The equation $$[a]t = [a]0 - kt$$ describes the concentration of a reactant at any given time during a zero-order reaction. In this context, $$[a]0$$ represents the initial concentration of the reactant, $$k$$ is the zero-order rate constant, and $$t$$ is the time elapsed since the reaction began. This linear relationship indicates that the concentration of the reactant decreases uniformly over time, which is a fundamental characteristic of zero-order kinetics.
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In a zero-order reaction, the rate of formation of products is constant, regardless of the concentration of reactants.
The units of the rate constant $$k$$ in a zero-order reaction are typically mol/L·s.
As time progresses, the concentration of the reactant decreases linearly until it reaches zero, assuming sufficient initial concentration.
This equation can be rearranged to determine the time it takes for a certain concentration to be reached by solving for $$t$$.
The plot of $$[a]t$$ versus time (t) yields a straight line with a slope of -k, confirming its zero-order behavior.
Review Questions
How does the equation $$[a]t = [a]0 - kt$$ illustrate the behavior of concentrations in a zero-order reaction?
The equation $$[a]t = [a]0 - kt$$ shows that in a zero-order reaction, the concentration of the reactant decreases at a constant rate over time. This means that no matter how much reactant is present initially, its concentration will drop linearly until it runs out. The constant rate is indicated by the term $$k$$, which remains unchanged regardless of the remaining concentration, illustrating that zero-order kinetics is dependent solely on time.
In what ways can you use the integrated rate law for zero-order reactions to calculate reaction times or concentrations?
You can manipulate the integrated rate law $$[a]t = [a]0 - kt$$ to find either time or concentration by rearranging it based on what you need. For example, if you know the initial concentration $$[a]0$$ and want to find out how long it takes for the concentration to drop to a specific value $$[a]t$$, you can rearrange it to solve for $$t$$. Additionally, if you want to find out how much reactant remains after a certain time period, you can plug in your values directly into the equation.
Evaluate how understanding the equation $$[a]t = [a]0 - kt$$ aids in predicting reaction outcomes in real-world applications.
Understanding this equation enables chemists and engineers to predict how long a reactant will last under specific conditions and what concentrations will be achieved over time. For instance, in pharmaceutical applications, knowing how quickly a drug's active ingredient depletes helps in determining dosing schedules and ensuring therapeutic effectiveness. Moreover, in industrial processes where reactions are monitored continuously, this knowledge allows for optimizing conditions to maintain desired reactant levels and improve yield.
Related terms
Zero-Order Reaction: A reaction where the rate of reaction is constant and independent of the concentration of reactants.
Rate Constant (k): A proportionality factor in rate equations that is unique to each chemical reaction at a given temperature.
Integrated Rate Law: An equation that expresses the concentration of reactants or products as a function of time.