Question

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 g of octane.

Short answer

The balanced chemical equations for the given reactions are: 1. Nitrogen reacting with oxygen to produce nitric oxide gas: \(N_2 + O_2 \rightarrow 2NO\) 2. Nitric oxide gas reacting with oxygen to produce nitrogen dioxide gas: \(2NO + O_2 \rightarrow 2NO_2\) 19 million tons of nitrogen dioxide is equal to \(1.9 \times 10^{13}\) grams. During the combustion of 500 g of octane, 471.61 grams of nitrogen dioxide would be produced.

Step-by-step solution

Write balanced chemical equations

We need to write balanced chemical equations for two reactions: 1. Nitrogen reacting with oxygen to produce nitric oxide gas: \[N_2 + O_2 \rightarrow 2NO\] 2. Nitric oxide gas reacting with oxygen to produce nitrogen dioxide gas: \[2NO + O_2 \rightarrow 2NO_2\]

Convert 19 million tons of nitrogen dioxide into grams

To convert 19 million tons of nitrogen dioxide into grams, we need to use the following conversion factors: 1 ton = 1,000,000 grams So, 19 million tons converted to grams is: \(19 \times 10^6 \, tons \times \frac{1 \times 10^6 \, g}{1 \, ton} = 1.9 \times 10^{13} g\) Thus, 19 million tons of nitrogen dioxide is equal to \(1.9 \times 10^{13}\) grams.

Calculate the grams of nitrogen dioxide produced during the combustion of 500 g of octane

First, we need to determine how much oxygen is required to combust 500 g of octane. The balanced equation for the combustion of octane is: \[C_8H_{18} + \dfrac{25}{2} O_2 \rightarrow 8CO_2 + 9H_2O \] From this equation, we can determine how much oxygen is required for 500 g of octane: 500 g of \(C_8H_{18}\) = \(\dfrac{500 \times \dfrac{25}{2} \, moles \, O_2}{1 \, mole \, C_8H_{18}}\), considering the molar mass \(M(C_8H_{18}) = 114.23 \, g/mol\), and \(M(O_2) = 32 \, g/mol\). which gives: \[\dfrac{500 \times \dfrac{25}{2} \times 32}{114.23} \approx 1093 \, g\, of \, O_2\] Now, considering that 15% of the oxygen produces nitrogen dioxide: \(0.15 \times 1093 = 163.95 \, g\, of \, O_2\) involved in the production of nitrogen dioxide. Using the balanced equation of nitric oxide gas reacting with oxygen: \(2NO + O_2 \rightarrow 2NO_2\) we can calculate the grams of nitrogen dioxide produced: \(163.95 \, g \, O_2 = \dfrac{163.95 \times 2 \, moles \, NO_2}{1 \, mole \, O_2}\), considering the molar mass of \(NO_2 = 46.01 \, g/mol\). which gives: \[\dfrac{163.95 \times 2 \times 46.01}{32} \approx 471.61 \, g\, of \, NO_2\] So, during the combustion of 500 g of octane, 471.61 grams of nitrogen dioxide would be produced.

Key concepts

Internal Combustion Engine

An internal combustion engine is a type of engine where fuel combustion occurs inside the engine itself. When you drive a car, the engine burns fuel to produce energy. This energy then powers the car. The engine gets oxygen from the air to burn the fuel. This process happens in a series of small explosions within the engine cylinders.

These explosions push pistons that turn the crankshaft, ultimately moving the car. The main task of an internal combustion engine is to transform fuel energy into mechanical energy. When gasoline or diesel burns, it produces gases that expand and create pressure.

• The engine converts thermal energy into mechanical motion.
• It primarily uses oxygen from the air for the combustion process.
• An unintended result is the production of nitrogen oxides (NOx) as pollutants.

By understanding how an engine operates, we gain insight into its efficiency and environmental impact.

Chemical Reactions

Chemical reactions in an internal combustion engine involve several processes. Two main ones are:

• Combustion of fuel: Octane (\(C_8H_{18}\)) reacts with oxygen (\(O_2\)) to form carbon dioxide (\(CO_2\)) and water (\(H_2O\)).
• Formation of nitrogen oxides: Nitrogen (\(N_2\)) from the air reacts with oxygen during the high-temperature combustion process to form nitric oxide (\(NO\)) and nitrogen dioxide (\(NO_2\)).

These reactions are carefully balanced to determine the reactants and products. For instance:

• Nitrogen and oxygen create nitric oxide: \[N_2 + O_2 \rightarrow 2NO\]
• Nitric oxide further reacts to form nitrogen dioxide: \[2NO + O_2 \rightarrow 2NO_2\]

These chemical reactions underline how cars contribute to pollution and why managing emissions is crucial.

Air Composition

Air is a mixture of gases essential for combustion in engines:

• \(N_2\) (Nitrogen): Approximately 79%, the most abundant gas.
• \(O_2\) (Oxygen): About 20%, vital for combustion.
• Other gases: Like carbon dioxide, make up a small portion.

This mixture provides the necessary oxygen for fuel combustion. However, when nitrogen in the air reacts with oxygen due to high temperatures, it forms nitrogen oxides like NO and NO2. This process occurs because of the immense heat inside an engine's cylinders.

The balance between these gases is critical for combustion efficiency and to minimize unwanted side reactions, such as the formation of pollutants.

Environmental Pollution

Nitrogen oxides (NOx) are significant pollutants produced by internal combustion engines. When cars emit NO and NO2, they contribute to environmental issues:

• Acid rain: Nitrogen oxides react with water vapor in the atmosphere to form nitric acid.
• Global warming: These gases can influence the Earth's heat balance.

In 2009, the U.S. emitted around 19 million tons of nitrogen dioxide, a clear indication of their impact.

Efforts to reduce NOx emissions focus on cleaner engine technologies and promoting alternative fuel sources. Catalytic converters in vehicles also help break down these gases before they escape into the atmosphere, reducing environmental damage and improving air quality.