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.
To find the molecular formula of the hydrated salt, we need to calculate the number of moles of the solute and determine the ratio of the moles of water to the solute.
Given:
Mass of hydrated magnesium sulphate crystals = 70 g
Mass of water = 90 g
Mole fraction of the solute = 0.039
First, we need to calculate the moles of the solute:
Moles of solute = mass of solute / molar mass of solute
The molar mass of hydrated magnesium sulphate (MgSO₄·xH₂O) can be calculated as follows:
Molar mass of MgSO₄ = atomic mass of Mg + atomic mass of S + 4 times atomic mass of O
= 24.31 g/mol + 32.07 g/mol + (4 * 16.00 g/mol)
= 120.38 g/mol
Next, we calculate the moles of solute:
Moles of solute = 70 g / 120.38 g/mol
= 0.581 mol
Now we need to determine the ratio of moles of water to moles of solute by dividing the mole fraction of the solute by the mole fraction of the water.
Mole fraction of water = 1 - mole fraction of solute
= 1 - 0.039
= 0.961
Ratio of moles of water to moles of solute = mole fraction of water / mole fraction of solute
= 0.961 / 0.039
= 24.64
From the ratio of moles of water to moles of solute, we can determine the value of x in the formula MgSO₄·xH₂O.
Let's assume x = 24 (since x cannot be a fraction in a molecular formula).
Substituting the value in the formula, we get:
MgSO₄·24H₂O
Therefore, the molecular formula of the hydrated salt is MgSO₄·24H₂O.