91影视

When we add a solute to a liquid, it increases the liquid鈥檚 boiling point, which is nailed by the principle of boiling point elevation. This happens because the solute particles disperse throughout the liquid, reducing the solvent's ability to vaporize, thus requiring a higher temperature to boil.

The equation for determining the boiling point elevation is: \( \Delta T_b = K_b \times \, m \, \times i \)

• \( \Delta T_b \) is the boiling point elevation.
• \( K_b \) is the ebullioscopic constant of the liquid.
• \( m \) stands for molality of the solution.
• \( i \) is the Van't Hoff factor, representing the number of particles the solute breaks into.

In the exercise, each solution鈥檚 boiling point change is calculated using this formula, and it's found that the 0.020 m HF solution has the same boiling point increase as the 0.040 m C6H12O6 solution. This exemplifies the importance of both the molality and Van't Hoff factor for determining boiling point changes.

Vapor pressure is lowered when a solute is added to a solvent. The presence of solute particles on the surface decreases the number of solvent molecules that can escape into the vapor phase, thus lowering the vapor pressure. This concept is key in colligative properties because it's only the number of solute particles, and not their type, that matters.

According to Raoult's Law: \( \Delta P = X_{\text{solute}} \times P_{\text{solvent}}^{0} \)

• \( \Delta P \): Change in vapor pressure.
• \( X_{\text{solute}} \): Mole fraction of the solute.
• \( P_{\text{solvent}}^{0} \): Vapor pressure of the pure solvent.

In the exercise, solutions are compared based on their concentration to identify which has the highest vapor pressure. The solution with the lowest concentration of solute, 0.010 m Na3PO4, is predicted to have the highest vapor pressure due to the least vapor pressure lowering.

Freezing point depression occurs when a solute is added to a liquid, lowering its freezing point. This is because solute particles disrupt the formation of the solid crystalline structure of the solvent, therefore requiring a lower temperature to solidify.

We use this formula to calculate the depression: \( \Delta T_f = K_f \times \ m \times i \)

• \( \Delta T_f \) is the freezing point depression.
• \( K_f \) is the cryoscopic constant of the liquid.
• \( m \) is the molality of the solution.
• \( i \) is the Van't Hoff factor.

In the given exercise, the solution with the largest freezing point depression has the highest product of molality and Van't Hoff factor. Here, 0.020 m CaBr2 demonstrates the most significant drop in freezing point, reflecting its relatively higher concentration of particles contributed by dissociation.

The Van鈥檛 Hoff factor, denoted by \( i \), is a measure of the number of particles into which a solute dissociates in solution. This factor plays a crucial role in determining the extent of colligative properties like boiling point elevation, freezing point depression, and vapor pressure lowering.

For instance:

• For a nonelectrolyte, \( i \) is 1 because it doesn鈥檛 dissociate into ions.
• For ionic compounds, \( i \) is determined by the total ions formed. For example, Na3PO4 dissociates into 4 ions, so its \( i \) is 4.

In the exercise, understanding the \( i \) for each solute helps in accurately calculating the boiling point, vapor pressure, and freezing point changes. This factor illustrates how solute behavior can drastically affect the solution's physical properties.