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The Ideal Gas Law is a fundamental principle to understand the behavior of gases. It combines several gas laws into one formula: \( PV = nRT \), where:

• \( P \) represents pressure,
• \( V \) is volume,
• \( n \) is the number of moles,
• \( R \) is the universal gas constant, and
• \( T \) is temperature in Kelvin.

This formula helps us relate the physical properties of gases. In this exercise, it is used to compare the pressures and volumes before and after combustion. By setting up the equation with the initial conditions and solving for the final conditions, we can understand how the volume of gases changes after a chemical reaction. The Ideal Gas Law is key for finding how much a gas can expand or contract under different conditions.

To determine the molecular formula of a hydrocarbon, we use data from experiments or given conditions after a chemical reaction. The first step is to ascertain the empirical formula or the simplest ratio of atoms in the molecule.
From the empirical formula, we can deduce the molecular formula by considering the molecular mass determined experimentally and comparing it with the molar mass of the empirical formula. The molecular formula is usually expressed as \(C_xH_y\), illustrating the number of carbon \(C\) and hydrogen \(H\) atoms.Subsequently, if the molar mass of the compound is known, we compare it with the empirical formula mass. This helps adjust the subscripts \(x\) and \(y\) to reflect the actual number of atoms in a molecule, providing the molecular formula. This requires solving for the totals using the actual molecular weight.

The concept of partial pressures is crucial when dealing with gas mixtures. According to Dalton's Law of Partial Pressures, each gas in a mixture contributes its own pressure as if it were the only gas present. It is calculated as the fraction of the total pressure exerted by that particular gas. In this exercise:

• The total pressure of the gaseous mixture of CO鈧� (carbon dioxide) and H鈧侽 (water vapor) is given.
• To find the individual partial pressures, we determine how each gas contributes to the total.

We use this information to find out how many moles are present, and ultimately, how many molecules are involved in the chemical reaction. Understanding partial pressures is important for analyzing results in reactions involving multiple gas products.

The empirical formula represents the simplest whole number ratio of atoms within a compound. It is derived from the amount of each element present. For example, if a compound contains carbon and hydrogen, we calculate the number of carbon and hydrogen atoms involved per molecule.
In a combustion reaction, a hydrocarbon's empirical formula can be deduced from the amount of CO鈧� and H鈧侽 generated. We compare their moles and establish ratios to express the formula as \(C_xH_y\), where \(x\) and \(y\) are whole numbers.
The empirical formula gives us a basic understanding of the composition and ratio but does not convey the exact number of atoms, which is highlighted in the molecular formula. This distinction is essential for accurately naming and understanding the properties of chemical compounds.