First-Order Kinetics

Definition

First-order kinetics is a type of reaction rate that describes the relationship between the concentration of reactants and the rate of the chemical reaction. In a first-order reaction, the rate of the reaction is directly proportional to the concentration of a single reactant.

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 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.
3. The rate constant, $k$, is a measure of the intrinsic reactivity of the reactants and is independent of the concentration of the reactants.
4. The half-life of a first-order reaction is constant and is given by the equation $t_{1/2} = \frac{\ln 2}{k}$, where $k$ is the rate constant.
5. First-order kinetics are commonly observed in chemical reactions involving the decomposition or radioactive decay of a single reactant.

Review Questions

• Explain the relationship between the rate of a first-order reaction and the concentration of the reactant.
  • 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 linearly. 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 allows for the prediction of reaction rates based on the concentration of the reactant, which is a crucial consideration in the context of the SN1 reaction mechanism.
• Describe the significance of the rate constant, $k$, in the context of first-order kinetics.
  • The rate constant, $k$, is a measure of the intrinsic reactivity of the reactants in a first-order reaction. It is independent of the concentration of the reactants and represents the inherent speed at which the reaction occurs. The rate constant is an important parameter in the study of reaction kinetics, as it allows for the comparison of reaction rates between different systems and the prediction of reaction progress over time. In the context of the SN1 reaction mechanism, the rate constant is a key factor in determining the overall rate of the reaction and the likelihood of the formation of the desired product.
• Analyze the relationship between the half-life of a first-order reaction and the rate constant.
  • The half-life of a first-order reaction, denoted as $t_{1/2}$, is the time it takes for the concentration of a reactant to decrease to half of its initial value. The relationship between the half-life and the rate constant, $k$, is given by the equation $t_{1/2} = \frac{\ln 2}{k}$. This equation demonstrates that the half-life of a first-order reaction is inversely proportional to the rate constant. A larger rate constant corresponds to a shorter half-life, indicating a faster reaction, while a smaller rate constant corresponds to a longer half-life and a slower reaction. Understanding this relationship is crucial in the context of the SN1 reaction mechanism, as it allows for the prediction of the rate at which the reaction will proceed and the likelihood of the desired product being formed.

Related terms

Reaction Rate: The change in the concentration of reactants or products over time, which determines the speed of a chemical reaction.

Rate Law:

An equation that describes the relationship between the rate of a reaction and the concentrations of the reactants.

Half-Life: The time it takes for the concentration of a reactant to decrease to half of its initial value in a first-order reaction.