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Chapter 3: Problem 114

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally \(\mathrm{N}_{2}(\sim 79 \%)\) and \(\mathrm{O}_{2}(\sim 20 \%) .\) In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "NO \(_{x}\) " gases. In 2009 , the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of \(\mathrm{NO}_{x}\) gases is an unwanted side reaction of the main engine combustion process that turns octane, \(\mathrm{C}_{8} \mathrm{H}_{18},\) into \(\mathrm{CO}_{2}\) and water. If \(85 \%\) of the oxygen in an engine is used to combust octane and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of \(500 \mathrm{~g}\) of octane.

Short Answer

Expert verified
(a) The balanced chemical equations are: \(N_2 + O_2 \rightarrow 2NO\) \(2NO + O_2 \rightarrow 2NO_2\) (b) 19 million tons of nitrogen dioxide is approximately equal to \(1.72 \times 10^{13}\) grams. (c) Approximately 887.99 grams of nitrogen dioxide will be produced during the combustion of 500 grams of octane.

Step by step solution

01

(a) Write Balanced Chemical Equations

To write the balanced chemical equations, we need to ensure that the number of atoms of each element on both sides of the equation is equal. For the formation of nitric oxide (NO): \[ N_2 + O_2 \rightarrow 2NO \] For the formation of nitrogen dioxide (NO鈧�): \[ 2NO + O_2 \rightarrow 2NO_2 \]
02

(b) Convert Nitrogen Dioxide Emissions to Grams

We are given that the United States emitted 19 million tons of nitrogen dioxide (NO鈧�) in 2009. To convert this amount to grams, first, we need to know the number of grams in a ton: \[ 1 \, \text{ton} = 907,184.74 \, \text{grams} \] Then, multiplying the number of tons by the number of grams per ton: \[ 19 \times 10^6 \, \text{tons} \times 907,184.74 \, \frac{\text{grams}}{\text{ton}} \approx 1.72 \times 10^{13} \, \text{grams} \] Hence, 19 million tons of nitrogen dioxide (NO鈧�) is approximately equal to \(1.72 \times 10^{13}\) grams.
03

(c) Calculate Nitrogen Dioxide Produced During Combustion

We are given that 85% of the oxygen in an engine is used to combust octane and the remaining 15% is used to produce nitrogen dioxide. We are also given that 500 grams of octane are combusted. To calculate the amount of nitrogen dioxide produced, we will follow these steps: 1. Write the balanced chemical equation for the combustion of octane: \[ 2C_8H_{18} + 25O_2 \rightarrow 16CO_2 + 18H_2O \] 2. Determine the number of moles of octane combusted using its molar mass (114.23 g/mol): \[ \frac{500 \, \text{g}}{114.23 \, \frac{\text{g}}{\text{mol}}} \approx 4.374 \, \text{moles} \] 3. Calculate the number of moles of oxygen used for combustion from the balanced chemical equation: \[ \frac{4.374 \, \text{moles} \times 25}{2} \approx 54.68 \, \text{moles} \] 4. Calculate the total moles of oxygen before the combustion, considering that 85% of it was used for combustion: \[ \frac{54.68 \, \text{moles}}{0.85} \approx 64.33 \, \text{moles} \] 5. Find the moles of oxygen used for producing nitrogen dioxide (the remaining 15%): \[ 0.15 \times 64.33 \, \text{moles} \approx 9.65 \, \text{moles} \] 6. Calculate the moles of nitrogen dioxide produced using the balanced chemical equation: \[ \frac{9.65 \, \text{moles} \times 2}{1} \approx 19.3 \, \text{moles} \] 7. Convert the moles of nitrogen dioxide to grams using its molar mass (46.01 g/mol): \[ 19.3 \, \text{moles} \times 46.01 \, \frac{\text{g}}{\text{mol}} \approx 887.99 \, \text{grams} \] Hence, approximately 887.99 grams of nitrogen dioxide will be produced during the combustion of 500 grams of octane.

