Calculate the freezing point and boiling point of each aqueous solution, assuming complete dissociation of the solute. a. 0.100 m K₂S b. 21.5 g of CuCl₂ in 4.50⨉10² g water

Verified step by step guidance

1. Determine the molality (m) of the solution by calculating the moles of CuCl_2 and dividing by the mass of water in kilograms.
2. Calculate the van't Hoff factor (i) for CuCl_2, which is the number of particles the solute dissociates into in solution.
3. Use the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \) to find the change in freezing point, where \( K_f \) is the freezing point depression constant for water.
4. Subtract \( \Delta T_f \) from the normal freezing point of water (0°C) to find the new freezing point of the solution.
5. Use the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \) to find the change in boiling point, where \( K_b \) is the boiling point elevation constant for water, and add \( \Delta T_b \) to the normal boiling point of water (100°C) to find the new boiling point of the solution.

Key Concepts

Colligative Properties

Colligative properties are physical 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 boiling point elevation and freezing point depression, which are crucial for calculating the changes in freezing and boiling points when a solute is added to a solvent.

Dissociation of Ionic Compounds

Ionic compounds, such as CuCl₂, dissociate into their constituent ions when dissolved in water. For CuCl₂, it dissociates into one copper ion (Cu²⁺) and two chloride ions (Cl⁻). This dissociation increases the total number of solute particles in the solution, which directly affects the colligative properties and must be accounted for in calculations.

Freezing Point Depression and Boiling Point Elevation Formulas

The freezing point depression and boiling point elevation can be calculated using the formulas ΔTf = i * Kf * m and ΔTb = i * Kb * m, respectively, where ΔTf and ΔTb are the changes in freezing and boiling points, i is the van 't Hoff factor (number of particles the solute dissociates into), Kf and Kb are the solvent's freezing and boiling point constants, and m is the molality of the solution.