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: MgSO4.7H2O)
To determine the molecular formula of the hydrated salt, we need to find the number of moles of the solute, which in this case is magnesium sulfate (MgSO4), and compare it with the given mass.
First, we need to calculate the number of moles of magnesium sulfate in 70 g of the pure crystals. The molar mass of MgSO4 is:
Mg: 24.31 g/mol
S: 32.06 g/mol
O (4 atoms): 16.00 g/mol = 64.00 g/mol
Therefore, the molar mass of MgSO4 is:
24.31 + 32.06 + 64.00 = 120.37 g/mol
Next, we can calculate the number of moles of MgSO4 in 70 g of the crystals:
moles of MgSO4 = mass of MgSO4 / molar mass of MgSO4
= 70 g / 120.37 g/mol
= 0.581 mol
Next, we can calculate the number of moles of water (H2O) in 90 g of the solution. The molar mass of water is:
H (2 atoms): 1.01 g/mol = 2.02 g/mol
O: 16.00 g/mol
Therefore, the molar mass of H2O is:
2.02 + 16.00 = 18.02 g/mol
moles of H2O = mass of H2O / molar mass of H2O
= 90 g / 18.02 g/mol
= 4.99 mol
Next, we can calculate the mole fraction of the solute (MgSO4) using the given information:
mole fraction of solute (X) = moles of MgSO4 / (moles of MgSO4 + moles of H2O)
= 0.581 mol / (0.581 mol + 4.99 mol)
= 0.104
Now, we can determine the number of moles of water per mole of MgSO4 using the mole fraction of the solute. Since the molecular formula of hydrated magnesium sulfate is MgSO4.xH2O, we can consider the molar ratio between MgSO4 and H2O to be 1: x.
x = moles of H2O / moles of MgSO4
= (moles of H2O / moles of solute) / (moles of MgSO4 / moles of solute)
= (moles of H2O / moles of solute) / (mole fraction of solute)
= (4.99 mol / 0.581 mol) / 0.104
= 86
Therefore, the molecular formula of the hydrated salt is MgSO4.7H2O.