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 depends on the mole fraction of the solvent, not the solute. As the mole fraction of the solvent decreases due to the presence of solute, its vapor pressure decreases. To correct this statement: '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. The addition of a solute to the water decreases the mole fraction of the water molecules and, subsequently, the vapor pressure of the water in solution. This effect is known as "vapor pressure lowering" and it is a colligative property.

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 are dependent on the number of solute particles (meaning the concentration of solute) and not on the nature of the solute particles. To correct this statement: '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 partially true but requires clarification. When sugar is added to water, the boiling point of the solution does indeed increase. However, the increase is not because sugar has a higher boiling point than water. Instead, it is due to the solute (sugar) lowering the vapor pressure of the solution, which leads to an increase in the boiling point. To improve this statement: 'When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} \mathrm{C}\) due to the decrease in vapor pressure caused by the presence of solute particles.'