What is the percent by mass of magnesium sulfate (MgSO_4) in magnesium sulfate heptahydrate (MgSO_4 · 7H_2O)?

• A. 44.8%
• B. 51.2%
• C. 60.3%
• D. 35.0%

Answer: (B)

Verified step by step guidance

1. Identify the chemical formula of magnesium sulfate heptahydrate as \(\mathrm{MgSO_4 \cdot 7H_2O}\), which means one formula unit contains one magnesium sulfate unit and seven water molecules.
2. Calculate the molar mass of magnesium sulfate (\(\mathrm{MgSO_4}\)) by summing the atomic masses of its elements: magnesium (Mg), sulfur (S), and oxygen (O). Use the atomic masses: Mg = 24.3 g/mol, S = 32.1 g/mol, O = 16.0 g/mol.
3. Calculate the molar mass of the seven water molecules (\$7 \times \mathrm{H_2O}$) by multiplying 7 by the molar mass of water. The molar mass of water is calculated from hydrogen (H = 1.0 g/mol) and oxygen (O = 16.0 g/mol).
4. Add the molar mass of magnesium sulfate and the molar mass of the seven water molecules to find the total molar mass of magnesium sulfate heptahydrate.
5. Calculate the percent by mass of magnesium sulfate in the hydrate using the formula: \(\text{Percent by mass} = \left( \frac{\text{Molar mass of } \mathrm{MgSO_4}}{\text{Molar mass of } \mathrm{MgSO_4 \cdot 7H_2O}} \right) \times 100\%\).