Ch.15 - Chemical Kinetics

Problem 54b

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Chapter 15, Problem 54b

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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Identify the order of the reaction by analyzing the plot. A straight line in a plot of 1/[AB] versus time indicates a second-order reaction.

For a second-order reaction, the rate law is expressed as: rate = k[AB]^2.

The slope of the line in the plot of 1/[AB] versus time is equal to the rate constant k for a second-order reaction.

Given that the slope is +0.55/Ms, this value represents the rate constant k.

Therefore, the rate law for the reaction is: rate = 0.55 [AB]^2.

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Key Concepts

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

Rate Law

The rate law of a chemical reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. Understanding the rate law is essential for predicting how changes in concentration affect the reaction rate.

Order of Reaction

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 is affected by the concentration of that reactant. In this case, since the plot of 1/[AB] versus time is linear, it suggests that the reaction is second-order with respect to AB, meaning the rate is proportional to the square of the concentration of AB.

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time and are derived from the differential rate laws. For a second-order reaction, the integrated rate law is given by 1/[AB] = kt + 1/[AB]0, where [AB]0 is the initial concentration. The linear relationship observed in the plot indicates that the reaction follows this integrated form, allowing us to determine the rate constant from the slope.

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Rate Law Fundamentals

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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.

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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Textbook Question

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?

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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Textbook Question

The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. How long will it take for 10% of the U-238 atoms in a sample of U-238 to decay?

The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. If a sample of U-238 initially contained 1.5⨉10¹⁸ atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms does it contain today?

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