key term - [A]t

Definition

[A]t is a key term in the context of Integrated Rate Laws, which describe the relationship between the concentration of reactants and the time elapsed during a chemical reaction. This term is crucial in understanding how the concentration of a reactant changes over time under different reaction conditions.

5 Must Know Facts For Your Next Test

1. The [A]t term in the integrated rate law represents the concentration of the reactant A at a specific time t during the reaction.
2. The integrated rate law equation allows you to determine the concentration of a reactant at any given time, provided you know the initial concentration and the rate constant of the reaction.
3. The form of the integrated rate law equation varies depending on the reaction order, with different equations for zero-order, first-order, and second-order reactions.
4. The [A]t term is essential for calculating the half-life of a reaction, which is the time it takes for the concentration of a reactant to decrease by half.
5. Understanding the [A]t term and its relationship to the integrated rate law is crucial for predicting the progress of a reaction and determining the optimal conditions for a desired outcome.

Review Questions

• Explain the significance of the [A]t term in the integrated rate law equation.
  • The [A]t term in the integrated rate law equation represents the concentration of the reactant A at a specific time t during the reaction. This term is crucial because it allows you to determine the concentration of the reactant at any given point in time, which is essential for understanding the progress and kinetics of the reaction. The [A]t term is used in the integrated rate law equation to relate the initial concentration of the reactant, the rate constant, and the elapsed time to the concentration of the reactant at that specific time.
• Describe how the form of the integrated rate law equation changes depending on the reaction order.
  • The form of the integrated rate law equation varies depending on the reaction order, which is the exponent to which the concentration of a reactant is raised in the rate law expression. For a zero-order reaction, the integrated rate law equation is [A]t = [A]0 - kt, where [A]0 is the initial concentration and k is the rate constant. For a first-order reaction, the integrated rate law equation is ln([A]t) = ln([A]0) - kt. For a second-order reaction, the integrated rate law equation is 1/[A]t = 1/[A]0 + kt. Understanding how the [A]t term is expressed in these different integrated rate law equations is crucial for analyzing and predicting the kinetics of chemical reactions.
• Explain the relationship between the [A]t term and the half-life of a reaction.
  • The [A]t term in the integrated rate law equation is closely related to the half-life of a reaction, which is the time it takes for the concentration of a reactant to decrease by half. For a first-order reaction, the half-life is independent of the initial concentration and is given by the equation t1/2 = ln(2)/k, where k is the rate constant. By rearranging the first-order integrated rate law equation, you can show that when t = t1/2, the [A]t term is equal to [A]0/2, meaning the concentration of the reactant has decreased by half. Understanding this relationship between the [A]t term and the half-life of a reaction is essential for predicting the progress and outcome of chemical processes.

Related terms

Integrated Rate Law:

The integrated rate law is an equation that describes the change in the concentration of a reactant over time for a given reaction order.

Reaction Order:

The reaction order is the exponent to which the concentration of a reactant is raised in the rate law expression.

Reaction Rate:

The reaction rate is the change in the concentration of a reactant or product per unit of time.