/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 86 The balance between \(\mathrm{SO... [FREE SOLUTION] | 91影视

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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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid Rain Formation
Acid rain is a phenomenon that occurs when pollutants, specifically sulfur oxides, combine with water vapor in the atmosphere and fall to the ground as acidic precipitation. This process is largely influenced by human activities, particularly the burning of fossil fuels, which releases sulfur oxides into the atmosphere. When sulfur dioxide ( ext{SO}_2) is emitted into the air, it undergoes oxidation to form sulfur trioxide ( ext{SO}_3). This conversion process plays a crucial role in the formation of acid rain. Sulfur trioxide reacts with water in the atmosphere to form sulfuric acid ( ext{H}_2 ext{SO}_4), which then precipitates as acid rain. Such events can cause environmental harm, impacting plant life and aquatic systems. The balance and reaction rates of ext{SO}_2 and ext{SO}_3 are pivotal in the chemistry of acid rain.
Chemical Reactions in Acid Rain Formation
The primary chemical reactions that lead to acid rain involve the conversion of sulfur and oxygen into sulfur oxides. Let's break these down:
  • Combustion of sulfur-containing compounds releases ext{SO}_2.
  • ext{SO}_2 can be further oxidized to form ext{SO}_3:\[2 \text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2 \text{SO}_3(g)\]
  • ext{SO}_3 then reacts with water vapor to form sulfuric acid:\[ ext{SO}_3(g) + ext{H}_2 ext{O}(g) \rightarrow ext{H}_2 ext{SO}_4(aq)\]
Understanding these reactions is crucial, as ext{SO}_3 formation is a critical step. The equilibrium constants of these reactions indicate the likelihood of the reactions occurring under given conditions and play a vital role in dictating how much ext{SO}_3 will form and thus how much ext{H}_2 ext{SO}_4 will eventually contribute to acid rain.
Sulfur Oxides Chemistry
Sulfur oxides are a group of compounds composed of sulfur and oxygen, with sulfur dioxide ( ext{SO}_2) and sulfur trioxide ( ext{SO}_3) being the most prevalent forms relevant to atmospheric chemistry. Their interactions are central to many environmental issues, notably acid rain. Sulfur dioxide is typically produced during the combustion of fossil fuels and is a precursor to sulfuric acid in the formation of acid rain. The conversion of ext{SO}_2 to ext{SO}_3 is a key reaction in this process, facilitated by the presence of catalysts in the atmosphere. Unlike ext{SO}_2, sulfur trioxide is more reactive and can readily combine with water to form sulfuric acid, a strong acid that accounts for the acidity in acid rain. The rate and extent of these chemical conversions depend heavily on equilibrium constants, which provide insight into the stability and likelihood of forming products under equilibrium conditions.

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Most popular questions from this chapter

The concentration of \(\mathrm{SO}_{2}\) in the troposphere over a certain region is 0.16 ppm by volume. The gas dissolves in rainwater as follows: $$ \mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HSO}_{3}^{-}(a q) $$ Given that the equilibrium constant for the preceding reaction is \(1.3 \times 10^{-2},\) calculate the \(\mathrm{pH}\) of the rainwater. Assume that the reaction does not affect the partial pressure of \(\mathrm{SO}_{2}\).

Peroxyacetyl nitrate (PAN) undergoes thermal decomposition as follows: $$ \mathrm{CH}_{3}(\mathrm{CO}) \mathrm{OONO}_{2} \longrightarrow \mathrm{CH}_{3}(\mathrm{CO}) \mathrm{OO}+\mathrm{NO}_{2} $$ The rate constant is \(3.0 \times 10^{-4} \mathrm{~s}^{-1}\) at \(25^{\circ} \mathrm{C}\). At the boundary between the troposphere and stratosphere, where the temperature is about \(-40^{\circ} \mathrm{C},\) the rate constant is reduced to \(2.6 \times 10^{-7} \mathrm{~s}^{-1} .\) (a) Calculate the activation energy for the decomposition of PAN. (b) What is the half-life of the reaction (in minutes) at \(25^{\circ} \mathrm{C} ?\)

In 1991 it was discovered that nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) is produced in the synthesis of nylon. This compound, which is released into the atmosphere, contributes both to the depletion of ozone in the stratosphere and to the greenhouse effect. (a) Write equations representing the reactions between \(\mathrm{N}_{2} \mathrm{O}\) and oxygen atoms in the stratosphere to produce nitric oxide (NO), which is then oxidized by ozone to form nitrogen dioxide. (b) Is \(\mathrm{N}_{2} \mathrm{O}\) a more effective greenhouse gas than carbon dioxide? Explain. (c) One of the intermediates in nylon manufacture is adipic acid [HOOC(CH \(\left._{2}\right)_{4}\) COOH]. About \(2.2 \times 10^{9} \mathrm{~kg}\) of adipic acid are consumed every year. It is estimated that for every mole of adipic acid produced, 1 mole of \(\mathrm{N}_{2} \mathrm{O}\) is generated. What is the maximum number of moles of \(\mathrm{O}_{3}\) that can be destroyed as a result of this process per year?

Name the gas that is largely responsible for the acid rain phenomenon.

As stated in the chapter, carbon monoxide has a much higher affinity for hemoglobin than oxygen does. (a) Write the equilibrium constant expression \(\left(K_{\mathrm{c}}\right)\) for the following process: $$ \mathrm{CO}(g)+\mathrm{HbO}_{2}(a q) \rightleftharpoons \mathrm{O}_{2}(g)+\mathrm{HbCO}(a q) $$ where \(\mathrm{HbO}_{2}\) and \(\mathrm{HbCO}\) are oxygenated hemoglobin and carboxyhemoglobin, respectively. (b) The composition of a breath of air inhaled by a person smoking a cigarette is \(1.9 \times 10^{-6} \mathrm{~mol} / \mathrm{L} \mathrm{CO}\) and \(8.6 \times 10^{-3} \mathrm{~mol} / \mathrm{L} \mathrm{O}_{2} .\) Calculate the ratio of \([\mathrm{HbCO}]\) to \(\left[\mathrm{HbO}_{2}\right]\), given that \(K_{\mathrm{c}}\) is 212 at \(37^{\circ} \mathrm{C}\).
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