Which of the following statements is(are) true? Correct the false statements. a. The vapor pressure of a solution is directly related to the mole fraction of solute. b. When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} \mathrm{C} .\) c. Colligative properties depend only on the identity of the solute and not on the number of solute particles present. d. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} \mathrm{C}\) because sugar has a higher boiling point than water.

The vapor pressure of a solution is directly related to the mole fraction of solute. This statement is false. The vapor pressure of a solution is directly related to the mole fraction of the solvent, not the solute. According to Raoult's Law, the vapor pressure of a solution is proportional to the mole fraction of the solvent. So the corrected statement is: "The vapor pressure of a solution is directly related to the mole fraction of the solvent."

When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} \mathrm{C}\). This statement is true. When a solute is added to water, the vapor pressure of the water in the solution decreases because the solute molecules occupy some of the water's surface, making it harder for water molecules to escape into the vapor phase. Since the vapor pressure of pure ice at \(0^{\circ} \mathrm{C}\) is higher than the vapor pressure of the water-solute solution, this statement is correct.

Colligative properties depend only on the identity of the solute and not on the number of solute particles present. This statement is false. Colligative properties, such as freezing-point depression, boiling-point elevation, osmotic pressure, and vapor pressure lowering, depend only on the number of solute particles present in the solution, regardless of their identity. So the corrected statement is: "Colligative properties depend only on the number of solute particles present and not on the identity of the solute."

When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} \mathrm{C}\) because sugar has a higher boiling point than water. This statement is true in the sense that the boiling point of the solution increases above \(100^{\circ} \mathrm{C}\), but not strictly because sugar has a higher boiling point than water. When a solute like sugar is added to water, the boiling point elevation occurs due to the decrease in vapor pressure of the solution as compared to the pure solvent. The boiling point increases because more energy is required to allow the solvent molecules to overcome the reduced vapor pressure and escape into the vapor phase. The boiling point increase doesn't directly depend on the boiling point of the solute itself.