First-order kinetics

Definition

First-order kinetics refers to a reaction rate that is directly proportional to the concentration of a single reactant. In this type of reaction, as the concentration of the reactant decreases, the rate of reaction also decreases, which can be represented mathematically by the equation: $$rac{d[A]}{dt} = -k[A]$$ where $[A]$ is the concentration and $k$ is the rate constant. This relationship indicates that half-lives of reactants remain constant regardless of their initial concentration.

5 Must Know Facts For Your Next Test

1. First-order kinetics implies that the reaction rate depends only on one reactant's concentration and not on others.
2. In first-order reactions, the integrated rate law can be expressed as: $$ln[A] = -kt + ln[A_0]$$, where $[A_0]$ is the initial concentration.
3. The half-life of a first-order reaction is independent of the initial concentration, making it unique among kinetic orders.
4. First-order kinetics is often observed in radioactive decay processes and many biological reactions, such as enzyme catalysis.
5. Graphically, a plot of ln[A] versus time results in a straight line for first-order reactions, allowing for easy determination of the rate constant.

Review Questions

• How does the rate of a first-order reaction change with varying concentrations of reactants?
  • In first-order reactions, the rate is directly proportional to the concentration of just one reactant. As this reactant's concentration decreases over time, the reaction rate also declines accordingly. This means that if you were to measure the rate at different concentrations, you'd find that as the amount of reactant reduces, the speed at which it reacts becomes slower.
• Discuss how you would determine whether a reaction follows first-order kinetics using experimental data.
  • To determine if a reaction exhibits first-order kinetics, you would collect concentration data at various times during the reaction. By plotting ln[A] against time and analyzing whether it produces a straight line, you can confirm first-order behavior. The slope of this line will give you the negative value of the rate constant, $-k$, allowing you to quantitatively describe the reaction's kinetics.
• Evaluate the significance of half-lives in understanding first-order kinetics and compare it to zero-order kinetics.
  • Half-lives are crucial in first-order kinetics because they remain constant regardless of initial concentration, making them predictable and useful in applications like pharmacokinetics. In contrast, zero-order reactions have half-lives that vary depending on initial concentrations. This distinction helps chemists predict how substances will behave over time under different conditions, enhancing our understanding of reaction dynamics and aiding in practical applications such as drug dosage management.

Related terms

Rate Constant: A specific constant that relates the rate of a reaction to the concentrations of the reactants, indicating how fast a reaction proceeds.

Half-life:

The time required for half of a given reactant to be consumed in a reaction, which remains constant for first-order reactions.

Reaction Mechanism: The step-by-step sequence of elementary reactions by which overall chemical change occurs, influencing the order of kinetics.