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.