Problem 25 - Chemistry An Atoms First Approach

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.

Step-by-Step Solution

Answer

a. False - The vapor pressure of a solution is directly related to the mole fraction of the solvent. b. True c. False - Colligative properties depend only on the number of solute particles present, not on the identity of the solute. d. True (with incorrect reasoning) - When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\) because of the boiling point elevation effect, a colligative property.

Step 1: Statement a

: 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 is directly related to the mole fraction of the solvent, not the solute. This relationship is described by Raoult's Law presented as: \(P_{solution} = x_{solvent} \cdot P_{solvent}^\circ\) Here, \(P_{solution}\) is the vapor pressure of the solution, \(x_{solvent}\) is the mole fraction of the solvent, and \(P_{solvent}^\circ\) is the vapor pressure of the pure solvent. Corrected Statement: The vapor pressure of a solution is directly related to the mole fraction of the solvent.

Step 2: Statement b

: b. When a solute is added to water, the water in solution has a lower vapor pressure than that of pure ice at \(0^{\circ} C\). This statement is true. When a non-volatile solute is added to water, the vapor pressure of water in the solution decreases. It happens because the solute molecules occupy the surface of the solution, reducing the number of water molecules that can escape to the vapor phase.

Step 3: Statement c

: 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 depend on the number of solute particles present in a solution, not on their identity. Examples of colligative properties include freezing point depression, boiling point elevation, osmotic pressure, and vapor pressure lowering. Corrected Statement: Colligative properties depend only on the number of solute particles present, not on the identity of the solute.

Step 4: Statement d

: d. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\) because sugar has a higher boiling point than water. This statement is true, but the reasoning is incorrect. When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\), but the reason is related to boiling point elevation, a colligative property. This increase in boiling point is proportional to the molality of the solute and does not depend on the boiling point of sugar. Corrected Statement: When sugar is added to water, the boiling point of the solution increases above \(100^{\circ} C\) because of the boiling point elevation effect, a colligative property.