Question

5.161 Power plants driven by fossil-fuel combustion generate substantial greenhouse gases (e.g., \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) ) as well as gases that contribute to poor air quality (e.g., \(\mathrm{SO}_{2}\) ). To evaluate exhaust emissions for regulation purposes, the generally inert nitrogen supplied with air must be included in the balanced reactions; it is further assumed that air is composed of only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) with a volume/volume ratio of \(3.76: 1.00,\) respectively. In addition to the water produced, the fuel's \(\mathrm{C}\) and \(\mathrm{S}\) are converted to \(\mathrm{CO}_{2}\) and \(\mathrm{SO}_{2}\) at the stack. Given these stipulations, answer the following for a power plant running on a fossil fuel having the formula \(\mathrm{C}_{18} \mathrm{H}_{10} \mathrm{~S}\). Including the \(\mathrm{N}_{2}\) supplied in air, write a balanced combustion equation for the complex fuel assuming \(120 \%\) stoichiometric combustion (i.e., when excess oxygen is present in the product gases). Except for \(\mathrm{N}_{2},\) use only integer coefficients. (See problem \(3.141 .\) ) What gas law is used to effectively convert the given \(\mathrm{N}_{2} / \mathrm{O}_{2}\) volume ratio to a molar ratio when deriving the balanced combustion equation in (a)? (i) Boyle's law (ii) Charles's law (iii) Avogadro's law (iv) ideal gas law c) Assuming the product water condenses, use the result from (b) to determine the stack gas composition on a "dry" basis by calculating the volume/volume percentages for \(\mathrm{CO}_{2}, \mathrm{~N}_{2},\) and \(\mathrm{SO}_{2}\) Assuming the product water remains as vapor, repeat (c) on a "wet" basis.Assuming the product water remains as vapor, repeat (c) on a "wet" basis. Some fuels are cheaper than others, particularly those with higher sulfur contents that lead to poorer air quality. In port, when faced with ever-increasing air quality regulations, large ships operate power plants on more costly, higher-grade fuels; with regulations nonexistent at sea, ships' officers make the cost-saving switch to lower-grade fuels. Suppose two fuels are available, one having the general formula \(\mathrm{C}_{18} \mathrm{H}_{10} \mathrm{~S}\) and the other \(\mathrm{C}_{32} \mathrm{H}_{18} \mathrm{~S} .\) Based on air quality concerns alone, which fuel is more likely to be used when idling in port? Support your answer to (d) by calculating the mass ratio of \(\mathrm{SO}_{2}\) produced to fuel burned for \(\mathrm{C}_{18} \mathrm{H}_{10} \mathrm{~S}\) and \(\mathrm{C}_{32} \mathrm{H}_{18} \mathrm{~S},\) assuming \(120 \%\) stoichiometric combustion.

Short answer

Use Avogadro's Law for gas ratios and prefer \(C_{32}H_{18}S\) for lower \(SO_2\) emissions.

Step-by-step solution

Determine Stoichiometric Combustion Equation

For the compound \(C_{18}H_{10}S\), the compound will burn with \(O_2\) in the presence of \(N_2\) (in the air). For stoichiometric combustion with excess oxygen (120%):\[\begin{align*}\text{Reactants:}\;& C_{18}H_{10}S + a\,O_2\,\rightarrow\, b\,CO_{2}+ c\,H_{2}O +d\,SO_2+e\,N_2,\text{Balanced equation:}\;&\quad \frac{18}{2}O_2\,+9\,H_2\,=\,\frac{9}{2}O_2,\&\quad \frac{1}{1}O_2 =&\,\frac{1}{1}O_2.\end{align*}\Rightarrow\begin{align*}& C_{18}H_{10}S + \frac{49}{2}O_2 + 92\,N_2 \rightarrow 18\,CO_{2} + 5\,H_{2}O + SO_2 + 92\,N_2 \end{align*}\]

Identify Gas Law for Volume to Molar Conversion

The volume ratio of gases can be directly converted to molar ratio using Avogadro's law, which states that equal volumes of all gases at the same temperature and pressure contain the same number of molecules or moles.

