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