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Boiling point elevation is a colligative property that represents the increase in the boiling point of a solution compared to the pure solvent. This happens because the addition of solute particles interferes with the formation of vapor, requiring higher temperatures for the solvent to transition into the vapor phase. The extent of boiling point elevation depends on several factors:

• The type of solute: Whether it dissociates into ions or not.
• The concentration of the solution: Measured in molality (moles of solute per kilogram of solvent).
• The van't Hoff factor (i): This indicates the number of particles a solute releases in solution.

The formula used to calculate boiling point elevation is:\[ \Delta T_b = i \times K_b \times m \]Where:

• \(\Delta T_b\) is the boiling point elevation.
• \(i\) is the van't Hoff factor.
• \(K_b\) is the ebullioscopic constant (unique for every solvent).
• \(m\) is the molality of the solution.

In the provided exercise, among the different solutions, Na鈧係O鈧� has the largest van鈥檛 Hoff factor and molality product, meaning it causes the highest boiling point elevation.

Freezing point depression occurs when a solute is added to a solvent, resulting in the lowering of the freezing point compared to the pure solvent. Like boiling point elevation, freezing point depression is also a colligative property, meaning it depends on the quantity of solute particles in the solution. The presence of solute particles inhibits the ability of the solvent molecules to organize into a solid structure, thereby requiring a lower temperature to reach the point of solidification.The calculation of freezing point depression uses the formula:\[ \Delta T_f = i \times K_f \times m \]Where:

• \(\Delta T_f\) is the freezing point depression.
• \(i\) is the van't Hoff factor, representing particle dissociation.
• \(K_f\) is the cryoscopic constant, specific to each solvent.
• \(m\) is the molality of the solution.

In the exercise example, Na鈧係O鈧� also has the greatest \(i \times m\) value, resulting in the lowest freezing point due to the most significant interference from solute particles.

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its solid or liquid phase at a given temperature. When a nonvolatile solute is added to a solvent, the vapor pressure of the solution becomes lower than that of the pure solvent. This is because solute particles occupy space at the surface, hindering solvent molecules from escaping into the vapor phase. Thus, vapor pressure is also a colligative property.The relationship of vapor pressure reduction can be explained using Raoult's Law, which states:\[ P_{solution} = X_{solvent} \times P_{solvent}\]Where:

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

According to the exercise, the solution containing HOCH鈧侰H鈧侽H (a nonvolatile nonelectrolyte) has the least number of dissociated particles, leading to the highest relative water vapor pressure among the given solutions.