A 100.0-mL aqueous sodium chloride solution is 13.5% NaCl by mass and has a density of 1.12 g/mL. What would you add (solute or solvent) and what mass of it to make the boiling point of the solution 104.4 °C? (Use i = 1.8 for NaCl.)

Verified step by step guidance

1. <Step 1: Calculate the mass of the solution.> Use the density and volume of the solution to find its mass. The formula is: \( \text{mass of solution} = \text{density} \times \text{volume} \).
2. <Step 2: Determine the mass of NaCl in the solution.> Use the percentage by mass to find the mass of NaCl. The formula is: \( \text{mass of NaCl} = \text{mass of solution} \times \frac{13.5}{100} \).
3. <Step 3: Calculate the molality of the solution.> First, find the mass of water by subtracting the mass of NaCl from the total mass of the solution. Then, convert the mass of water to kilograms. Finally, calculate the molality using: \( \text{molality} = \frac{\text{moles of NaCl}}{\text{mass of water in kg}} \).
4. <Step 4: Use the boiling point elevation formula.> The formula is: \( \Delta T_b = i \cdot K_b \cdot m \), where \( \Delta T_b \) is the change in boiling point, \( i \) is the van 't Hoff factor, \( K_b \) is the ebullioscopic constant for water (0.512 °C/m), and \( m \) is the molality. Set \( \Delta T_b = 104.4 - 100 \) and solve for the new molality.
5. <Step 5: Adjust the solution to achieve the desired boiling point.> Determine whether to add solute (NaCl) or solvent (water) to reach the calculated molality. Calculate the mass of the solute or solvent needed to achieve this change.>

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, freezing point depression, vapor pressure lowering, and osmotic pressure. In this question, the boiling point elevation is crucial for determining how much solute or solvent to add to achieve the desired boiling point.

Boiling Point Elevation Formula

The boiling point elevation can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the change in boiling point, i is the van 't Hoff factor (which accounts for the number of particles the solute dissociates into), K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution. For sodium chloride (NaCl), i is 2 because it dissociates into two ions: Na⁺ and Cl⁻. This formula is essential for calculating how much solute is needed to reach the target boiling point.

Density and Mass Calculations

Density is defined as mass per unit volume and is crucial for converting between mass and volume in solution calculations. In this problem, the density of the sodium chloride solution (1.12 g/mL) allows us to determine the mass of the solution from its volume (100.0 mL). Understanding how to manipulate density and mass is vital for calculating the total mass of solute or solvent needed to achieve the desired boiling point.