Rearrange the integrated rate equations for (a) a...

Rearrange the integrated rate equations for (a) a first-order reaction, (b) a second-order reaction, and (c) a zero-order reaction to calculate $[A]_{t}$. Use the symbol $[A]_{0}$ to represent the initial concentration if needed.

Key Concepts

First-Order Reaction

A first-order reaction has a rate proportional to the concentration of a single reactant. Its integrated rate law is characterized by an exponential decay of reactant concentration over time, often written in the logarithmic form as ln[A]t = ln[A]0 - k·t, which can be rearranged to solve for [A]t.

Zero-Order Reaction

In a zero-order reaction, the rate of the reaction is independent of the concentration of the reactant. The integrated rate law shows that the concentration decreases linearly with time, typically expressed as [A]t = [A]0 - k·t, where k is the rate constant.

Second-Order Reaction

For a second-order reaction, the rate depends either on the square of the concentration of one reactant or on the product of the concentrations of two different reactants. The integrated rate law typically takes the form 1/[A]t = 1/[A]0 + k·t, indicating that the inverse of the concentration increases linearly with time.

Integrated Rate Law

The integrated rate law is a fundamental equation in chemical kinetics that relates the concentration of reactants to time by integrating the differential rate law. It provides a way to predict how the concentration of a reactant or product changes as the reaction proceeds, depending on the reaction order.

Reaction Order

The reaction order indicates how the rate of a chemical reaction depends on the concentration of the reactants. It is defined by the exponents in the rate law and determines the mathematical form of the integrated rate equation, which varies for zero-, first-, and second-order kinetics.

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