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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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. c. What is the half-life?

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. d. If the initial concentration of A is 0.250 M, what is the concentration after 225 s?

Textbook Question

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.

a. What is the value of the rate constant (k) for this reaction at this temperature?

Textbook Question

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. c. What is the half-life when the initial concentration is 0.55 M?

Textbook Question

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.

d. If the initial concentration of AB is 0.250 M, and the reaction mixture initially contains no products, what are the concentrations of A and B after 75 s?