Question

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.

Short answer

The corrected statements are: a. The vapor pressure of a solution is directly related to the mole fraction of the solvent. b. When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} \mathrm{C}\) (True statement). c. Colligative properties depend only on the number of solute particles present and not on the identity of the solute. d. 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.

Step-by-step solution

Statement a

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.'

Statement b

When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} \mathrm{C}\). 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.

Statement c

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.'

Statement 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. 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.'

Key concepts

Vapor Pressure Lowering

When a solute is added to a solvent, the solution exhibits a phenomenon known as vapor pressure lowering. This occurs because the solute molecules occupy space at the surface of the liquid, reducing the number of solvent molecules that can escape into the vapor phase. As a result, the vapor pressure of the solution is lower than that of the pure solvent.
This concept is crucial in understanding how solutes affect the properties of solutions. It is a colligative property, meaning it depends only on the number of solute particles in the solution, not their identity. When the solvent's vapor pressure decreases, it influences other properties such as boiling and freezing points, altering them compared to the pure solvent.

Boiling Point Elevation

The phenomenon of boiling point elevation can be explained by the presence of solute in a solvent. When a non-volatile solute is dissolved, it disrupts the normal phase equilibrium between liquid and gas. This means that more heat is required to cause the solvent molecules to escape into the vapor phase.
The result is an increase in the boiling point of the solution compared to the pure solvent. This effect is directly proportional to the molal concentration of the solute and is vital in applications where temperature control is crucial, like in cooking or antifreeze production. Understanding boiling point elevation helps us grasp how solutes can change the physical properties of a solution.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a solution. It is defined as the ratio of moles of one component to the total number of moles in the solution.
This concept is instrumental in determining colligative properties such as vapor pressure lowering. For example, the vapor pressure of a solution is dependent on the mole fraction of the solvent—if more solute is added, reducing the mole fraction of the solvent, the vapor pressure of the solution decreases.

• Formula: Mole Fraction of Solvent = (Moles of Solvent) / (Total Moles of Solution)
• Formula: Mole Fraction of Solute = (Moles of Solute) / (Total Moles of Solution)

Grasping mole fraction helps in analyzing how solutions behave and in predicting changes in their physical properties.

Solute and Solvent Interactions

When a solute is dissolved in a solvent, the interactions between them have significant effects on the solution's properties. These effects are known as colligative properties, which depend on the number of solute particles in the solution and not on their type.
The main interactions include:

• Reduction of solvent's ability to vaporize, leading to vapor pressure lowering.
• Disruption of the solvent structure, leading to boiling point elevation and freezing point depression.

Understanding solute and solvent interactions helps predict the changes in solution behavior, such as how the addition of a solute affects the phase transition points of the solvent.
This concept aids in numerous practical applications, from antifreeze mixtures to cooking, where altering solution properties is essential.