A first-order reaction is a type of chemical reaction in which the rate of reaction is directly proportional to the concentration of one reactant. This means that if the concentration of that reactant increases, the reaction rate increases as well. The integrated rate law for a first-order reaction allows us to express the concentration of the reactant as a function of time, which is essential for understanding how quickly a reaction proceeds.
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For a first-order reaction, the integrated rate law can be expressed as $$ ext{ln}[ ext{A}] = -kt + ext{ln}[ ext{A}_0]$$, where [A] is the concentration at time t, k is the rate constant, and [A₀] is the initial concentration.
The units of the rate constant (k) for first-order reactions are typically s⁻¹ (inverse seconds), indicating how the concentration changes over time.
The half-life of a first-order reaction is given by $$t_{1/2} = rac{0.693}{k}$$, showing that it does not depend on initial concentration, making it unique compared to other reaction orders.
Graphing a first-order reaction results in a straight line when plotting ln[A] versus time, indicating its linear relationship with time.
Common examples of first-order reactions include radioactive decay and certain enzyme-catalyzed reactions, demonstrating how these principles apply in real-world scenarios.
Review Questions
How does the rate of a first-order reaction change with varying concentrations of the reactant?
In a first-order reaction, the rate is directly proportional to the concentration of one reactant. This means that if you increase the concentration of that reactant, the rate of the reaction will also increase proportionally. This relationship is crucial for predicting how quickly a reaction will occur based on changes in reactant concentration.
Discuss how you can determine if a reaction is first-order using experimental data.
To determine if a reaction is first-order, you can conduct experiments to measure the concentration of reactants over time. By plotting ln[A] versus time and observing if you obtain a straight line, you can confirm that it follows first-order kinetics. Additionally, analyzing the half-life values can further support this classification, as they should remain constant regardless of initial concentration.
Evaluate the implications of half-life being constant for first-order reactions in practical applications like pharmacokinetics.
The constant half-life for first-order reactions has significant implications in fields like pharmacokinetics, where it simplifies dosage calculations and predictions about drug levels in the bloodstream over time. Since each half-life reduces drug concentration by half regardless of starting amount, it allows healthcare providers to estimate how long it takes for drugs to reach therapeutic levels or be eliminated from the body efficiently. This predictable behavior aids in developing treatment plans and understanding drug interactions.
A proportionality constant in the rate equation that relates the rate of a reaction to the concentrations of the reactants, specific to each reaction at a given temperature.
Half-Life: The time required for the concentration of a reactant to decrease to half of its initial value, which is constant for first-order reactions and independent of initial concentration.
Second-Order Reaction: A chemical reaction where the rate is proportional to the square of the concentration of one reactant or to the product of the concentrations of two different reactants.