How many grams of MgO are required to be dissolved in 1.25 kg of water to prepare a 1.0 molal (1.0 m) solution?

• A. 50.0 g
• B. 72.5 g
• C. 30.0 g
• D. 60.0 g

Answer: (D)

Verified step by step guidance

1. Understand that molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula is: \[m = \frac{\text{moles of solute}}{\text{kg of solvent}}\]
2. Identify the given values: molality \(m = 1.0\) mol/kg, mass of solvent (water) = 1.25 kg, and the solute is MgO.
3. Calculate the number of moles of MgO needed using the molality formula rearranged: \[\text{moles of MgO} = m \times \text{kg of solvent} = 1.0 \times 1.25\]
4. Find the molar mass of MgO by adding the atomic masses of Mg (approximately 24.3 g/mol) and O (approximately 16.0 g/mol): \[M_{MgO} = 24.3 + 16.0\]
5. Calculate the mass of MgO required by multiplying the moles of MgO by its molar mass: \[\text{mass of MgO} = \text{moles of MgO} \times M_{MgO}\]