Assuming complete ionisation, the solution having maximum freezing point will be: (a) \(1 \mathrm{M} \mathrm{CaF}_{2}\) (b) \(1.5 \mathrm{M} \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (c) \(2 \mathrm{M} \mathrm{NaCl}\) (d) \(1 \mathrm{M} \mathrm{AgNO}_{3}\)

Understanding freezing point depression is essential when studying colligative properties of solutions. Put simply, adding a solute to a solvent will result in the lowering of that solution's freezing point. This is not due to the chemical nature of the solute but rather the increase in the number of solute particles.

Freezing point depression can be calculated 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 (which accounts for the ionisation of the solute), \( K_f \) is the freezing point depression constant (specific to the solvent), and \( m \) is the molarity of the solution. The more particles present due to solute dissolution, the greater the effect on the freezing point.

The Van't Hoff factor, symbolized as \( i \), serves to show the degree to which a solute dissociates into ions when dissolved in a solvent. This factor is crucial because it helps to determine the actual number of particles in solution.

For non-electrolytes that do not dissociate, \( i \) is typically 1, since the solute remains as intact molecules. However, for electrolytes that do ionise, \( i \) can be greater than 1. For instance, NaCl splits into two ions, Na\textsuperscript{+} and Cl\textsuperscript{−}, so its Van't Hoff factor is 2. Its importance becomes clear when calculating colligative properties such as boiling point elevation, osmotic pressure, and freezing point depression, where \( i \) is multiplied by the molality or molarity of the solution.

Ionisation in solutions is a chemical process where molecules separate into charged particles (ions) when a solute dissolves in a solvent. For example, table salt, NaCl, ionises into \( Na^{+} \) and \( Cl^{-} \) in water.

The degree to which a compound ionises varies—is influenced greatly by the nature of the solute and the solvent. Some substances, like strong acids and bases, ionise almost completely in water (considered good ionisers), leading to a high Van't Hoff factor. In contrast, weak acids and bases partially ionise, resulting in lower values of \( i \). Understanding the extent of ionisation is fundamental in predicting the behavior of solutions and their associated colligative properties.

Molarity is a measure of concentration that refers to the number of moles of a solute per liter of solution—it is denoted by the letter \( M \). It lets us know how concentrated a solution is, which is directly linked to colligative properties such as freezing point depression.

The formula for molarity is \( \text{Molarity} = \frac{\text{number of moles of solute}}{\text{liters of solution}} \). It’s important because it's used to calculate the number of solute particles in a solution, which is essential when considering the solution's colligative properties. For example, the greater the molarity of a solution, the more significant the freezing point depression will be, assuming the solute dissociates into ions.