💏intro to chemistry review

key term - First-Order Reaction

Definition

A first-order reaction is a chemical reaction where the rate of the reaction is directly proportional to the concentration of a single reactant. The reaction rate is independent of the concentrations of other reactants or products involved in the reaction.

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 a single reactant.
  2. The rate of a first-order reaction is independent of the concentrations of other reactants or products involved in the reaction.
  3. The rate law for a first-order reaction is $\text{rate} = k[A]$, where $k$ is the rate constant and $[A]$ is the concentration of the reactant.
  4. The half-life of a first-order reaction is constant and independent of the initial concentration of the reactant.
  5. The integrated rate law for a first-order reaction is $\ln[A] = \ln[A]_0 - kt$, where $[A]_0$ is the initial concentration of the reactant and $t$ is the reaction time.

Review Questions

  • Explain the relationship between the reaction rate and the concentration of a single reactant in a first-order reaction.
    • In a first-order reaction, the rate of the reaction is directly proportional to the concentration of a single reactant. This means that as the concentration of the reactant increases, the rate of the reaction also increases proportionally. The rate law for a first-order reaction is expressed as $\text{rate} = k[A]$, where $k$ is the rate constant and $[A]$ is the concentration of the reactant. This relationship indicates that the reaction rate depends only on the concentration of the reactant and not on the concentrations of any other reactants or products involved in the reaction.
  • Describe the integrated rate law for a first-order reaction and explain how it can be used to determine the reaction rate constant.
    • The integrated rate law for a first-order reaction is $\ln[A] = \ln[A]_0 - kt$, where $[A]_0$ is the initial concentration of the reactant, $[A]$ is the concentration of the reactant at time $t$, and $k$ is the rate constant. This equation shows that the natural logarithm of the reactant concentration decreases linearly with time. By plotting $\ln[A]$ against $t$, the slope of the resulting straight line will be $-k$, allowing the rate constant $k$ to be determined from the experimental data. This integrated rate law is useful for analyzing the kinetics of first-order reactions and calculating the rate constant, which is a fundamental parameter in understanding the reaction mechanism.
  • Discuss how the half-life of a first-order reaction is related to the rate constant and explain the significance of this relationship.
    • The half-life of a first-order reaction, denoted as $t_{1/2}$, is the time required for the concentration of the reactant to decrease to half of its initial value. For a first-order reaction, the half-life is constant and independent of the initial concentration of the reactant. The relationship between the half-life and the rate constant is given by the equation $t_{1/2} = \frac{\ln 2}{k}$, where $k$ is the rate constant. This relationship is significant because it allows the rate constant to be determined from the measured half-life of the reaction, which is often easier to obtain experimentally. Additionally, the half-life provides a practical way to describe the kinetics of a first-order reaction and is useful for predicting the time required for a certain fraction of the reactant to be consumed.