91Ó°ÊÓ

Solutions have unique properties compared to their pure solvents. One of those is boiling point elevation. When a solute is dissolved into a solvent, the boiling point of the resultant solution is higher than that of the pure solvent. This is known as boiling point elevation. This happens because the solute particles interfere with the escape of solvent molecules into the gas phase, which increases the temperature required for the vapor pressure to equal atmospheric pressure. The formula to calculate boiling point elevation is \[ \Delta T_b = i \cdot K_b \cdot m \] Where:

• \( \Delta T_b \) is the boiling point elevation
• \( i \) is the van’t Hoff factor, which represents the number of particles the solute splits into
• \( K_b \) is the ebullioscopic constant of the solvent
• \( m \) is the molality of the solution

In the situation provided, upon dissolving sodium chloride and calcium chloride, the solution boiled at a higher temperature of 103.3°C due to a 3.3°C increase from the pure water boiling point of 100°C.

When a non-volatile solute is added to a solvent, it lowers the solvent's vapor pressure. This is known as vapor pressure lowering, a key colligative property. Vapor pressure decreases because solute particles occupy space at the surface that would otherwise be taken by evaporating solvent molecules. This blockage requires a higher vapor pressure for the solvent particles to escape into the atmosphere. Raoult's Law provides the relationship \[ P_{\text{solution}} = \chi_{\text{solvent}} \cdot P^0_{\text{water}} \] Where:

• \( P_{\text{solution}} \) represents the vapor pressure of the solution
• \( \chi_{\text{solvent}} \) is the mole fraction of the solvent in the solution
• \( P^0_{\text{water}} \) is the vapor pressure of the pure solvent, water, at a given temperature

In the given exercise, the vapor pressure of the solution was calculated to be 22.69 mm Hg, lower than the pure water's vapor pressure of 23.8 mm Hg.

Molality is an essential concept when dealing with colligative properties as it affects both boiling point elevation and vapor pressure lowering. Molality is defined as the moles of solute per kilogram of solvent and is represented by the symbol m. It is a handy concentration unit because it is independent of temperature changes, unlike molarity, which relies on volume. To calculate molality, we use the formula: \[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \] In our problem, we found the molality for both NaCl and CaCl2 separately.

• NaCl moles were divided by the mass of the solvent to give a molality of 1.80 m
• CaCl2 moles led to a molality of 0.95 m

The combined effect after dissociation accounted for a total ion molality of 6.45 m, crucial for calculating the boiling point elevation.

Raoult's Law helps us understand how a solute affects the vapor pressure of a solvent in a solution. It states that the vapor pressure of an ideal solution is dependent on the mole fraction of the solvent present. The principle under Raoult's Law is simple: more solute leads to less volatile solvent at the surface, which lowers the overall vapor pressure in proportion to the mole fraction of the solvent. It is given by \[ P_{\text{solution}} = \chi_{\text{solvent}} \cdot P^0 \] Where:

• \( P_{\text{solution}} \) is the resulting vapor pressure of the solution
• \( \chi_{\text{solvent}} \) is the mole fraction of the solvent
• \( P^0 \) stands for the vapor pressure of the pure solvent

In our example, the decrease in vapor pressure due to the dissolved salts was calculated using Raoult’s Law. This highlighted how the introduction of solutes diminished the mole fraction of water, thereby lowering the vapor pressure.