Problem 114 - Chemistry The Central Science In Si Units

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 \({ }^{\prime \prime} \mathrm{NO}_{x}{\underline{\phantom{xx}}}^{\prime \prime}\) 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.

Step-by-Step Solution

Answer

(a) Balanced equations: \(\text{N}_2 + \text{O}_2 \rightarrow 2\text{NO} \) and \(2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2 \). (b) 1.72 × 10¹³ grams. (c) 754.25 grams of \(\text{NO}_2\).

Step 1: Write and Balance the Chemical Equations

The first reaction is the formation of nitric oxide: \( \text{N}_2 + \text{O}_2 \rightarrow 2 \text{NO} \). The balanced chemical equation for this reaction is \( \text{N}_2 + \text{O}_2 \rightarrow 2\text{NO} \). The second reaction is the formation of nitrogen dioxide: \( 2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2 \). The balanced chemical equation for this reaction is \( 2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2 \).

Step 2: Calculate Grams of Nitrogen Dioxide from Tons

Start by converting the nitrogen dioxide from tons to grams. Convert 19 million tons to grams: \(19 \times 10^6 \text{ tons}\). Since 1 ton = 907,185 grams, the total mass in grams is \(19 \times 10^6 \times 907,185 = 1.7235315 \times 10^{13}\) grams.

Step 3: Determine Mass of Octane Used and Oxygen Utilization

Calculate the moles of octane in 500 grams. The molar mass of \(\text{C}_8\text{H}_{18}\) is approximately 114.22 g/mol. Thus, the moles of \(\text{C}_8\text{H}_{18}\) is \(\frac{500}{114.22} \approx 4.378 \text{ moles}\). According to the reaction \(2\text{C}_8\text{H}_{18} + 25\text{O}_2 \rightarrow 16\text{CO}_2 + 18\text{H}_2\text{O}\), 1 mole of octane requires 12.5 moles of \(\text{O}_2\). Hence, 4.378 moles of \(\text{C}_8\text{H}_{18}\) requires \(4.378 \times 12.5 = 54.725 \text{ moles of } \text{O}_2\).

Step 4: Calculate Oxygen Used for NOx Formation

Since 85% of oxygen is used for octane, 15% is left for NOx formation. Calculate available moles of \(\text{O}_2\) for NO formation: \(0.15 \times 54.725 \approx 8.209 \, \text{moles of } \text{O}_2\) are available for forming NOx.

Step 5: Compute Mass of Nitrogen Dioxide Formed

Using the equation \(2\text{NO} + \frac{1}{2}\text{O}_2 \rightarrow \text{NO}_2\), calculate moles of \(\text{NO}_2\) produced from 8.209 moles \(\text{O}_2\). Since every mole of \(\text{O}_2\) forms 2 moles \(\text{NO}_2\), \(8.209 \text{ moles of } \text{O}_2\) produce \(8.209 \times 2 \approx 16.418 \) moles of \(\text{NO}_2\). With a molar mass of 46.0055 g/mol for \(\text{NO}_2\), the mass is \(16.418 \times 46.0055 \approx 754.25\, \text{grams}\).

Key Concepts

Chemical Equations Balancing

Balancing chemical equations is a fundamental skill in chemistry. It ensures that the same number of atoms of each element is present on both sides of the equation, reflecting the law of conservation of mass, which states that matter cannot be created or destroyed. When balancing an equation, one must adjust the coefficients in front of the chemical formulas. These coefficients indicate the number of units (such as atoms, molecules, or moles) involved in the reaction.

For example, consider the balanced equations for the formation of nitric oxide and nitrogen dioxide:

• For nitric oxide: \( ext{N}_2 + ext{O}_2 \rightarrow 2 ext{NO} \)
• For nitrogen dioxide: \( 2 ext{NO} + ext{O}_2 \rightarrow 2 ext{NO}_2 \)

Notice how the numbers of nitrogen and oxygen atoms are the same on both sides of each equation. This ensures that we are complying with the conservation of atoms and mass.

Balancing equations becomes a more intuitive process with practice. Students should remember to start by balancing atoms of elements that appear only once on each side of the equation and leave elements like oxygen and hydrogen, which are often found in multiple compounds, until last.

Nitrogen Oxides Formation

Nitrogen oxides, often referred to as NOx gases, primarily consist of nitric oxide (NO) and nitrogen dioxide (NO2). In an internal combustion engine, high temperatures can cause nitrogen in the air to react with oxygen, forming NO. This reaction can be represented as \( ext{N}_2 + ext{O}_2 \rightarrow 2 ext{NO} \).

As NO is emitted from the vehicle's exhaust, it can further react with more oxygen in the atmosphere to form NO2, shown by the equation \( 2 ext{NO} + ext{O}_2 \rightarrow 2 ext{NO}_2 \). These reactions highlight why combustion processes in engines can be significant sources of NOx pollutants.

NOx gases are not only formed during the combustion of octane but can also be a result of other combustion processes. This understanding helps in recognizing the environmental challenges posed by vehicle emissions and the need to develop cleaner combustion techniques.

Environmental Impact of Pollutants

NOx gases have significant environmental impacts. They are key contributors to the formation of smog and can lead to the development of respiratory problems in humans. They also play a role in forming acid rain, as they can react with water vapor in the atmosphere to create nitric acid. This acid rain can damage forests, soils, and aquatic ecosystems.

Furthermore, nitrogen oxides contribute to global warming by affecting the ozone layer. They have a complex interaction with sunlight and other atmospheric chemicals, influencing the concentration of greenhouse gases like ozone.

The release of 19 million tons of NO2 into the atmosphere poses a considerable threat. Understanding their impact emphasizes the importance of stringent environmental regulations and the development of alternative energy sources to reduce our reliance on fossil fuels and minimize emissions.

Combustion Reactions

Combustion reactions occur when a substance combines with oxygen to release energy in the form of heat and light. In the context of an internal combustion engine, the main goal is to burn fuel (such as octane) to power the engine. The typical combustion reaction for octane is \(2 ext{C}_8 ext{H}_{18} + 25 ext{O}_2 \rightarrow 16 ext{CO}_2 + 18 ext{H}_2 ext{O}\).

However, these reactions are not always clean. Part of the oxygen may react with nitrogen to form nitrogen oxides, a byproduct that we wish to minimize. Incomplete combustion can also occur, leading to carbon monoxide and other pollutants.

By understanding the ratios in which oxygen is consumed for various reactions and the byproducts formed, scientists can work towards optimizing engine designs and fuel compositions to enhance efficiency and reduce harmful emissions. This highlights the broader challenge of creating sustainable technologies that balance energy demands with environmental considerations.