What will be the boiling point of bromine when \(174.5 \mathrm{mg}\) of octaatomic sulphur is added to \(78 \mathrm{~g}\) of bromine. \(K_{\mathrm{b}}^{\prime}\) for \(\mathrm{Br}_{2}\) is \(5.2 \mathrm{~K}\) mol \({ }^{1} \mathrm{~kg}\) and b.pt. of \(\mathrm{Br}_{2}\) is \(332.15 \mathrm{~K}\).

Colligative properties are unique characteristics of solutions that depend solely on the number of solute particles dissolved, irrespective of their specific identity. A fascinating aspect of these properties is their universal nature, which means they apply to all solvents and solutes. The most commonly discussed colligative properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

In the context of boiling point elevation, a non-volatile solute's presence causes the solvent's boiling point to rise. This is because adding solute particles to a solvent disrupts its molecular interactions, requiring additional energy to reach the boiling point. The degree of boiling point elevation is directly proportional to the amount of solute particles. Thus, by understanding colligative properties, students can predict how a solution will behave compared to the pure solvent, which is invaluable for applications in chemistry and industry.

Understanding the Role of the Ebullioscopic Constant

The ebullioscopic constant, typically symbolized as \(K_b\), is a unique value for each solvent that defines how much the boiling point of a solution is raised per molal concentration of a solute. Essentially, it's a measure of the boiling point elevation effect a solvent exhibits when a solute is added. The value of \(K_b\) reflects the physical properties of the solvent, like its enthalpy of vaporization.

For instance, bromine has an \(K_b\) value of 5.2 K kg/mol as given in the exercise, which means for every mole of solute dissolved per kilogram of bromine, the boiling point will increase by 5.2 K, provided the solute does not dissociate (non-electrolyte). This constant is essential for accurately determining the change in boiling point in practice and is crucial for chemists when designing processes involving boiling or evaporation.

Difference Between Molality and Molarity

Molality is a concentration measurement used in chemistry to quantify the amount of a solute in a solution. It is defined as the number of moles of solute per kilogram of solvent, denoted as \(m\). This is different from molarity, which measures the number of moles per liter of solution. Molality is especially useful in colligative properties calculation because it remains unaffected by temperature changes.

Calculating Molality

To compute the molality, one can divide the moles of solute by the mass of the solvent in kilograms. This approach makes molality an essential concept for solving problems involving boiling point elevation or freezing point depression, as it directly relates to the number of solute particles in the solution without being influenced by the solution's volume. Grasping the concept of molality is crucial for understanding how solute concentration affects the physical properties of a solution.