70 g of a pure, hydrated magnesium sulphate crystals were dissolved in 90 g of water and mole fraction of solute in
the solution was found to be 0.039. Determine the molecular formula of hydrated salt. (Ans: MgSO4.30H2O)
To determine the molecular formula of the hydrated salt, we need to calculate the number of moles of the solute and the number of moles of water in the solution.
1. Calculate the number of moles of magnesium sulphate (MgSO4):
- The molar mass of MgSO4 is 120.37 g/mol.
- The mass of the solute is 70 g.
- Number of moles of solute = mass of solute / molar mass = 70 g / 120.37 g/mol ≈ 0.5813 moles.
2. Calculate the number of moles of water:
- The molar mass of water (H2O) is 18.02 g/mol.
- The mass of water is 90 g.
- Number of moles of water = mass of water / molar mass = 90 g / 18.02 g/mol ≈ 4.9945 moles.
3. Calculate the mole fraction of water:
- Mole fraction of water = moles of water / (moles of solute + moles of water).
- Mole fraction of water = 4.9945 moles / (0.5813 moles + 4.9945 moles) ≈ 0.8952.
4. Calculate the mole fraction of solute:
- Mole fraction of solute = 0.039.
5. Determine the ratio of moles of water to moles of solute:
- Let the ratio be n:H2O.
- We know that the mole fraction of water can be written as n/(n+1).
- n/(n+1) = 0.8952.
- Solving for n, we find n ≈ 7.86.
6. Determine the molecular formula of the hydrated salt:
- The molecular formula of hydrated magnesium sulphate is MgSO4 · nH2O.
- Plugging in the value of n, we get MgSO4 · 7.86H2O.
- Multiply through by the nearest whole number to remove the decimal: MgSO4 · 8H2O.
Therefore, the molecular formula of the hydrated salt is MgSO4 · 8H2O.