Consider the following concentration–time data for the decomposition reaction AB → A + B.
(a) Determine the order of the reaction and the value of the rate constant.

Verified step by step guidance

1. Step 1: Understand the problem. We need to determine the order of the reaction and the rate constant for the decomposition reaction AB → A + B using concentration-time data.
2. Step 2: Analyze the concentration-time data. Look for patterns that indicate whether the reaction is zero-order, first-order, or second-order.
3. Step 3: For zero-order reactions, the concentration of the reactant decreases linearly with time. For first-order reactions, the natural logarithm of the concentration decreases linearly with time. For second-order reactions, the inverse of the concentration decreases linearly with time.
4. Step 4: Plot the appropriate graphs: concentration vs. time for zero-order, ln(concentration) vs. time for first-order, and 1/concentration vs. time for second-order. Determine which plot gives a straight line.
5. Step 5: Once the order is determined, use the slope of the straight-line plot to calculate the rate constant (k). For zero-order, k = -slope; for first-order, k = -slope; for second-order, k = slope.

Key Concepts

Reaction Order

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction depends on the concentration of reactants. For example, a first-order reaction has a rate that is directly proportional to the concentration of one reactant, while a second-order reaction depends on the square of the concentration. Understanding the order helps in predicting how changes in concentration affect the reaction rate.

Rate Constant (k)

The rate constant, denoted as 'k', is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. Its value is specific to a given reaction at a particular temperature and is influenced by factors such as temperature and the presence of catalysts. The rate constant is crucial for calculating the rate of reaction and understanding the kinetics of the process.

Integrated Rate Laws

Integrated rate laws are mathematical expressions that relate the concentration of reactants to time for different orders of reactions. They allow for the determination of concentration at any given time and can be used to analyze experimental data. For example, the integrated rate law for a first-order reaction is ln[A] = -kt + ln[A]₀, which can be used to find the rate constant and reaction order from concentration-time data.