Problem 62 - Chemistry The Central Science In Si Units

Question

You make a solution of a nonvolatile solute with a liquid solvent. Indicate if each of the following statements is true or false. (a) The freezing point of the solution is unchanged by addition of the solvent. (b) The solid that forms as the solution freezes is nearly pure solute. (c) The freezing point of the solution is independent of the concentration of the solute. (d) The boiling point of the solution increases in proportion to the concentration of the solute. \((\mathbf{e})\) At any temperature, the vapor pressure of the solvent over the solution is lower than what it would be for the pure solvent.

Step-by-Step Solution

Answer

Statements (d) and (e) are true; (a), (b), and (c) are false.

Step 1: Understand the Effect of Solute on Freezing Point

When a nonvolatile solute is added to a solvent, the freezing point of the solution decreases. This is known as freezing point depression. Hence, statement (a) is false because the freezing point of the solution is lowered, not unchanged.

Step 2: Analyze the Composition of the Solid

As a solution freezes, the solvent solidifies, leaving most of the solute behind in the liquid phase. Therefore, the solid that forms is primarily the pure solvent, not the pure solute. Thus, statement (b) is false.

Step 3: Examine the Freezing Point and Solute Concentration

The freezing point depression is directly related to the concentration of the solute in the solution. Therefore, statement (c) is false because the freezing point of the solution depends on the concentration of the solute.

Step 4: Assess Boiling Point Elevation

The boiling point of a solution increases with the addition of a nonvolatile solute. This is called boiling point elevation, and it is proportional to the concentration of the solute. Thus, statement (d) is true.

Step 5: Consider Vapor Pressure of the Solvent

The presence of a nonvolatile solute reduces the vapor pressure of the solvent above the solution compared to the pure solvent. Thus, statement (e) is true.

Key Concepts

Freezing Point Depression

When you dissolve a nonvolatile solute into a liquid solvent, the freezing point of that solution decreases. This phenomenon is known as freezing point depression. But why does this happen? It occurs because the solute particles disrupt the formation of the solid lattice that the solvent molecules need to form when freezing.

• Solute particles interfere with crystal formation of the solvent.
• More energy (lower temperature) is needed for the solution to solidify.

The extent of freezing point depression depends on the concentration of the solute. Specifically, it is directly proportional to the molality of the solute. You can calculate the change in freezing point using the formula \[\Delta T_f = i \cdot K_f \cdot m\]where \(\Delta T_f\) is the freezing point depression, \(i\) is the van't Hoff factor, *\(K_f\)* is the freezing point depression constant for the solvent, and \(m\) is the molality of the solution.

Boiling Point Elevation

Adding a nonvolatile solute to a solvent doesn’t just impact freezing points; it also raises the boiling point. This is known as boiling point elevation. The presence of solute particles in a solution makes it harder for solvent molecules to escape into the vapor phase, therefore, requiring a higher temperature to reach boiling.

• Solute particles create more disorder in the liquid state.
• More heat is required to allow solvent molecules to vaporize.

Just like freezing point depression, boiling point elevation is also dependent on the concentration of the solute, specifically the molality. The mathematical formula that expresses this relationship is given by \[\Delta T_b = i \cdot K_b \cdot m\]where \(\Delta T_b\) is the boiling point elevation, \(i\) is the van't Hoff factor, \(K_b\) is the boiling point elevation constant, and \(m\) is the molality of the solution. The more solute present, the more the boiling point is raised.

Vapor Pressure Lowering

When a nonvolatile solute is added to a pure solvent, the vapor pressure of the resulting solution is less than that of the pure solvent. This effect is known as vapor pressure lowering. The addition of solute creates fewer escaping solvent molecules, thus reducing vapor pressure.

• Solute molecules take up space at the liquid surface.
• Fewer solvent molecules are able to enter the vapor phase.

This principle is quantitatively described by Raoult's law, which states that the vapor pressure of the solvent over the solution \(P_1\) is equal to the mole fraction of the solvent \(X_1\) times the vapor pressure of the pure solvent \(P_{1}^{0}\).\[P_1 = X_1 \cdot P_{1}^{0}\]Understanding these colligative properties reveals the profound impact even a small amount of solute can have on a solution’s physical properties.