Problem 58 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The ebullioscopic constant of a liquid solvent is the elevation of boiling point of (a) one molar solution of non-volatile, non-electrolyte solute in it. (b) one normal solution of non-volatile, non-electrolyte solute in it. (c) one formal solution of non-volatile, non-electrolyte solute in it. (d) one molal solution of non-volatile, non-electrolyte solute in it.

Step-by-Step Solution

Answer

(d) one molal solution of non-volatile, non-electrolyte solute in it.

Step 1: Understanding what ebullioscopic constant is

The ebullioscopic constant (K_b) of a solvent is defined as the elevation in the boiling point experienced when a one molal solution of a non-volatile, non-electrolyte solute is dissolved in the solvent. Therefore, it is associated with molality, which is the number of moles of solute per kilogram of solvent.

Step 2: Reviewing options

Option (a) refers to a 'molar' solution which depends on the number of moles of solute per liter of solution. Option (b) mentions a 'normal' solution which is another term for equivalent per liter that depends on the equivalent concept which is not relevant to the molality concept. Option (c) describes a 'formal' solution, which is another concentration term not relevant to molality. Option (d) correctly refers to a 'molal' solution, which is the concentration term directly used in defining the ebullioscopic constant.

Step 3: Identifying the correct statement

According to the definition of the ebullioscopic constant, the elevation in the boiling point is specifically measured for a one molal solution of a non-volatile, non-electrolyte solute. Therefore, the correct choice is the one that refers to molality.

Key Concepts

Boiling Point Elevation

Boiling point elevation is a physical property observed when a solute is added to a pure solvent, resulting in the increase of the boiling point of that solvent. This occurs because the presence of a solute lowers the solvent's vapor pressure, requiring a higher temperature to achieve boiling. The boiling point elevation can be calculated using the formula: \( \text{Boiling Point Elevation} = K_b \times m \times i \), where \( K_b \) is the ebullioscopic constant, \( m \) stands for molality, and \( i \) represents the van't Hoff factor, indicating the number of particles the solute dissociates into.

To foster understanding, consider that pure water boils at 100°C. If a non-volatile substance such as table salt is added, the boiling point may rise to, say, 102°C. This effect is directly proportional to the number of particles of solute in the solution. Hence, a higher concentration of solute corresponds to a more significant elevation in boiling point.

Molality

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. Unlike molarity, which depends on the total volume of the solution, molality is solely based on the mass of the solvent, making it a more accurate measurement in situations where temperature variations occur, as it is not affected by changes in volume.

For instance, consider you're dissolving sugar in water to make a simple syrup. If you dissolve one mole of sugar in one kilogram of water, the solution's molality is one molal. An essential aspect of molality is its use in colligative properties, such as boiling point elevation, which applies when analyzing the impact of adding solutes to a solvent.

Non-Volatile Solutes

Non-volatile solutes are substances that have a low tendency to evaporate and thus, do not significantly contribute to the vapor pressure of a solution. These solutes, when dissolved in a solvent, lead to colligative properties like boiling point elevation. Because they do not vaporize easily, the solute particles remain in the solution and exert a colligative effect.

To visualize this concept, picture adding salt to water – the resulting solution will have a higher boiling point than the pure solvent. The salt, a non-volatile solute, has little to no vapor pressure of its own at the temperature of the boiling water, and so its presence disrupts the interactions between water molecules, leading to increased boiling points and decreased freezing points.

Physical Chemistry

Physical chemistry is the branch of chemistry focused on understanding the physical properties of molecules, the forces that act upon them, and the interactions between matter and energy. It involves studying concepts like thermodynamics, kinetics, quantum chemistry, and surface chemistry, among others. The principles of physical chemistry are essential for explaining the behavior of solutions, such as boiling point elevation due to the addition of non-volatile solutes.

This field blends principles from physics and chemistry to explain how and why chemical reactions happen, and to predict the properties of new substances. When we discuss boiling point elevation using the ebullioscopic constant, we're applying the theories of physical chemistry to understand the relationship between solute concentration and the physical changes in the boiling point of a liquid.