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. b. Write the rate law for the reaction.

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Identify the order of the reaction: Since a plot of \( \ln[A] \) versus time yields a straight line, the reaction follows first-order kinetics.

Write the general form of the rate law for a first-order reaction: The rate law for a first-order reaction is \( \text{Rate} = k[A] \), where \( k \) is the rate constant.

Determine the rate constant: The slope of the line in a plot of \( \ln[A] \) versus time for a first-order reaction is equal to \(-k\). Given that the slope is \(-0.0045/s\), the rate constant \( k \) is 0.0045/s.

Combine the information to write the rate law: Substitute the rate constant into the rate law expression to get \( \text{Rate} = 0.0045[A] \).

Conclude with the rate law: The rate law for the reaction is \( \text{Rate} = 0.0045[A] \), indicating that the reaction is first-order with respect to \( A \).

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Key Concepts

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

First-Order Reactions

A first-order reaction is one where the rate of reaction is directly proportional to the concentration of one reactant. In this case, the linear plot of ln[A] versus time indicates that the reaction follows first-order kinetics, as the natural logarithm of the concentration decreases linearly over time.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For a first-order reaction, the rate law can be written as rate = k[A], where k is the rate constant. This law allows us to predict how changes in concentration will affect the reaction rate.

Slope of the Line

In the context of a first-order reaction, the slope of the ln[A] versus time plot is equal to -k, where k is the rate constant. The given slope of -0.0045/s indicates the rate constant for the reaction, which is crucial for calculating the rate of reaction at different concentrations.

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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?

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?

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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?