If \(0.44 \mathrm{~g}\) of substance dissolved in \(22.2 \mathrm{~g}\) of benzene lowers the freezing point of benzene by \(0.567^{\circ} \mathrm{C}\), then the molecular mass of substance is, (the molal depression constant \(\left.=5.12^{\circ} \mathrm{C} \mathrm{mol}^{-1} \mathrm{~kg}\right)\) (a) \(128.4\) (b) \(156.6\) (c) \(178.9\) (d) \(232.4\)

Colligative properties are critical for understanding physical processes in solutions. These properties depend solely on the number of solute particles in a solvent, not the nature of the solute itself. Examples of colligative properties include boiling point elevation, osmotic pressure, vapor pressure lowering, and freezing point depression.
Freezing point depression is particularly interesting because it explains how adding a solute to a solvent, such as salt to water, lowers the solvent's freezing point. The more solute particles present, the greater the effect. This phenomenon is used in real-world applications, such as de-icing roads and creating freeze-resistant fluids. Understanding how the addition of a solute can affect a solvent's freezing point provides valuable insight into solving problems related to molecular mass determination and molality calculations.

Molality is an essential concept when working with colligative properties. It measures concentration, defined as the number of moles of a solute present in one kilogram of a solvent. Unlike molarity, which is affected by temperature changes due to volume expansion or contraction, molality remains unchanged because it is based on mass.
To calculate molality, you must know the mass of the solute and the mass of the solvent in kilograms. The formula is simple: \[\begin{equation} m = \frac{\text{moles of solute}}{\text{kg of solvent}} \end{equation}\]In practice, you often have to convert grams to kilograms for the solvent and may need to use the molecular mass of the solute to find the number of moles. This calculation is a step toward finding the molecular mass of an unknown solute, as demonstrated in the Freezing Point Depression problem.

Determining molecular mass is a fundamental skill in chemistry, especially when analyzing colligative properties. When given the freezing point depression and the molal depression constant of a solvent, we can reverse engineer the equation to find the molecular mass of a solute. The molecular mass can be expressed as:\[\begin{equation}\text{Molecular Mass} = \frac{\text{mass of solute in grams} \times \text{molal depression constant}}{\text{freezing point depression} \times \text{mass of solvent in kg}} \end{equation}\]By rearranging the formula for freezing point depression, the molecular mass can be isolated and calculated from the known quantities. This technique provides scientists and students with a practical method for identifying unknown substances by their physical properties.