaction is ln[A] = -kt + ln[A]₀, where [A] is the concentration of the reactant at time t, [A]₀ is the initial concentration of the reactant, and k is the rate constant. By rearranging this equation, one can determine the rate constant, k, from the slope of a plot of ln[A] versus t. Additionally, the initial concentration of the reactant, [A]₀, can be determined from the y-intercept of the same plot. This analysis allows for the extraction of crucial kinetic information about a first-order reaction, which is essential for understanding the underlying mechanisms and predicting the progress of the reaction over time.

Related terms

Reaction Order: The reaction order is the exponent to which the concentration of a reactant is raised in the rate law expression. A first-order reaction has a reaction order of 1 with respect to a particular reactant.

Rate Law: The rate law is an equation that expresses the relationship between the reaction rate and the concentrations of the reactants. For a first-order reaction, the rate law has the form rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Half-Life: The half-life of a first-order reaction is the time it takes for the concentration of the reactant to decrease to half of its initial value. The half-life is inversely proportional to the rate constant, allowing the rate constant to be determined from the half-life.