Problem 64 - Chemistry Matter and Change

Question

Greenhouse Gas Carbon dioxide is a greenhouse gas that is linked to global warming. It is released into the atmosphere through the combustion of octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) in gasoline. Write the balanced chemical equation for the combustion of octane and calculate the mass of octane needed to release 5.00 \(\mathrm{mol}\) of \(\mathrm{CO}_{2} .\)

Step-by-Step Solution

Answer

71.39 grams of octane are needed to produce 5.00 moles of CO2.

Step 1: Write the Unbalanced Chemical Equation

The combustion of octane involves the reaction of octane with oxygen to produce carbon dioxide and water. The unbalanced chemical equation is: \( \text{C}_8\text{H}_{18} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \).

Step 2: Balance the Chemical Equation

To balance the chemical equation, ensure the same number of each type of atom appears on both sides of the equation. The balanced equation is: \( 2\text{C}_8\text{H}_{18} + 25\text{O}_2 \rightarrow 16\text{CO}_2 + 18\text{H}_2\text{O} \). This balances the carbon, hydrogen, and oxygen atoms.

Step 3: Relate Moles of Octane to Moles of CO2

From the balanced equation, 2 moles of octane produce 16 moles of carbon dioxide. Thus, to release 5.00 moles of \( \text{CO}_2 \), we set up a ratio: \( \frac{2 \text{ moles of C}_8\text{H}_{18}}{16 \text{ moles of CO}_2} = \frac{x \text{ moles of C}_8\text{H}_{18}}{5.00 \text{ moles of CO}_2} \). Solve for \( x \).

Step 4: Calculate Moles of Octane Needed

Using the ratio from Step 3, solve for \( x \): \( x = \frac{2}{16} \times 5.00 = 0.625 \text{ moles of octane} \). This is the amount of octane needed to produce 5.00 moles of \( \text{CO}_2 \).

Step 5: Calculate Mass of Octane Needed

Calculate the mass of 0.625 moles of octane using its molar mass. The molar mass of octane \((\text{C}_8\text{H}_{18})\) is \( 8\times12.01 + 18\times1.01 = 114.22 \text{ g/mol} \). Therefore, \( 0.625 \times 114.22 = 71.39 \text{ grams of octane} \).

Key Concepts

Combustion Reactions

Combustion reactions are an essential part of chemistry, particularly when discussing energy release. In a typical combustion reaction, a hydrocarbon like octane (which is found in gasoline) reacts with oxygen to form carbon dioxide and water. This process releases energy, making such reactions very important for fuel generation.
To thoroughly understand these reactions, it's crucial to note a few things:

• Reactants and Products: Combustion involves a fuel (like octane) and an oxidizer (oxygen). Together, they produce carbon dioxide and water as products.
• Exothermic Reaction: Combustion reactions release a significant amount of energy in the form of heat, which is why they are exothermic.
• Balanced Equations: Writing a balanced equation is essential to represent the exact ratios of reactants and products to reflect the law of conservation of mass.

Balancing such chemical equations ensures that the number of atoms for each element is the same on both sides of the reaction.

Greenhouse Gases

Greenhouse gases like carbon dioxide are vital to our atmosphere. They trap heat from the Earth and help regulate temperature, but an excess of these gases leads to global warming.
Here's why you should know about them:

• Sources: The combustion of fossil fuels, like octane, releases significant amounts of carbon dioxide, contributing to increased greenhouse gases.
• Effects: The accumulation of these gases in the atmosphere traps more heat, leading to climate change and altering weather patterns.
• Environmental Impact: Understanding and controlling emissions from combustions are crucial steps in mitigating climate change.

Carbon dioxide is a primary greenhouse gas emitted through human activities. When fuels like octane burn, balancing the chemical reactions can further help in calculating potential emissions accurately.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental skill in chemistry to determine the amounts needed for a reaction. For octane, the molar mass is calculated based on its chemical formula, \( ext{C}_8 ext{H}_{18}\).
Here's how you can calculate it:

• Identify the Elements: Octane consists of carbon and hydrogen. The formula tells us there are 8 carbon atoms and 18 hydrogen atoms.
• Atomic Mass: The atomic mass of carbon (C) is approximately 12.01 \( ext{g/mol}\), and hydrogen (H) is about 1.01 \( ext{g/mol}\).
• Calculation: Multiply the number of atoms by their respective atomic masses. Thus, for octane: \[ \text{Molar Mass} = (8 \times 12.01) + (18 \times 1.01) = 114.22 \text{ g/mol} \]

Having the molar mass is critical in converting between the mass of a substance and the amount of substance in moles, enabling accurate calculations in chemical reactions.