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). 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 of the solution as compared to the pure solvent.

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 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."

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. 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.

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, 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."

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 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.

Key concepts

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a liquid on its liquid phase when they are in equilibrium. This concept is crucial in understanding colligative properties. A key factor affecting vapor pressure is the arrangement and type of molecules present:

• Pure substances typically have a higher vapor pressure compared to solutions because a greater mole fraction of the solvent translates to more solvent molecules in the vapor phase.
• In solutions, the presence of a solute decreases the number of free solvent molecules available to escape into the vapor phase, thus lowering the vapor pressure.

By understanding how vapor pressure works, students can see why adding a non-volatile solute to a solvent lowers the vapor pressure of the solution compared to the pure solvent.
This is explained by the fact that solute molecules occupy part of the liquid's surface, hindering the escape of solvent molecules.

Raoult's Law

Raoult's Law is the principle stating that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solvent present. This law can be expressed mathematically as:$$P_{extsolution}=P_{extsolvent}^{extpure}\times X_{extsolvent}$$where:

• $P_{\text{solution}}$ is the vapor pressure of the solution.
• $P_{\text{solvent}}^{\text{pure}}$ is the vapor pressure of the pure solvent.
• $X_{\text{solvent}}$ is the mole fraction of the solvent in the solution.

It's important to note that Raoult's Law applies to ideal solutions where interactions between molecules of different components are similar to those between molecules of the same component. This means deviations can occur in real solutions, especially those involving strong intermolecular forces or highly non-ideal behavior.

Boiling Point Elevation

Boiling point elevation is another essential aspect of colligative properties. It occurs when a solute is added to a solvent, resulting in an increase in the boiling point of the solution. This phenomenon is characterized by several factors:

• The addition of solute particles disrupts the equilibrium between the liquid state and the vapor state of the solvent.
• This disruption results in a decreased vapor pressure, meaning it requires more energy (a higher temperature) for the solution to reach the boiling point where the vapor pressure equals the external pressure.

The increase in boiling point, $$\mathrm{\Delta }{T}_b=i\cdot K_b\cdot m$$where:

• $\mathrm{\Delta }{T}_b$ is the boiling point elevation.
• $i$ is the van't Hoff factor (ionization factor).
• $K_b$ is the ebullioscopic constant of the solvent.
• $m$ is the molality of the solution.

Through this understanding, it becomes clear that boiling point elevation is not about the solute's own boiling point, but how its presence affects the dynamics of solvent molecules, thus requiring more energy to boil.