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Chapter 11: Problem 16

The type of rate law for a reaction, either the differential rate law or the integrated rate law, is usually determined by which data is easiest to collect. Explain.

Short Answer

Expert verified
The choice between using a differential rate law or an integrated rate law for a reaction depends on the available data or which data is easiest to collect. Differential rate laws relate the reaction rate to the instantaneous concentrations of reactants, and are appropriate when such data is available. Integrated rate laws describe how reactant concentrations change over time and should be used when data on concentration changes over time is more readily accessible. Choose the appropriate rate law based on your data, and then apply it to analyze the reaction rates and better understand the reaction mechanism.

Step by step solution

01

Understand the difference between differential and integrated rate laws

Differential rate laws express the reaction rate as a function of the instantaneous concentrations of reactants. This means that they describe how fast the reaction is happening at a particular moment in time. In contrast, integrated rate laws relate the reaction rate to how the concentrations of reactants change over time. Instead of providing a snapshot of the reaction rate at a specific time, they describe how the reaction progresses overall.
02

Consider the data available

The choice between using a differential rate law or an integrated rate law depends on what kind of data is available or easiest to collect. If you have data on the instantaneous concentrations of reactants at different points in time, it is more appropriate to use a differential rate law to analyze the reaction. If, on the other hand, you have data on how the concentrations of reactants change over time, an integrated rate law would be most suitable.
03

Choose the appropriate rate law

Once you have evaluated the available data, you can choose the appropriate rate law based on your findings. For example, if you find that it is easiest to collect data on the instantaneous concentrations of reactants, you should choose to use a differential rate law for the reaction. Conversely, if the data on how the concentrations of reactants change over time is more readily available or easier to collect, you should choose to use an integrated rate law.
04

Analyze the reaction using the chosen rate law

After selecting the appropriate rate law, you can then apply it to analyze the reaction rates and determine how different factors, such as the concentrations of reactants, affect the reaction. This will allow you to better understand the reaction mechanism and make predictions about the behavior of the reaction under various conditions.

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Most popular questions from this chapter

A reaction of the form $$aA \longrightarrow Products$$gives a plot of \(\ln [\mathrm{A}]\) versus time (in seconds), which is a straight line with a slope of \(-7.35 \times 10^{-3} .\) Assuming \([\mathrm{A}]_{0}=\) \(0.0100 M,\) calculate the time (in seconds) required for the reaction to reach \(22.9 \%\) completion.

A popular chemical demonstration is the "magic genie" procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is \(70.0 \space\mathrm{kJ} / \mathrm{mol}\). When the catalyst is added, the activation energy (at \(20 .^{\circ} \mathrm{C}\) ) is \(42.0 \space\mathrm{kJ} / \mathrm{mol} .\) Theoretically, to what temperature \(\left(^{\circ} \mathrm{C}\right)\) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at \(20 .^{\circ} \mathrm{C} ?\) Assume the frequency factor \(A\) is constant, and assume the initial concentrations are the same.

Consider the reaction $$4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g)$$ If, in a certain experiment, over a specific time period, 0.0048 mole of \(\mathrm{PH}_{3}\) is consumed in a 2.0 - \(\mathrm{L}\) container each second of reaction, what are the rates of production of \(\mathbf{P}_{4}\) and \(\mathbf{H}_{2}\) in this experiment?

A certain reaction has the following general form: $$\text { aA } \longrightarrow \mathrm{bB}$$ At a particular temperature and \([\mathrm{A}]_{0}=2.00 \times 10^{-2} \mathrm{M}, \)concentration versus time data were collected for this reaction, and a plot of \(\ln [\mathrm{A}]\) versus time resulted in a straight line with a slope value of \(-2.97 \times 10^{-2} \mathrm{min}^{-1}\)a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to \(2.50 \times 10^{-3} \mathrm{M} ?\)

Experiments during a recent summer on a number of fireflies (small beetles, Lampyridaes photinus) showed that the average interval between flashes of individual insects was \(16.3 \mathrm{s}\) at \(21.0^{\circ} \mathrm{C}\) and \(13.0 \mathrm{s}\) at \(27.8^{\circ} \mathrm{C}\). a. What is the apparent activation energy of the reaction that controls the flashing? b. What would be the average interval between flashes of an individual firefly at \(30.0^{\circ} \mathrm{C} ?\) c. Compare the observed intervals and the one you calculated in part b to the rule of thumb that the Celsius temperature is 54 minus twice the interval between flashes.
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