Problem 108 - Chemistry: The Central Science

Question

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, which are 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 2004, 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 \(\mathrm{NO}_{\mathrm{x}}\) 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 grams of octane.

Step-by-Step Solution

Answer

In this exercise, we determined that (a) the balanced chemical equations for the given reactions are \(N_2 + O_2 \rightarrow 2NO\) and \(2NO + O_2 \rightarrow 2NO_2\). (b) The United States emitted 19 trillion grams of nitrogen dioxide in 2004. And (c) during the combustion of 500 grams of octane, approximately \(\frac{86250}{114}\) grams of nitrogen dioxide would be produced.

Step 1: (Part a - Balanced Chemical Equations)

To find the balanced chemical equations for the reactions mentioned in the exercise: 1. Nitrogen reacts with oxygen to produce nitric oxide (NO): \(N_2 + O_2 \rightarrow 2NO\) 2. Nitric oxide reacts with more oxygen to produce nitrogen dioxide (NO2): \(2NO + O_2 \rightarrow 2NO_2\)

Step 2: (Part b - Mass of Nitrogen Dioxide Emissions)

To convert the given nitrogen dioxide emissions (19 million tons) to grams, follow these steps: 1. Convert tons to grams: \(1 ton = 1000 kg = 1,000,000 g\) 2. Calculate the mass of nitrogen dioxide: \(19,000,000 tons * 1,000,000 g/ton = 19,000,000,000,000 g\) So, the United States emitted 19 trillion grams of nitrogen dioxide in 2004.

Step 3: (Part c - Calculation of Nitrogen Dioxide Produced during Combustion of Octane)

To find the grams of nitrogen dioxide produced during the combustion of 500 grams of octane, follow these steps: 1. Write the balanced chemical equation for the combustion of octane: \(C_8H_{18} + 12.5O_2 \rightarrow 8CO_2 + 9H_2O\) 2. Calculate the moles of oxygen needed for the combustion of 500 grams of octane: \(1 mol \: of \: C_8H_{18} = 12 * 8 + 18 = 114 g\) \(500 g \: of \: C_8H_{18} = \frac{500}{114}mol \: of \: C_8H_{18}\) \(Moles \: of \: O_2 \: needed = 12.5 * \frac{500}{114} mol = \frac{6250}{114} mol\) 3. Calculate the moles of oxygen used to combust octane (85%): \(0.85 * \frac{6250}{114}mol = \frac{5312.5}{114} mol\) 4. Calculate the moles of oxygen used to produce nitrogen dioxide (the remaining 15%): \(0.15 * \frac{6250}{114}mol = \frac{937.5}{114} mol\) 5. Write the balanced chemical equation for the production of nitrogen dioxide in this case: \(N_2 + 2O_2 \rightarrow 2NO_2\) 6. Calculate the moles of nitrogen dioxide produced: \(\frac{937.5}{114} mol \: of \: O_2 = \frac{937.5}{114} * 2 mol \: of \: NO_2 = \frac{1875}{114} mol \: of \: NO_2\) 7. Convert moles of nitrogen dioxide into grams: \(1 mol \: of \: NO_2 = 14 + 2 * 16 = 46 g\) \(\frac{1875}{114} mol \: of \: NO_2 = \frac{1875}{114} * 46 g \: of \: NO_2\) So, during the combustion of 500 grams of octane, approximately \(\frac{86250}{114}\) grams of nitrogen dioxide would be produced.

Key Concepts

Internal Combustion Engine

The internal combustion engine is at the heart of most automobiles. It uses the controlled burning of fuel to produce energy. This energy propels the vehicle forward. A key factor in the combustion process is air. Air provides the necessary oxygen to ignite the fuel within the engine cylinders.
When fuel like octane, typically found in gasoline, burns in the presence of oxygen inside the engine, it drives pistons that turn the car's wheels.

• The engine sucks in air from the environment, which is mixed with the fuel.
• In the compressed state, the spark plug ignites the air-fuel mixture.
• The explosion from the ignition creates a lot of pressure that pushes against the engine's pistons.
• This pushing motion of the pistons turns the crankshaft, which eventually moves the car.

However, it's not just energy that comes from this process. Byproducts, including nitrogen oxides, can form, especially when fuel is not fully combusted.

Acid Rain

Acid rain results from pollutants like nitrogen oxides (NO and NO₂) and sulfur dioxide mixing with rainwater in the atmosphere. When these gases react with water vapor, they form acids. This makes the rain more acidic.
This acid rain has numerous harmful effects.

• It can damage aquatic environments by lowering the pH of water bodies.
• It harms forests by leaching nutrients from the soil.
• It can corrode buildings and monuments, especially those made of limestone and marble.

Most of these nitrogen oxides originate from the emissions of vehicles and industrial processes, making it crucial to manage emissions to minimize acid rain formation.

Global Warming

Global warming refers to the rise in Earth's average surface temperature due to the accumulation of greenhouse gases in the atmosphere.
Gases like carbon dioxide (CO₂) receive most of the attention, but nitrogen oxides also play a role.
How do they contribute?

• Nitrogen oxides help form ozone (O₃) at ground level, which is a potent greenhouse gas.
• They can also deteriorate the quality of the environment, indirectly affecting how heat is absorbed and reflected by Earth's surface.

Both NO and NO₂ from combustion engines can be mitigated with modern technologies such as catalytic converters, helping to reduce their contribution to global warming.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the reactants and the products. In the context of the combustion engine, there are two critical chemical equations to remember:

• The formation of nitric oxide: \(N_2 + O_2 \rightarrow 2NO\)
• The conversion of nitric oxide to nitrogen dioxide:\(2NO + O_2 \rightarrow 2NO_2\)

These equations show how nitrogen from the air reacts in the heat of the engine to form nitrogen oxides. This transformation is key to understanding both pollution control and the broader environmental impacts associated with vehicle emissions.

Stoichiometry

Stoichiometry is a concept in chemistry that involves calculating the amounts of reactants and products in chemical reactions. It is essential for comprehending the production of nitrogen oxides in combustion engines.
Using stoichiometry, we can predict how many grams of a product will be formed from a given amount of reactant. For example:

• Given the balanced equation for nitrogen dioxide formation, we can determine the moles and then the grams of NO₂ produced when a certain amount of oxygen reacts.
• It's crucial for determining the efficiency of resource usage in reactions.

This knowledge allows automotive engineers and chemists to optimize fuel usage, reducing unwanted side-products like NO and NO₂, and minimizing their adverse environmental effects.