Calculate Dry Basis Gas Composition

The combustion products include \(CO_{2},\,N_{2},\,\text{and}\,SO_{2}\). Total moles of stack gases on a dry basis: \(18+10+1=29\).\[\begin{align*}\%\,CO_2 &= \frac{18}{29}\times100\,=62\.07\%.\%\,N_2 &= \frac{10}{29}\,\times100\,=34\.48\%.\%\,SO_2 &= \frac{1}{29}\times100\,=3\.45\%.\end{align*}\]

Calculate Wet Basis Gas Composition

Including water vapor, the total moles of stack gases on a wet basis would be \(18+5+1+92=115\).\[\begin{align*}\%\,CO_2 &= \frac{18}{115}\,\times100\,=15\.65\%.\%\,N_2 &= \frac{92}{115}\,\times100\,=80\.0\%.\%\,SO_2 &= \frac{1}{115}\,\times100\,=0\.87\%.\%\,H_2O &= \frac{5}{115}\,\times100\,=4\.35\%.\end{align*}\]

Compare Fuels by Sulfur Dioxide Mass Ratio

For \(C_{18}H_{10}S\), \(SO_2\) mass ratio: \(\frac{1\text{ mole }SO_2\times64\text{ g/mole}}{254\text{ g/mole})}=0\.252\).\For \(C_{32}H_{18}S\):\(\frac{1\text{ mole }SO_2\times64\text{ g/mole}}{434\text{ g/mole})}=0\.147\).\Conclusion: Based on reducing \(SO_2\) emissions, \(C_{32}H_{18}S\) is preferably used for port operations.

Key concepts

Greenhouse Gases

Greenhouse gases play a significant role in trapping heat within Earth's atmosphere. This not only leads to global warming but also creates ripple effects, impacting ecosystems and climate systems. When fossil fuels burn, they often release significant amounts of greenhouse gases, primarily carbon dioxide (CO₂) and water vapor.
These gases have high heat-trapping capacities, which when released in large amounts, can contribute to climate change. Understanding and controlling emissions from power plants and vehicles is crucial.

• Carbon Dioxide (CO₂): A common by-product of combustion, primarily from fossil fuel burning.
• Water Vapor: Though naturally present, it increases as more is emitted due to combustion processes.

Reducing emissions from these sources is a step towards diminishing their environmental impact. Hence, calculating and controlling output from fossil-fuel-driven processes is essential for reducing the overall carbon footprint.

Air Quality

Air quality is directly affected by the types of gases released from burning fuels. Poor air quality is often a result of pollutants like sulfur dioxide (SO₂) and nitrogen oxides that originate from combustion processes.
Sulfur dioxide is a particularly harmful pollutant that can cause respiratory issues and contribute to acid rain, which affects crops, bodies of water, and infrastructure.

• Sulfur Dioxide (SO₂): Emits from the burning of sulfur-containing fuels and significantly impacts air quality.
• Nitrogen Oxides (NOx): Though not mentioned in the problem, these are also significant pollutants resulting from combustion.

In ports or urban areas, regulations often demand the use of low-sulfur fuels to mitigate these effects. This is vital for protecting public health and maintaining environmental standards.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry involving the calculation of reactants and products in chemical reactions. In combustion calculations, stoichiometry helps determine how much oxygen is required to completely burn a given amount of fuel.
This also includes considering the nitrogen present in the air, which does not react but appears in the final combustion equation.

• Reactants: These include the fuel and oxygen, with nitrogen being inert but present.
• Products: Typically forms CO₂, water vapor, and other gases like SO₂.

The balanced combustion equation ensures that the correct proportions of reactants produce the desired combustion products, critical for optimizing fuel usage and reducing emissions in power plants.

Avogadro's Law

Avogadro's Law is crucial in understanding the behavior of gases. It states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This principle allows for the conversion of gas volume ratios to molar ratios, essential for balancing combustion equations.
When calculating the balanced equation for a combustion process, using Avogadro’s Law helps ensure the correct ratios of nitrogen and oxygen in the reaction inputs are achieved.

• Volume to Moles: Using Avogadro's Law helps convert volume ratios into precise molar ratios for balanced equations.
• Relevance in Combustion: Facilitates accurate calculations when balancing large-scale reactions involving air components, such as nitrogen.

This law simplifies stoichiometric calculations, making it easier to determine the quantities required for various chemical processes, like combustion of fuels.