A 500.0 mL aqueous solution has a concentration of 0.500 molal (m) NaBr. What mass of NaBr (in grams) must be present in the solution? (Assume the density of water is 1.00 g/mL.)

• A. 10.5 g
• B. 41.0 g
• C. 15.5 g
• D. 25.5 g

Answer: (D)

Verified step by step guidance

1. Understand that molality (m) is defined as moles of solute per kilogram of solvent. The formula is \(m = \frac{\text{moles of solute}}{\text{kg of solvent}}\).
2. Calculate the mass of the solvent (water) in kilograms. Since the solution volume is 500.0 mL and the density of water is 1.00 g/mL, the mass of water is \$500.0 \ \text{mL} \times 1.00 \ \text{g/mL} = 500.0 \ \text{g} = 0.5000 \ \text{kg}$.
3. Use the molality value to find the moles of NaBr: \(\text{moles of NaBr} = m \times \text{kg of solvent} = 0.500 \times 0.5000\).
4. Calculate the molar mass of NaBr by adding the atomic masses of Na (approximately 22.99 g/mol) and Br (approximately 79.90 g/mol): \(M_{\text{NaBr}} = 22.99 + 79.90\).
5. Find the mass of NaBr by multiplying the moles of NaBr by its molar mass: \(\text{mass of NaBr} = \text{moles of NaBr} \times M_{\text{NaBr}}\).