T1/2

Definition

t1/2, or half-life, is the time it takes for the concentration or amount of a substance to decrease to half of its initial value. It is a fundamental concept in the study of chemical kinetics and is particularly relevant in the context of 12.4 Integrated Rate Laws.

5 Must Know Facts For Your Next Test

1. The half-life of a reaction is independent of the initial concentration of the reactants, and it is a characteristic property of the reaction.
2. The half-life of a first-order reaction is related to the rate constant (k) by the equation: $t_{1/2} = \frac{\ln 2}{k}$.
3. For a first-order reaction, the concentration of the reactant decreases exponentially over time, and the half-life remains constant throughout the reaction.
4. In a pseudo-first-order reaction, the half-life is still related to the rate constant, but the rate constant is dependent on the concentration of the reactant that is kept constant.
5. The half-life of a reaction can be used to determine the time required for a certain percentage of the reactant to be consumed or a product to be formed.

Review Questions

• Explain how the half-life of a reaction is related to the rate constant for a first-order reaction.
  • For a first-order reaction, the half-life (t1/2) is inversely proportional to the rate constant (k). Specifically, the relationship is given by the equation: $t_{1/2} = \frac{\ln 2}{k}$. This means that as the rate constant increases, the half-life decreases, and vice versa. The half-life is a characteristic property of the reaction and is independent of the initial concentration of the reactants. This relationship allows for the prediction of how the concentration of a reactant will change over time in a first-order reaction, which is a key concept in the study of 12.4 Integrated Rate Laws.
• Describe the differences in how half-life is determined for a first-order reaction versus a pseudo-first-order reaction.
  • For a first-order reaction, the half-life is solely determined by the rate constant (k) of the reaction, as given by the equation $t_{1/2} = \frac{\ln 2}{k}$. In a pseudo-first-order reaction, however, the half-life is still related to the rate constant, but the rate constant itself is dependent on the concentration of the reactant that is kept constant. This means that the half-life of a pseudo-first-order reaction can change over the course of the reaction, unlike a true first-order reaction where the half-life remains constant. Understanding these differences is crucial when applying the concepts of 12.4 Integrated Rate Laws to different reaction types.
• Explain how the half-life of a reaction can be used to determine the time required for a certain percentage of the reactant to be consumed or a product to be formed.
  • The half-life of a reaction can be used to predict the time required for a specific fraction of the reactant to be consumed or a product to be formed. For example, if the half-life of a reaction is 10 minutes, then after 10 minutes, 50% of the reactant will have been consumed. After 20 minutes (two half-lives), 75% of the reactant will have been consumed, and after 30 minutes (three half-lives), 87.5% of the reactant will have been consumed. This exponential relationship between time and the fraction of reactant remaining is a key concept in the study of 12.4 Integrated Rate Laws and allows for the prediction of reaction progress over time.

Related terms

Integrated Rate Law: The integrated rate law describes the relationship between the concentration of a reactant and time, allowing the prediction of how the concentration changes over time.

First-Order Reaction: A first-order reaction is a reaction where the rate of the reaction is proportional to the concentration of a single reactant.

Pseudo-First-Order Reaction: A pseudo-first-order reaction is a reaction where the concentration of one or more reactants is kept constant, effectively making the reaction behave as a first-order reaction.