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Raoult's Law is a fundamental principle used to determine the vapor pressure of a solution. It expresses that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution. This relationship is expressed through the formula:\[ P_{\text{solution}} = \chi_{\text{solvent}} \times P_{\text{pure}} \]where:

• \( P_{\text{solution}} \) is the vapor pressure of the solution.
• \( \chi_{\text{solvent}} \) is the mole fraction of the solvent.
• \( P_{\text{pure}} \) is the vapor pressure of the pure solvent.

In this exercise, Raoult's Law is used to calculate the vapor pressure of water in a solution containing calcium chloride. The mole fraction of water is determined and then multiplied by the vapor pressure of pure water at a given temperature to find the solution's vapor pressure.

The van't Hoff factor (\(i\)) measures the number of particles per formula unit generated from a solute when dissolved in a solvent. It directly affects colligative properties like vapor pressure depression, boiling point elevation, and freezing point depression. For ionic compounds like calcium chloride, \(i\) can be higher than 1 since such compounds dissociate into multiple ions.In this scenario involving calcium chloride (\(\text{CaCl}_2\)), the theoretical van't Hoff factor is 3, because it dissociates into three ions (one \(\text{Ca}^{2+}\) and two \(\text{Cl}^-\)). However, due to incomplete dissociation or ion interactions, the effective van't Hoff factor could be different. Therefore, in the solution, an experimental \(i\) of 2.7 was used to account for these factors and give a more accurate result.

The mole fraction is an important term which represents the ratio of the number of moles of a specific component to the total number of moles in a mixture. It offers a way to express the concentration of a component in a solution without dependence on units of mass or volume. The mole fraction \(\chi\) is calculated using the formula:\[\chi = \frac{\text{moles of component}}{\text{total moles in solution}}\]In this exercise, the moles of water (the solvent) and the effective moles of ions from calcium chloride (solute) are calculated first. Then the mole fraction of water is determined using these moles to apply Raoult’s Law accurately. This involves:

• Calculating moles of \(\text{H}_2\text{O}\) and corrected moles of solute.
• Finding mole fraction of \(\text{H}_2\text{O}.\)

Calcium chloride (\(\text{CaCl}_2\)) is a common ionic compound that strongly influences colligative properties when dissolved in water due to its dissociation into multiple ions. This solute is particularly noted for its ability to lower the freezing point, making it useful in de-icing and a variety of industrial applications. When dissolved, calcium chloride dissociates into one calcium ion (\(\text{Ca}^{2+}\)) and two chloride ions (\(\text{Cl}^-\)).This dissociation increases the number of solute particles, thereby affecting properties such as vapor pressure. For this reason, the van't Hoff factor is used to correct for the number of particles in solution, representing how the presence of \(\text{CaCl}_2\) in water lowers the vapor pressure more than most molecular solutes would.

Vapor pressure depression is a colligative property that occurs when a non-volatile solute is added to a solvent, resulting in a lower vapor pressure compared to the pure solvent. This effect happens because the solute particles occupy surface space, preventing some solvent molecules from escaping into the vapor phase as easily as they would from a pure solvent surface. The exercise demonstrates this effect by showing how adding calcium chloride to water lowers its vapor pressure. Using Raoult's Law, we calculate the decrease in vapor pressure as part of understanding vapor pressure depression. This emphasis on mole fraction and the van't Hoff factor is crucial for calculating the magnitude of depression caused by the solute.