key term - First-order reaction

Definition

A first-order reaction is a type of chemical reaction where the rate of the reaction is directly proportional to the concentration of one reactant. This means that if you double the concentration of that reactant, the rate will also double. Understanding first-order reactions is crucial for analyzing rate laws and determining how the concentration of reactants affects the speed of a reaction.

5 Must Know Facts For Your Next Test

1. In a first-order reaction, the unit of the rate constant (k) is typically s^-1, indicating that the rate is dependent on time.
2. The integrated rate law for a first-order reaction can be expressed as $$ ext{ln}([A]_t/[A]_0) = -kt$$, where $$[A]_t$$ is the concentration at time t and $$[A]_0$$ is the initial concentration.
3. The half-life of a first-order reaction remains constant regardless of initial concentration, making it easy to predict how long it takes for a substance to reduce its concentration by half.
4. Graphing the natural logarithm of the concentration of a reactant against time results in a straight line with a slope of -k for first-order reactions.
5. First-order reactions are common in processes like radioactive decay and certain enzymatic reactions, illustrating their wide-ranging significance in both chemistry and biology.

Review Questions

• How does changing the concentration of a reactant affect the rate of a first-order reaction?
  • In a first-order reaction, changing the concentration of one reactant has a direct effect on the rate. Specifically, if the concentration is doubled, the rate of the reaction also doubles. This proportional relationship is key to understanding how these reactions behave and allows chemists to predict changes in reaction rates based on varying concentrations.
• Describe how you would derive the integrated rate law for a first-order reaction and what information it provides about reactant concentrations over time.
  • To derive the integrated rate law for a first-order reaction, you start with the differential rate law, which states that the rate equals k times the concentration raised to the first power. By separating variables and integrating, you arrive at $$ ext{ln}([A]_t/[A]_0) = -kt$$. This equation shows how reactant concentrations decrease exponentially over time and allows predictions about remaining concentrations at any given time.
• Evaluate the significance of half-life in first-order reactions and how it impacts real-world applications such as drug metabolism.
  • The half-life in first-order reactions is significant because it remains constant regardless of initial concentration, making it easier to predict how quickly a substance will diminish over time. In real-world applications like drug metabolism, knowing the half-life helps healthcare providers determine dosing schedules and understand how long it takes for a drug's effects to wear off or for it to be eliminated from the body. This knowledge is critical for effective patient care and medication management.

Related terms

Rate Constant:

A constant that links the reaction rate to the concentration of reactants in a rate law expression, specific to a particular reaction at a given temperature.

Integrated Rate Law:

An equation that relates the concentration of reactants to time for a specific order of reaction, providing insight into how concentrations change as the reaction proceeds.

Half-life:

The time required for the concentration of a reactant in a first-order reaction to decrease by half, which is constant and independent of initial concentration.