What mass (in g) of NH_3 must be dissolved in 475 g of methanol to prepare a 0.250 m (molal) solution?

• A. 4.03 g
• B. 8.08 g
• C. 1.00 g
• D. 2.02 g

Answer: (D)

Verified step by step guidance

1. Identify the given information: molality (m) = 0.250 mol/kg, mass of solvent (methanol) = 475 g, and the solute is NH_3. Note that molality is defined as moles of solute per kilogram of solvent.
2. Convert the mass of the solvent from grams to kilograms because molality uses kilograms of solvent: \(\text{mass of solvent (kg)} = \frac{475}{1000}\).
3. Use the molality definition to find the moles of NH_3 needed: \(m = \frac{\text{moles of solute}}{\text{kg of solvent}} \Rightarrow \text{moles of NH}_3 = m \times \text{kg of solvent}\).
4. Calculate the molar mass of NH_3 by adding the atomic masses: N (14.01 g/mol) + 3 × H (1.008 g/mol) = molar mass of NH_3.
5. Convert moles of NH_3 to grams using its molar mass: \(\text{mass of NH}_3 = \text{moles of NH}_3 \times \text{molar mass of NH}_3\).