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Key Concepts

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

Air Composition
Air is the main source of oxygen for combustion engines in vehicles. It's made up of various gases. The two main components are nitrogen (\(N_2\)) and oxygen (\(O_2\)). Nitrogen accounts for about 79% of air. Oxygen makes up around 20%.
These gases are crucial for the combustion process in engines. Oxygen is essential for burning fuel like gasoline or octane, providing the energy needed to power vehicles.
  • The remaining 1% of air consists of other gases like argon and carbon dioxide.
  • Knowing the composition of air helps in understanding its role in combustion and emissions.
Pollutants
In combustion engines, not all reactions are beneficial. Some lead to pollutants. For example, when nitrogen (\(N_2\)) reacts with oxygen (\(O_2\)), it forms nitric oxide (NO). This further reacts to form nitrogen dioxide (\(NO_2\)). These compounds are collectively known as NOx gases.
NOx gases contribute to environmental issues. They cause acid rain and enhance the greenhouse effect, leading to global warming.
  • Understanding the chemical reactions that form NOx is crucial to reducing these pollutants.
  • Efforts are being made globally to limit NOx emissions from vehicles and industrial sources.
Stoichiometry
Stoichiometry is a branch of chemistry that deals with the calculation of reactants and products in a chemical reaction. In the context of combustion engines, stoichiometry is used to balance chemical equations, like those for octane combustion and NOx formation.
For example, the balanced equation for forming nitric oxide is \(N_2 + O_2 \rightarrow 2NO\). This highlights the exact number of molecules needed for the reaction.
  • Understanding stoichiometry helps in calculating the amount of NOx produced from a given amount of fuel.
  • It also assists in determining how much oxygen is needed for complete fuel combustion.
Environmental Impact
The emissions from combustion engines have a significant environmental impact. Pollutants like NOx contribute to air quality degradation. They participate in forming acid rain, which harms ecosystems and buildings.
Moreover, engines emit carbon dioxide, a major greenhouse gas, adding to climate change issues.
  • Efforts to improve engine efficiency and reduce emissions are critical to mitigating these impacts.
  • Innovations like catalytic converters help decrease the amount of harmful gases emitted by vehicles.
  • Transitioning to cleaner energy sources can further reduce the environmental footprint of transportation.

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Most popular questions from this chapter

Detonation of nitroglycerin proceeds as follows: $$ \begin{aligned} 4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}(l) & \longrightarrow \\ & 12 \mathrm{CO}_{2}(g)+6 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) \end{aligned} $$ (a) If a sample containing \(2.00 \mathrm{~mL}\) of nitroglycerin (density \(=\) \(1.592 \mathrm{~g} / \mathrm{mL}\) ) is detonated, how many moles of gas are produced? (b) If each mole of gas occupies \(55 \mathrm{~L}\) under the conditions of the explosion, how many liters of gas are produced? (c) How many grams of \(\mathrm{N}_{2}\) are produced in the detonation?

A chemical plant uses electrical energy to decompose aqueous solutions of \(\mathrm{NaCl}\) to give \(\mathrm{Cl}_{2}, \mathrm{H}_{2},\) and \(\mathrm{NaOH}\) : \(2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)\) If the plant produces \(1.5 \times 10^{6} \mathrm{~kg}\) ( 1500 metric tons) of \(\mathrm{Cl}_{2}\) daily, estimate the quantities of \(\mathrm{H}_{2}\) and \(\mathrm{NaOH}\) produced.

Write balanced chemical equations to correspond to each of the following descriptions: (a) When sulfur trioxide gas reacts with water, a solution of sulfuric acid forms. (b) Boron sulfide, \(\mathrm{B}_{2} \mathrm{~S}_{3}(s),\) reacts violently with water to form dissolved boric acid, \(\mathrm{H}_{3} \mathrm{BO}_{3},\) and hydrogen sulfide gas. (c) Phosphine, \(\mathrm{PH}_{3}(g)\), combusts in oxygen gas to form water vapor and solid tetraphosphorus decaoxide. (d) When solid mercury(II) nitrate is heated, it decomposes to form solid mercury(II) oxide, gaseous nitrogen dioxide, and oxygen. (e) Copper metal reacts with hot concentrated sulfuric acid solution to form aqueous copper(II) sulfate, sulfur dioxide gas, and water.

\(\mathrm{NO}_{x}\) is a generic term for the nitrogen oxides, \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) \(\mathrm{NO}_{x}\) gases are air pollutants that react to form smog and acid rain. In order to reduce \(\mathrm{NO}_{x}\) emission from vehicle, catalytic converters are installed in car exhausts to decompose NO and \(\mathrm{NO}_{2}\) respectively into \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}(\mathbf{a})\) Write the balanced chemical equations for the decomposition of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) respectively. (b) If the car produces \(100 \mathrm{~g} \mathrm{NO}_{x}\) a day, with equal mole ratio of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\), how many grams of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) are produced respectively?

A key step in balancing chemical equations is correctly identifying the formulas of the reactants and products. For example, consider the reaction between calcium oxide, \(\mathrm{CaO}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) to form aqueous calcium hydroxide. (a) Write a balanced chemical equation for this combination reaction, having correctly identified the product as \(\mathrm{Ca}(\mathrm{OH})_{2}(a q)\) (b) Is it possible to balance the equation if you incorrectly identify the product as \(\mathrm{CaOH}(a q)\), and if so, what is the equation?
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