Some nonelectrolyte solute (molar mass =142 g / mol ) was dissolved in 150 . mL of a solvent (de

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Some nonelectrolyte solute (molar mass =142 g / mol ) was...

Some nonelectrolyte solute (molar mass $=142 \mathrm{g} / \mathrm{mol}$ ) was dissolved in $150 . \mathrm{mL}$ of a solvent (density $=0.879 \mathrm{g} / \mathrm{cm}^{3}$ ). The elevated boiling point of the solution was $355.4 \mathrm{K} .$ What mass of solute was dissolved in the solvent? For the solvent, the enthalpy of vaporization is $33.90 \mathrm{kJ} / \mathrm{mol},$ the entropy of vaporization is $95.95 \mathrm{J} / \mathrm{K} \cdot \mathrm{mol},$ and the boiling-point elevation constant is $2.5 \mathrm{K} \cdot \mathrm{kg} / \mathrm{mol}.$

Key Concepts

Density and Mass-Volume Relationship

Density relates the mass of a substance to its volume, allowing conversion between these two quantities. In the context of solution chemistry, knowing the density of a solvent enables the calculation of its mass from a given volume, which is essential for determining accurate molal concentrations when assessing colligative properties.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is particularly useful in problems dealing with boiling point elevation and freezing point depression because it is independent of temperature, making it a stable measure for quantifying solute concentration in a solution.

Boiling Point Elevation

Boiling point elevation is a colligative property that occurs when a nonvolatile solute is added to a solvent, causing the boiling point of the solvent to increase. This effect happens because the solute particles disrupt the ability of the solvent molecules to escape into the vapor phase, requiring a higher temperature to reach the vapor pressure necessary for boiling.

Colligative Properties

Colligative properties are characteristics of solutions that depend solely on the number of dissolved particles and not on their particular nature. Examples include boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering. These properties are instrumental in determining solute quantities and molar masses in solutions.

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