The reaction A¡products was monitored as a function of time. The results are shown here. Time (s) [A] (M) 0 1.000 25 0.914 50 0.829 75 0.744 100 0.659 125 0.573 150 0.488 175 0.403 200 0.318 Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [A] = 0.10 M?

Verified step by step guidance

1. Step 1: Plot the concentration [A] versus time (t) to visually inspect the data and determine if it follows a zero-order, first-order, or second-order reaction.
2. Step 2: For a zero-order reaction, plot [A] versus time (t). For a first-order reaction, plot ln[A] versus time (t). For a second-order reaction, plot 1/[A] versus time (t).
3. Step 3: Determine which plot gives a straight line. The straight-line plot indicates the order of the reaction.
4. Step 4: Calculate the slope of the straight-line plot. The slope will give the rate constant (k) for the reaction.
5. Step 5: Use the rate law expression for the determined order of the reaction to calculate the rate of reaction when [A] = 0.10 M.

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 linear relationship between the concentration of the reactant and the rate, while a second-order reaction has a quadratic relationship. Determining the order is essential for understanding the kinetics of the reaction.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. It is specific to a given reaction at a particular temperature and is influenced by factors such as temperature and the presence of catalysts. The value of k can be determined from experimental data and is crucial for calculating reaction rates at different concentrations.

Integrated Rate Laws

Integrated rate laws express the concentration of reactants as a function of time, allowing for the determination of reaction order and rate constants. For zero, first, and second-order reactions, different mathematical relationships describe how concentration changes over time. By analyzing concentration data over time, one can identify the reaction order and calculate the rate constant, which is essential for predicting reaction behavior.