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The ideal gas law is a fundamental principle that helps relate the physical properties of a gas. It can be expressed with the formula:\[ PV = nRT \]In this equation, \( P \) represents pressure measured in atmospheres, \( V \) stands for the volume in liters, \( n \) refers to the number of moles of gas, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin. The ideal gas law allows us to calculate any one of the variables if the others are known.In the analysis of xylene, we convert all measurements accordingly:- Volume: Convert from milliliters to liters by dividing by 1000.- Temperature: Convert Celsius to Kelvin by adding 273.15.By rearranging the ideal gas law to solve for moles \( n \):\[ n = \frac{PV}{RT} \]we can find the quantity of gas present, which is an essential step for further calculations.

An empirical formula represents the simplest whole-number ratio of atoms within a compound. To determine this, we convert the percent composition of each element to moles. For xylene: - Carbon is 90.50% by mass. Divide this by carbon's atomic mass, 12.01 g/mol. - Hydrogen is 9.50% by mass. Divide this by hydrogen's atomic mass, 1.008 g/mol. These calculations give us the number of moles of each element. We then establish the simplest ratio by dividing all values by the smallest one obtained. This simplified ratio forms the empirical formula, giving us a foundational understanding of the compound's composition. For xylene, this ensures we know the basic atomic structure before determining its full molecular formula.

Molar mass is an important concept, representing the mass of one mole of a substance. It’s calculated by dividing the mass of the sample by the number of moles.For xylene, we first found moles using the ideal gas law:\[ n = \frac{PV}{RT} \]With the known mass of the sample \( 2.334 \) grams and the calculated moles \( n \), the molar mass can be determined:\[ \text{Molar Mass} = \frac{\text{mass}}{\text{moles}} = \frac{2.334}{n} \]This step is crucial, as it connects the physical mass of the compound with its chemical identity, allowing us to bridge between the empirical formula and the actual structure, the molecular formula.

Percent composition analysis involves determining the percentage by mass of each element within a compound. This is crucial for the initial steps of identifying the empirical formula. For example, in xylene: - Carbon forms 90.50% of the compound's weight. - Hydrogen accounts for 9.50% of the weight. By assuming a 100 g sample, these percentages directly translate to mass. From here, we calculate the moles for each element by dividing the mass by the respective atomic weights. This process provides insight into the element proportions, forming the basis for solving both empirical and molecular formulas, highlighting the relationship between the chemical makeup and its atomic components.