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?

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Identify the order of the reaction. Since a plot of 1/[AB] versus time yields a straight line, the reaction is second order.

Use the second-order half-life formula: \( t_{1/2} = \frac{1}{k[A]_0} \), where \( k \) is the rate constant and \( [A]_0 \) is the initial concentration.

Recognize that the slope of the line in a second-order reaction plot is equal to the rate constant \( k \). Therefore, \( k = 0.55 \text{ M}^{-1}\text{s}^{-1} \).

Substitute the given initial concentration \( [A]_0 = 0.55 \text{ M} \) and the rate constant \( k = 0.55 \text{ M}^{-1}\text{s}^{-1} \) into the half-life formula.

Calculate the half-life using the formula: \( t_{1/2} = \frac{1}{0.55 \times 0.55} \).

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Key Concepts

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

Rate Laws and Reaction Order

Rate laws describe the relationship between the concentration of reactants and the rate of a chemical reaction. The order of a reaction indicates how the rate is affected by the concentration of each reactant. In this case, the reaction AB → A + B is second-order, as indicated by the linear plot of 1/[AB] versus time, which is characteristic of second-order kinetics.

Half-Life of a Reaction

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For second-order reactions, the half-life is dependent on the initial concentration of the reactant. The formula for the half-life (t1/2) of a second-order reaction is t1/2 = 1/(k[AB]0), where k is the rate constant and [AB]0 is the initial concentration.

Slope of the Rate Plot

In the context of reaction kinetics, the slope of 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 directly represents the rate constant used in calculating the half-life. Understanding how to interpret the slope is crucial for determining the kinetics of the reaction.

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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. 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. b. Write the rate law for the reaction.

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?