The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally N₂(79%) and O₂(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. (c) The production of NOx gases is an unwanted side reaction of the main engine combustion process that turns octane, C₈H₁₈, into CO₂ 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.

Verified step by step guidance

1. Determine the balanced chemical equation for the combustion of octane: \(2 \text{C}_8\text{H}_{18} + 25 \text{O}_2 \rightarrow 16 \text{CO}_2 + 18 \text{H}_2\text{O}\).
2. Calculate the moles of octane (\(\text{C}_8\text{H}_{18}\)) using its molar mass.
3. Use the stoichiometry of the balanced equation to find the moles of \(\text{O}_2\) required for the combustion of the given moles of octane.
4. Calculate the moles of \(\text{O}_2\) that are not used for octane combustion (15% of total \(\text{O}_2\)).
5. Use the stoichiometry of the reaction \(2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2\) to find the moles of \(\text{NO}_2\) produced and convert it to grams using the molar mass of \(\text{NO}_2\).

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equations. It allows chemists to determine the proportions of substances involved in reactions, which is essential for predicting how much product will be formed from given amounts of reactants. In this question, stoichiometry is crucial for calculating the grams of nitrogen dioxide produced from the combustion of octane.

Combustion Reactions

Combustion reactions are exothermic reactions that occur when a substance reacts with oxygen, typically producing heat, light, carbon dioxide, and water. In the context of this question, the combustion of octane (C8H18) is the primary reaction, and understanding the products and byproducts, such as nitrogen oxides (NOx), is vital for calculating the amounts produced during the process.

Gas Laws and Molar Mass

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature, while molar mass is the mass of one mole of a substance. In this problem, knowing the molar mass of nitrogen dioxide (NO2) is necessary to convert moles of NO2 produced into grams, allowing for the final calculation of how much nitrogen dioxide is generated from the combustion of octane.