Answer: 9.8g
Explanation:
This calculation assumes complete removal of water from the compound.
From there, I will determine the mass of the evaporated water and subtract that from the initial 20.0 g sample.
To do this, follow these steps:
1) Calculate the number of moles of hydrated magnesium sulfate, represented as MgSO₄⋅7H₂O
Number of moles = mass in grams / molar mass
The molar mass of MgSO₄⋅7H₂O can be calculated using the atomic masses of its constituent atoms multiplied by the number of each atom present:
Molar mass = 24.305 g/mol + 32.065 g/mol + 4×15.999g/mol + 7×2×1.008g/mol + 7×15.999 g/mol = 246.471 g/mol
Therefore, moles of MgSO₄⋅7H₂O = 20.0g / 246.471 g/mol = 0.0811 moles
2) Now calculate the number of moles of water, using the ratios derived from the chemical formula:
7 moles of H₂O / 1 mole of MgSO₄⋅7H₂O = x / 0.0811 moles of MgSO₄⋅7H₂O
⇒ x = 0.0811 × 7 moles H₂O = 0.568 moles H₂O
3) Convert moles of H₂O to grams:
Number of moles = mass in grams × molar mass = 0.568 moles × 18.015 g/mol = 10.2 g
4) Thus, the remaining mass is 20.0g - 10.2g = 9.8g