Problem 101 - Chemistry

Question

A combustion reaction involves the reaction of a substance with oxygen gas. The complete combustion of any hydrocarbon (binary compound of carbon and hydrogen) produces carbon dioxide and water as the only products. Octane is a hydrocarbon that is found in gasoline. Complete combustion of octane produces 8 liters of carbon dioxide for every 9 liters of water vapor (both measured at the same temperature and pressure). What is the ratio of carbon atoms to hydrogen atoms in a molecule of octane?

Step-by-Step Solution

Answer

The ratio of carbon atoms to hydrogen atoms in a molecule of octane is 4:9.

Step 1: Analyze the combustion reaction

A combustion reaction involves the reaction of a substance with oxygen gas. In a complete combustion of a hydrocarbon, carbon dioxide (CO2) and water (H2O) are produced as the only products. The general equation of combustion for a hydrocarbon with a generic formula CxHy can be written as: CxHy + O2 -> CO2 + H2O

Step 2: Use the given ratio of products to determine the number of carbon and hydrogen atoms

We are given that 8 liters of CO2 are produced for every 9 liters of H2O. Since the volume ratio is the same as the molar ratio (at the same temperature and pressure), we can deduce that: 8 moles of CO2 are produced per 9 moles of H2O In one mole of CO2, there is one mole of carbon. Thus, 8 moles of CO2 implies 8 moles of carbon. In one mole of H2O, there are two moles of hydrogen. As a result, 9 moles of H2O implies 9 * 2 = 18 moles of hydrogen.

Step 3: Find the ratio of carbon atoms to hydrogen atoms in octane

Now, we know that octane produces 8 moles of carbon and 18 moles of hydrogen during complete combustion. The ratio of carbon atoms to hydrogen atoms in octane is: \(\frac{\text{moles of carbon}}{\text{moles of hydrogen}} = \frac{8}{18}\) Simplifying this fraction: \(\frac{8}{18} = \frac{4}{9}\) Thus, the ratio of carbon atoms to hydrogen atoms in a molecule of octane is 4:9.