Ch.15 - Chemical Kinetics

Problem 52

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Chapter 15, Problem 52

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?

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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.

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).

Step 3: Determine which plot gives a straight line. The straight-line plot indicates the order of the reaction.

Step 4: Calculate the slope of the straight-line plot. The slope will give the rate constant (k) for the reaction.

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Rate Law Fundamentals

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Related Practice

Textbook Question

Indicate the order of reaction consistent with each observation.

a. The half-life of the reaction gets shorter as the initial concentration is increased.

b. A plot of the natural log of the concentration of the reactant versus time yields a straight line.

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Textbook Question

Indicate the order of reaction consistent with each observation c. The half-life of the reaction gets longer as the initial concentration is increased.

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Textbook Question

The tabulated data show the concentration of AB versus time for this reaction: AB( g)¡A( g) + B( g) Time (s) [AB] (M) 0 0.950 50 0.459 100 0.302 150 0.225 200 0.180 250 0.149 300 0.128 350 0.112 400 0.0994 450 0.0894 500 0.0812 Determine the order of the reaction and the value of the rate constant. Predict the concentration of AB at 25 s.

This reaction was monitored as a function of time: A → B + C A plot of ln[A] versus time yields a straight line with slope -0.0045/s. a. What is the value of the rate constant (k) for this reaction at this temperature?

This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms. b. Write the rate law for the reaction.

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Textbook Question

The decomposition of XY is second order in XY and has a rate constant of 7.02⨉10^-3 M^-1• s^-1 at a certain temperature. a. What is the half-life for this reaction at an initial concentration of 0.100 M?

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