1/[a] = kt + 1/[a]0

Definition

This equation represents the integrated rate law for a second-order reaction, where the concentration of a reactant is inversely related to time. It shows how the concentration of a reactant decreases as the reaction progresses, emphasizing the relationship between concentration and reaction rate. This law is essential for understanding how reactants behave over time in chemical kinetics.

5 Must Know Facts For Your Next Test

1. The integrated rate law applies specifically to reactions where two reactant molecules collide, making it second order with respect to one reactant.
2. In this equation, [a] represents the concentration of the reactant at time t, and [a]0 is the initial concentration before the reaction begins.
3. The term kt represents how much the concentration has changed over time due to the reaction, illustrating that as time increases, 1/[a] will increase if the reaction is proceeding.
4. This equation can be rearranged to find either time or concentration if two of the three variables (k, [a], [a]0) are known.
5. Understanding this equation helps predict how quickly a reaction will go to completion based on its initial conditions and rate constant.

Review Questions

• How does the integrated rate law for second-order reactions inform us about the relationship between concentration and time?
  • The integrated rate law for second-order reactions, expressed as 1/[a] = kt + 1/[a]0, reveals that as time progresses, the inverse of the concentration increases. This means that as a reactant is consumed during a reaction, its concentration decreases in such a way that one can calculate how long it takes to reach a certain concentration. This relationship emphasizes how important initial concentrations are in determining the speed at which a reaction occurs.
• In what ways can you manipulate the integrated rate law equation to find unknown variables, and why is this useful in chemical kinetics?
  • The equation 1/[a] = kt + 1/[a]0 can be rearranged to solve for any variable if two are known. For instance, if you know k and [a]0, you can calculate how long it will take to reach a specific concentration [a]. This manipulation allows chemists to predict reaction behavior under different conditions, making it a valuable tool in chemical kinetics for designing experiments or understanding processes.
• Evaluate how knowing the integrated rate law for second-order reactions could impact real-world applications like pharmaceuticals or environmental science.
  • Understanding the integrated rate law for second-order reactions has significant implications in fields like pharmaceuticals and environmental science. In pharmaceuticals, it allows scientists to determine how quickly drugs will be metabolized in the body based on their concentrations. In environmental science, it aids in predicting how pollutants degrade over time when interacting with other substances. By accurately modeling these reactions with this law, better strategies can be devised for drug administration or pollution control.

Related terms

Rate Constant (k): A proportionality constant that links the reaction rate to the concentration of reactants, unique to each reaction and dependent on temperature.

Half-life: The time required for the concentration of a reactant to decrease by half, which for second-order reactions is dependent on the initial concentration.

Order of Reaction: The exponent that indicates the relationship between the rate of a reaction and the concentration of its reactants, determining how changes in concentration affect the reaction rate.