Carbon disulfide (CS₂) boils at 46.30 °C and has a density of 1.261 g/mL. (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS₂, the solution boils at 47.08 °C. What is the molar mass of the unknown?

Key Concepts

Boiling Point Elevation

Boiling point elevation is a colligative property that describes how the boiling point of a solvent increases when a solute is dissolved in it. This phenomenon occurs because the presence of solute particles disrupts the formation of vapor above the liquid, requiring a higher temperature to reach the boiling point. The change in boiling point can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van 't Hoff factor, K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution.

Molality

Molality (m) is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is particularly useful in colligative property calculations because it is independent of temperature and volume changes. To calculate molality, one must first determine the number of moles of the solute and the mass of the solvent in kilograms, which allows for accurate determination of the solution's properties.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of an unknown solute, one can use the relationship between the mass of the solute, the change in boiling point, and the molality of the solution. By rearranging the boiling point elevation formula and substituting known values, one can solve for the molar mass, which is essential for identifying the unknown substance.