The complete combustion of octane, C8H18, a component of gasoline, proceeds as follows: 2 C₈H₁₈(l) + 25 O₂(g) → 16 CO₂(g) + 18 H₂O(g) (a) How many moles of O₂ are needed to burn 1.50 mol of C₈H₁₈?

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Identify the balanced chemical equation for the combustion of octane: \(2 \text{C}_8\text{H}_{18} + 25 \text{O}_2 \rightarrow 16 \text{CO}_2 + 18 \text{H}_2\text{O}\).

Determine the mole ratio between \(\text{C}_8\text{H}_{18}\) and \(\text{O}_2\) from the balanced equation. The ratio is 2 moles of \(\text{C}_8\text{H}_{18}\) to 25 moles of \(\text{O}_2\).

Set up a proportion to find the moles of \(\text{O}_2\) needed for 1.50 moles of \(\text{C}_8\text{H}_{18}\): \(\frac{2 \text{ moles C}_8\text{H}_{18}}{25 \text{ moles O}_2} = \frac{1.50 \text{ moles C}_8\text{H}_{18}}{x \text{ moles O}_2}\).

Solve the proportion for \(x\) to find the moles of \(\text{O}_2\) required.

Verify the calculation by checking the units and ensuring the mole ratio is correctly applied.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to calculate how much of each substance is needed or produced in a reaction based on balanced chemical equations. Understanding stoichiometry is essential for solving problems involving the amounts of reactants and products.

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction with equal numbers of each type of atom on both sides of the equation. In the combustion of octane, the equation shows the ratio of octane to oxygen and the products formed. This balance is crucial for determining the exact amounts of reactants needed for a complete reaction.

Mole Concept

The mole concept is a fundamental principle in chemistry that defines a mole as 6.022 x 10^23 particles (atoms, molecules, etc.). It provides a bridge between the atomic scale and macroscopic quantities, allowing chemists to count particles by weighing them. In this question, the mole concept is used to relate the amount of octane to the required amount of oxygen for combustion.

The complete combustion of octane, C8H18, a component of gasoline, proceeds as follows: 2 C8H18(l) + 25 O2(g) → 16 CO2(g) + 18 H2O(g) (a) How many moles of O2 are needed to burn 1.50 mol of C8H18?