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Chapter 20: Problem 86

The balance between \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\) is important in understanding acid rain formation in the troposphere. From the following information at \(25^{\circ} \mathrm{C}\) $$ \begin{aligned} \mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightleftharpoons \mathrm{SO}_{2}(g) & K_{1} &=4.2 \times 10^{52} \\ 2 \mathrm{~S}(s)+3 \mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{SO}_{3}(g) & K_{2} &=9.8 \times 10^{128} \end{aligned} $$ calculate the equilibrium constant for the reaction $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$

Short Answer

Expert verified
The equilibrium constant for the reaction \(2SO_{2}(g)+O_{2}(g)\rightleftharpoons2SO_{3}(g)\) is \(1.789 \times 10^{-24}\)

Step by step solution

01

Analyze the given and target reactions

Firstly, it needs to be figured out how to obtain the reaction \(2SO_{2}(g)+O_{2}(g)\rightleftharpoons2SO_{3}(g)\) from the given initial reactions. The first reaction converts S(s) and O2(g) to SO2(g), and the second reaction converts S(s) and O2(g) to SO3(g). To obtain the target reaction, multiply the first reaction by 2 to get \(2SO_{2}(g)\), then subtract the second reaction from this new reaction.
02

Manipulate the initial reactions

Multiply the first reaction by 2 and write it down. Then write down the second reaction. Subtract the second reaction from the new first reaction to get the target reaction: 2[S(s) + O2(g) \rightleftharpoons SO2(g)] - [2S(s) + 3O2(g) \rightleftharpoons 2SO3(g)] = 2SO2(g) +O2(g) \rightleftharpoons 2SO3(g)
03

Manipulate the initial equilibrium constants

After manipulation of the reactions, do the same manipulations on the equilibrium constants. When a reaction is multiplied by a factor, it's equilibrium constant is raised to the power of that factor. When a reaction is subtracted, the equilibrium constants are divided. Hence, \(K_{3}\) for the target reaction will be \((K_{1})^{2}/K_{2}\) = \(((4.2 \times 10^{52}))^2/(9.8 \times 10^{128})\)
04

Calculate the target equilibrium constant

Perform the calculations to obtain the value of \(K_{3}\): \((4.2 \times 10^{52})^2 /(9.8 \times 10^{128}) = 1.789 \times 10^{-24}\).

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Most popular questions from this chapter

How are past temperatures determined from ice cores obtained from the Artic or Antarctica? (Hint: Look up the stable isotopes of hydrogen and oxygen. How does energy required for vaporization depend on the masses of \(\mathrm{H}_{2} \mathrm{O}\) molecules containing different isotopes? How would you determine the age of an ice core?)

Briefly describe the absorption of solar radiation in the stratosphere by \(\mathrm{O}_{2}\) and \(\mathrm{O}_{3}\) molecules.

Although the hydroxyl radical (OH) is present only in a trace amount in the troposphere, it plays a central role in its chemistry because it is a strong oxidizing agent and can react with many pollutants as well as some CFC substitutes (see Section 20.3 ). The hydroxyl radical is formed by the following reactions: $$ \begin{array}{r} \mathrm{O}_{3} \stackrel{\lambda<320 \mathrm{nm}}{\longrightarrow} \mathrm{O}^{*}+\mathrm{O}_{2} \\ \mathrm{O}+\mathrm{H}_{2} \mathrm{O} \longrightarrow 2 \mathrm{OH} \end{array} $$ where \(\mathrm{O}^{*}\) denotes an electronically excited atom. (a) Explain why the concentration of \(\mathrm{OH}\) is so small even though the concentrations of \(\mathrm{O}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}\) are quite large in the troposphere. (b) What property makes OH a strong oxidizing agent? (c) The reaction between \(\mathrm{OH}\) and \(\mathrm{NO}_{2}\) contributes to acid rain. Write an equation for this process. (d) The hydroxyl radical can oxidize \(\mathrm{SO}_{2}\) to \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) The first step is the formation of a neutral \(\mathrm{HSO}_{3}\) species, followed by its reaction with \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) to form \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and the hydroperoxyl radical \(\left(\mathrm{HO}_{2}\right)\). Write equations for these processes.

Why are CFCs more effective greenhouse gases than methane and carbon dioxide?

Describe the properties that make radon an indoor pollutant. Would radon be more hazardous if \({ }^{222} \mathrm{Rn}\) had a longer half-life?
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