The following phase diagram shows part of the liquid–vapor phase-transition boundaries for pure ether and a solution of a nonvolatile solute in ether.
(b) What is the approximate mo#lal concentration of the sol-ute? [Kb for ether is 2.021°C kg2>mol.]

Verified step by step guidance

1. Identify the boiling points of pure ether and the solution from the phase diagram at the vapor pressure of 760 torr.
2. Calculate the boiling point elevation (ΔT_b) by subtracting the boiling point of pure ether from the boiling point of the solution.
3. Use the boiling point elevation formula ΔT_b = K_b * m, where K_b is the ebullioscopic constant (2.021°C kg/mol for ether) and m is the molal concentration of the solute.
4. Rearrange the formula to solve for the molal concentration (m): m = ΔT_b / K_b.
5. Substitute the values of ΔT_b and K_b into the equation to find the molal concentration of the solute.

Key Concepts

Phase Diagrams

A phase diagram is a graphical representation that shows the phases of a substance as a function of temperature and pressure. It illustrates the boundaries between different phases, such as solid, liquid, and gas, and indicates conditions under which these phases coexist. In this case, the phase diagram for ether and a solution helps visualize how the vapor pressure changes with temperature for both pure ether and a solution containing a nonvolatile solute.

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent present. This principle is crucial for understanding how the addition of a nonvolatile solute affects the vapor pressure of the solvent, leading to a decrease in vapor pressure compared to that of the pure solvent. This law is fundamental in calculating the molal concentration of the solute based on the observed changes in vapor pressure.

Colligative Properties

Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure. In this question, the focus is on vapor pressure lowering, which is essential for determining the molal concentration of the solute in the ether solution.