First-order

Definition

First-order refers to a type of chemical reaction in which the rate is directly proportional to the concentration of one reactant. In these reactions, as the concentration of that reactant decreases, the rate of reaction also decreases linearly. This relationship is crucial for understanding how different factors affect reaction rates and is foundational in the study of reaction mechanisms.

5 Must Know Facts For Your Next Test

1. In a first-order reaction, the rate constant (k) has units of time^-1, indicating that it is dependent on time rather than concentration.
2. The integrated rate law for a first-order reaction can be expressed as $$ ext{ln} rac{[A_0]}{[A]} = kt $$, where [A_0] is the initial concentration and [A] is the concentration at time t.
3. Graphically, plotting $$ ext{ln} [A] $$ versus time yields a straight line with a slope of -k, confirming first-order kinetics.
4. First-order reactions are commonly observed in processes like radioactive decay and certain enzyme-catalyzed reactions.
5. For first-order reactions, the half-life is independent of the initial concentration and is given by the equation $$ t_{1/2} = rac{0.693}{k} $$.

Review Questions

• How does the rate law express the relationship between concentration and reaction rate in first-order reactions?
  • In first-order reactions, the rate law shows that the reaction rate is directly proportional to the concentration of one reactant. This means that if you double the concentration of that reactant, the rate of reaction will also double. The mathematical representation typically takes the form Rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.
• Explain how the concept of half-life applies to first-order reactions and why it remains constant over varying initial concentrations.
  • In first-order reactions, half-life is a unique feature because it remains constant regardless of the initial concentration of reactants. This means that no matter how much reactant you start with, it takes the same amount of time for half of it to be consumed. The half-life formula $$ t_{1/2} = rac{0.693}{k} $$ illustrates that this time only depends on the rate constant k, making it a defining characteristic of first-order kinetics.
• Analyze how understanding first-order kinetics influences experimental design and interpretation in biophysical chemistry.
  • Understanding first-order kinetics is vital for designing experiments in biophysical chemistry because it informs how to set up reaction conditions and interpret results. For instance, knowing that concentration impacts rate linearly allows researchers to predict how changing reactant levels affects overall kinetics. Additionally, this knowledge helps in analyzing data accurately; when plotting ln[A] against time yields a straight line, it confirms a first-order process, guiding further investigations into reaction mechanisms or related systems.

Related terms

Rate Law: An equation that relates the reaction rate to the concentration of reactants, revealing the order of the reaction with respect to each reactant.

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

Integrated Rate Equation: An equation that provides a mathematical description of how concentration changes over time for different orders of reactions, including first-order.