What specific fact about a physical property of a solution must be true to call it a colligative property?

The phenomenon of boiling point elevation is a classic example of a colligative property. It involves the increase in the boiling point of a solvent upon the addition of a non-volatile solute.

This occurs because the solute particles disrupt the solvent's evaporation process, thereby requiring a higher temperature to reach boiling. The boiling point elevation can be quantitatively described by the formula: \[ \Delta T_b = K_b \cdot m \cdot i \] where \( \Delta T_b \) is the boiling point elevation, \( K_b \) is the ebullioscopic constant of the solvent, \( m \) is the molality of the solution, and \( i \) is the van't Hoff factor, representing the number of particles the solute dissociates into.

For instance, adding table salt to water increases its boiling point slightly, meaning the water will boil at a temperature higher than 100°C.

Freezing point depression is another colligative property where the freezing point of a solvent decreases due to the presence of a solute. Similar to boiling point elevation, this effect is not based on the solute's specific identity but on the number of particles it contributes to the solution.

The quantitative relationship for freezing point depression is given by: \[ \Delta T_f = K_f \cdot m \cdot i \] Here, \( \Delta T_f \) is the freezing point depression, \( K_f \) is the cryoscopic constant of the solvent, and the other variables are as above.

Applying salt on icy roads is a practical application of this principle: the added salt lowers the freezing point of water, causing the ice to melt even at temperatures below water's ordinary freezing point.

Vapor pressure lowering is the reduction in vapor pressure of a solvent when a non-volatile solute is added. This colligative property is because the solute particles occupy space at the liquid's surface, inhibiting solvent molecules' escape into the vapor phase.

The effect can be represented with Raoult's Law, which states: \[ P_1 = X_1 \cdot P_1^\circ \] where \( P_1 \) is the vapor pressure of the solvent with the solute present, \( X_1 \) is the mole fraction of the solvent, and \( P_1^\circ \) is the vapor pressure of the pure solvent.

This property has practical implications in cooking, such as when making a sugar syrup. The presence of sugar reduces the evaporation rate of water, hence increasing the cooking time.

Osmotic pressure is the pressure required to prevent the flow of solvent molecules through a semipermeable membrane from a dilute solution to a concentrated solution. This colligative property is key in biological and chemical processes where the solvent and solute concentrations differ on either side of a membrane.

The mathematical expression for osmotic pressure \( \Pi \) is: \[ \Pi = i \cdot M \cdot R \cdot T \] where \( M \) is the molarity of the solution, \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, and \( i \) is the van't Hoff factor as previously discussed.

Osmotic pressure plays a crucial role in the medical field, particularly in administering intravenous solutions where the osmotic balance between the blood and the solution must be maintained.