An aqueous solution containing \(35.9 \mathrm{~g}\) of an unknown molecular (nonelectrolyte) compound in \(150.0 \mathrm{~g}\) of water has a freezing point of \(-1.3^{\circ} \mathrm{C}\). Calculate the molar mass of the unknown compound.

Understanding molality is critical when examining properties of solutions. In chemistry, molality (\( m \)) is defined as the number of moles of solute per kilogram of solvent. It's a helpful concentration unit because it remains constant regardless of temperature changes, unlike molarity which can vary with temperature.

To calculate the molality, you can use the formula:
\[ m = \frac{n}{\text{mass of solvent in kg}} \]
where \( n \) is the number of moles of the solute, and the mass of the solvent is given in kilograms. In our exercise example, noting that the solute had a mass of 35.9g and was dissolved in 150.0 g (0.150 kg) of water, the molality was calculated based on the provided mass, the known freezing point depression of the solution, and the properties of water as the solvent.

It is also important to consider the context—molality is particularly useful in boiling point elevation and freezing point depression calculations where temperature's effect on the volume of the solvent does not have to be accounted for, making it a practical tool in such measurements of colligative properties.

Molar mass determination can often be challenging; however, it is an essential aspect of chemical calculations. The molar mass (\( M \) is the mass in grams of one mole of a substance. To ascertain the molar mass from experimental data, you can apply the following relationship:
\[ M = \frac{\text{mass of solute}}{n} \]
where the mass of the solute is the quantity of the solute in grams, and \( n \) represents the moles of the solute. In the given exercise, once the molality was found, the next step was to determine the moles of solute and subsequently use the mass of the solute to find the molar mass. The molar mass calculation provides not just the weight of a mole of particles but also offers insights into the identity of the unknown compound by comparing it with known values.

Colligative properties depend on the number of particles in a solution, not on their identity. One key colligative property is freezing point depression, which describes how the freezing point of a solvent decreases when a solute is dissolved in it. The quantitative relationship is given by:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where \( \Delta T_f \) is the freezing point depression, \( i \) is the van't Hoff factor, \( K_f \) is the freezing point depression constant specific to each solvent, and \( m \) is the molality of the solution. Van't Hoff's factor represents the number of particles the solute breaks into or forms in solution, which in the case of nonelectrolytes, is typically 1, meaning the compound doesn't dissociate into smaller molecules or ions. This formula was utilized to find the molality in Step 2 of our example problem, which then served as a pivotal step in finding the molar mass of the unknown compound. Understanding how to manipulate this property is essential for chemists and industry professionals when creating solutions with precise characteristics.