To determine the original weight of the magnesium carbonate trihydrate (MgCO₃·3H₂O) that was heated, follow these steps:
1. Calculate the Molecular Weight (Molar Mass) of Magnesium Carbonate (MgCO₃):
- Magnesium (Mg): 24.305 g/mol
- Carbon (C): 12.011 g/mol
- Oxygen (O): 16.00 g/mol (three atoms of oxygen)
Therefore, the molecular weight of MgCO₃ is:
[tex]\[
24.305 \, \text{g/mol} + 12.011 \, \text{g/mol} + 3 \times 16.00 \, \text{g/mol} = 84.316 \, \text{g/mol}
\][/tex]
2. Calculate the Molecular Weight (Molar Mass) of Water (H₂O):
- Hydrogen (H): 1.008 g/mol (two atoms of hydrogen)
- Oxygen (O): 16.00 g/mol (one atom of oxygen)
Therefore, the molecular weight of H₂O is:
[tex]\[
2 \times 1.008 \, \text{g/mol} + 16.00 \, \text{g/mol} = 18.016 \, \text{g/mol}
\][/tex]
3. Calculate the Molecular Weight (Molar Mass) of Magnesium Carbonate Trihydrate (MgCO₃·3H₂O):
- Molecular weight of MgCO₃: 84.316 g/mol
- Molecular weight of 3 moles of H₂O: 3 \times 18.016 g/mol
Therefore, the molecular weight of MgCO₃·3H₂O is:
[tex]\[
84.316 \, \text{g/mol} + 3 \times 18.016 \, \text{g/mol} = 138.364 \, \text{g/mol}
\][/tex]
4. Given Mass of Released Water:
[tex]\[
\text{Mass of released water} = 40.37 \, \text{grams}
\][/tex]
5. Calculate the Moles of Water Released:
[tex]\[
\text{Moles of water released} = \frac{\text{Mass of water}}{\text{Molar mass of H₂O}} = \frac{40.37 \, \text{grams}}{18.016 \, \text{g/mol}} = 2.2407859680284195 \, \text{moles}
\][/tex]
6. Determine the Moles of the Hydrate (MgCO₃·3H₂O):
In MgCO₃·3H₂O, there are 3 moles of water for every mole of the hydrate.
[tex]\[
\text{Moles of hydrate} = \frac{\text{Moles of water released}}{3} = \frac{2.2407859680284195 \, \text{moles}}{3} = 0.7469286560094731 \, \text{moles}
\][/tex]
7. Calculate the Original Mass of the Hydrate:
[tex]\[
\text{Mass of hydrate} = \text{Moles of hydrate} \times \text{Molar mass of MgCO₃·3H₂O} = 0.7469286560094731 \, \text{moles} \times 138.364 \, \text{g/mol} = 103.34803656009474 \, \text{grams}
\][/tex]
Therefore, the original magnesium carbonate trihydrate (MgCO₃·3H₂O) weighed approximately 103.35 grams.
