Using the van’t Hoff factors in Table 13.9, calculate the mass of solute required to make each aqueous solution: a. a sodium chloride solution containing 1.50 * 10^2 g of water that has a melting point of -1.0 °C; b. 2.50 * 10^2 mL of a magnesium sulfate solution that has an osmotic pressure of 3.82 atm at 298 K; c. an iron(III) chloride solution containing 2.50 * 10^2 g of water that has a boiling point of 102 °C.

Verified step by step guidance

1. Identify the colligative property involved in each part of the problem: freezing point depression for part (a), osmotic pressure for part (b), and boiling point elevation for part (c).
2. Use the appropriate formula for each colligative property: \( \Delta T_f = i \cdot K_f \cdot m \) for freezing point depression, \( \Pi = i \cdot M \cdot R \cdot T \) for osmotic pressure, and \( \Delta T_b = i \cdot K_b \cdot m \) for boiling point elevation.
3. For each part, solve for the molality \( m \) or molarity \( M \) using the given data and the van’t Hoff factor \( i \) from Table 13.9.
4. Calculate the number of moles of solute needed using the molality or molarity and the mass or volume of the solvent.
5. Convert the moles of solute to mass using the molar mass of the solute.

Key Concepts

van't Hoff Factor (i)

The van't Hoff factor (i) is a measure of the number of particles a solute dissociates into when dissolved in a solvent. For example, sodium chloride (NaCl) dissociates into two ions, Na+ and Cl-, giving it a van't Hoff factor of 2. This factor is crucial for calculating colligative properties, such as boiling point elevation and freezing point depression, as it directly affects the extent of these changes in solution.

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. Key examples include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Understanding these properties is essential for solving problems related to the effects of solutes on solvent behavior, as seen in the question regarding melting and boiling points.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane, and it is directly proportional to the concentration of solute particles in the solution. The formula for osmotic pressure (π) is π = iCRT, where i is the van't Hoff factor, C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin. This concept is vital for calculating the mass of solute needed to achieve a specific osmotic pressure.