Final answer:
The value of x in Epsom salts, MgSO₄ · xH₂O, is calculated by subtracting the mass of anhydrous MgSO₄ from the hydrated form and then dividing the moles of water by the moles of MgSO₄. The value of x is typically 7, forming MgSO₄ · 7H₂O.
Step-by-step explanation:
The value of x in the formula for Epsom salts, MgSO₄ · nH₂O, can be determined by considering the mass loss when the water of hydration is removed through heating. If a sample containing 5.0 g of magnesium sulphate is heated until all the water has evaporated and the final mass is 2.6 g, the mass of the water lost is 5.0 g - 2.6 g = 2.4 g. The molar mass of water (H₂O) is approximately 18.015 g/mol, so we can calculate the moles of water:
Moles of water = 2.4 g / 18.015 g/mol
The number of moles of MgSO₄ in 2.6 g is calculated using the molar mass of anhydrous MgSO₄, which is approximately 120.37 g/mol:
Moles of MgSO₄ = 2.6 g / 120.37 g/mol
To find the value of x, which is the number of moles of water per mole of MgSO₄, divide the moles of water by the moles of MgSO₄:
x = Moles of water / Moles of MgSO₄
By solving these expressions, we will get the value of x, which is typically around 7 for Epsom salts, forming MgSO₄ · 7H₂O.