Problem 62 - Chemistry: The Central Science in SI Units, Global Edition

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. (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

(a) False - The freezing point decreases when adding a solvent to a nonvolatile solute. (b) False - The solid formed during freezing is nearly pure solvent. (c) False - The freezing point is dependent on the concentration of the solute. (d) True - The boiling point increases in proportion to the concentration of the solute. (e) True - The vapor pressure of the solvent over the solution is lower than in the pure solvent.

Step 1: a) The freezing point of the solution is unchanged by the addition of the solvent.

This statement is false. When a nonvolatile solute is added into a solvent, the freezing point of the solution decreases. This phenomenon is called freezing point depression and can be explained by the fact that solute particles interfere with the formation of the solid structure of the solvent, thus lowering the temperature at which the solution freezes.

Step 2: b) The solid that forms as the solution freezes is nearly pure solute.

This statement is false. When a solution freezes, the solid formed is generally composed of nearly pure solvent. This is because solute particles disrupt the regular structure of the solid solvent when it freezes. As freezing occurs, the solvent freezes preferentially, leaving behind a more concentrated solution with the remaining solute particles.

Step 3: c) The freezing point of the solution is independent of the concentration of the solute.

This statement is false. The freezing point depression includes the relationship between the freezing point of the solution and the concentration of the solute. The lower the freezing point of the solution, the greater the concentration of the solute.

Step 4: d) The boiling point of the solution increases in proportion to the concentration of the solute.

This statement is true. An increase in the concentration of a nonvolatile solute leads to an increase in the boiling point of the solution. This phenomenon is called boiling point elevation and can be explained by solute particles disrupting the escaping tendency of solvent molecules from the liquid phase into the gas phase. As a result, a higher temperature is needed to provide the extra energy required for solvent molecules to escape, thus raising the boiling point of the solution.

Step 5: e) At any temperature, the vapor pressure of the solvent over the solution is lower than what it would be for the pure solvent.

This statement is true. A nonvolatile solute lowers the vapor pressure of the solvent over the solution as compared to the vapor pressure of the pure solvent. This is because the solute particles decrease the number of solvent particles at the surface of the liquid phase, reducing their chance of escaping into the gas phase. Consequently, the vapor pressure of the solvent in a solution containing a nonvolatile solute is lower than its vapor pressure when it's pure.

Key Concepts

Freezing Point Depression

Freezing point depression occurs when a nonvolatile solute is added to a liquid solvent, causing the freezing point of the resulting solution to be lower than that of the pure solvent. This happens because solute particles interfere with the orderly structure required for the solvent to solidify. These particles disrupt the formation of the solid lattice, meaning more energy (in the form of lower temperatures) is needed to freeze the solution. This is why the solution freezes at a temperature lower than that of the pure solvent.

The extent of freezing point depression is directly related to the concentration of the solute. This relationship is quantitatively expressed by the formula: \[ \Delta T_f = i \cdot K_f \cdot m \] Where:

• \(\Delta T_f\) is the decrease in freezing point.
• \(i\) is the van't Hoff factor (number of particles the solute splits into).
• \(K_f\) is the freezing point depression constant of the solvent.
• \(m\) is the molality of the solution.

Thus, the more solute you dissolve in the solvent, the greater the depression of the freezing point will be.

Boiling Point Elevation

Boiling point elevation is observed when a nonvolatile solute is added to a liquid solvent. This results in an increase in the boiling point of the solution compared to the pure solvent. When solute particles are mixed with solvent particles, they obstruct the solvent molecules from entering the vapor phase. Therefore, more heat (and thus a higher temperature) is required to provide the energy necessary for the solvent molecules to overcome this barrier and escape as gas.

This increase in boiling point is calculated using the following formula: \[ \Delta T_b = i \cdot K_b \cdot m \] Where:

• \( \Delta T_b \) is the boiling point elevation.
• \( i \) is the van't Hoff factor.
• \( K_b \) is the boiling point elevation constant of the solvent.
• \( m \) is the molality of the solution.

Increasing the amount of solute leads to a higher boiling point elevation, making this effect proportional to the solute concentration.

Vapor Pressure Lowering

Vapor pressure lowering is a colligative property that occurs when a nonvolatile solute is added to a solvent. This means the solution's vapor pressure is less than that of the pure solvent. Vapor pressure is a measure of the tendency of particles to escape from the liquid phase into the gas phase. When a solute is present, it reduces the number of solvent molecules at the surface, limiting the number that can escape as vapor.

The phenomenon can be described by Raoult's Law, which states that the vapor pressure of the solvent above a solution is proportional to the mole fraction of the solvent in the solution. Mathematically, the relationship is expressed as: \[ P_{solution} = X_{solvent} \cdot P^0_{solvent} \] Where:

• \( P_{solution} \) is the vapor pressure of the solution.
• \( X_{solvent} \) is the mole fraction of the solvent.
• \( P^0_{solvent} \) is the vapor pressure of the pure solvent.

This phenomenon has practical applications, such as in antifreeze used in car engines, where lowering vapor pressure helps maintain fluid levels over a range of temperatures.