Calculate the freezing point and boiling point of each aqueous solution, assuming complete dissociation of the solute. c. 5.5% NaNO₃ by mass (in water)

Verified step by step guidance

1. Determine the molality of the solution: Calculate the mass of NaNO_3 in 100 g of solution, then find the moles of NaNO_3 using its molar mass. Use the mass of water to find molality (moles of solute per kg of solvent).
2. Calculate the van't Hoff factor (i): Since NaNO_3 dissociates into Na^+ and NO_3^-, the van't Hoff factor is 2.
3. Use the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( K_f \) is the freezing point depression constant for water, and \( m \) is the molality. Subtract \( \Delta T_f \) from the normal freezing point of water (0°C) to find the new freezing point.
4. Use the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( K_b \) is the boiling point elevation constant for water, and \( m \) is the molality. Add \( \Delta T_b \) to the normal boiling point of water (100°C) to find the new boiling point.
5. Summarize the results: Present the calculated freezing and boiling points 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 understanding how solutes affect the phase changes of solvents.

Dissociation of Ionic Compounds

Ionic compounds, such as sodium nitrate (NaNO3), dissociate into their constituent ions when dissolved in water. For NaNO3, it dissociates into Na+ and NO3- ions. This dissociation increases the total number of solute particles in the solution, which directly influences the colligative properties.

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, where ΔTf and ΔTb are the changes in freezing and boiling points, respectively, 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.