First-order reaction

Definition

A first-order reaction is a type of chemical reaction where the rate of reaction is directly proportional to the concentration of one reactant. This means that if the concentration of that reactant doubles, the rate of reaction also doubles. The relationship between concentration and rate in first-order reactions leads to a specific mathematical representation and plays a crucial role in understanding reaction mechanisms.

5 Must Know Facts For Your Next Test

1. In a first-order reaction, the rate can be expressed with the equation: Rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.
2. Graphing the natural logarithm of the concentration of the reactant versus time yields a straight line, with a slope equal to -k, indicating first-order behavior.
3. For first-order reactions, the half-life does not depend on the initial concentration; it remains constant and is given by t(1/2) = 0.693/k.
4. First-order reactions are common in processes such as radioactive decay and certain enzyme-catalyzed reactions, making them important in both chemistry and biochemistry.
5. The units of the rate constant (k) for a first-order reaction are typically expressed in s^-1, indicating that the reaction rate depends on time.

Review Questions

• How does changing the concentration of a reactant affect the rate of a first-order reaction?
  • In a first-order reaction, increasing the concentration of the reactant directly increases the rate of the reaction in a linear manner. This means if you double the concentration, you double the rate. The relationship can be described mathematically as Rate = k[A], where 'k' is the rate constant and '[A]' is the concentration. This direct proportionality makes first-order reactions distinct from other orders, where rates may change differently based on concentration changes.
• Describe how you can determine whether a reaction is first order using experimental data.
  • To determine if a reaction is first order, you can analyze experimental data by plotting the natural logarithm of reactant concentration versus time. If this plot results in a straight line, it indicates that the reaction follows first-order kinetics. The slope of this line will give you -k, allowing you to calculate the rate constant. Additionally, observing that the half-life remains constant across different initial concentrations supports this classification as first-order.
• Evaluate the significance of understanding first-order reactions in real-world applications such as pharmacokinetics or environmental chemistry.
  • Understanding first-order reactions is crucial in fields like pharmacokinetics, where drug concentrations in the bloodstream often follow first-order kinetics during elimination processes. This knowledge helps in determining appropriate dosages and understanding how long drugs remain effective in patients. Similarly, in environmental chemistry, pollutant degradation often follows first-order kinetics; knowing this helps predict how quickly substances will break down in ecosystems. Mastering these concepts enables scientists to make informed decisions regarding health and environmental management.

Related terms

Rate constant:

A proportionality factor in the rate equation that is specific to each reaction at a given temperature, reflecting the speed of the reaction.

Half-life: The time required for half of the reactant to be consumed in a reaction, which remains constant for first-order reactions regardless of the initial concentration.

Integrated rate law: A mathematical expression that relates the concentration of a reactant to time, providing a way to analyze the kinetics of a reaction.