The combustion of gasoline produces carbon dioxide and water. Assume gasoline to be pure octane (C₈H₁₈) and calculate the mass (in kg) of carbon dioxide that is added to the atmosphere per 1.0 kg of octane burned. (Hint: Begin by writing a balanced equation for the combustion reaction.)

Verified step by step guidance

1. Write 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 molar mass of octane (C8H18) using the atomic masses of carbon (C) and hydrogen (H).
3. Determine the number of moles of octane in 1.0 kg by dividing the mass of octane by its molar mass.
4. Use the stoichiometry of the balanced equation to find the moles of CO2 produced per mole of octane burned.
5. Calculate the mass of CO2 produced by multiplying the moles of CO2 by its molar mass, and convert the result to kilograms.

Key Concepts

Combustion Reaction

A combustion reaction is a chemical process in which a substance (typically a hydrocarbon) reacts with oxygen to produce carbon dioxide and water, releasing energy. For octane (C8H18), the balanced equation for its complete combustion is C8H18 + 12.5 O2 → 8 CO2 + 9 H2O. Understanding this reaction is crucial for determining the products and their quantities when octane is burned.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the mass of products formed from a given mass of reactants. In this case, stoichiometry will help calculate the mass of carbon dioxide produced from burning 1.0 kg of octane by using molar ratios derived from the balanced combustion equation.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For octane (C8H18), the molar mass is approximately 114.22 g/mol. Knowing the molar mass is essential for converting between mass and moles, which is necessary for applying stoichiometry to find the mass of carbon dioxide produced from the combustion of octane.