Question

Bath salts such as Epsom contain hydrate salts such as MgSO 4 ·7H 2 O (magnesium sulfate heptahydrate). When heated, water is released as vapor and anhydrous MgSO 4 remains. Determine how many moles of vapor are released when 15.5 g of MgSO 4 ·7H 2 O are heated. Hint: Include H 2 O when calculating the molar mass.

Answer 1

Answer:

0.369 moles of H₂O.

Explanation:

The molar mass of the hydrate salt is equal to the molar mass of the anhydrous salt plus the molar mass of water times the moles of water.

M(MgSO₄·7H₂O) = M(MgSO₄) + 7 × M(H₂O)

M(MgSO₄·7H₂O) = 168 g/mol + 7 × 18 g/mol

M(MgSO₄·7H₂O) = 294 g/mol

Every 294 g of MgSO₄·7H₂O there are 126 g of H₂O. So, for 15.5 g of MgSO₄·7H₂O,

$15.5gMgSO_{4}.7H_{2}O.\frac{126gH_{2}O}{294gMgSO_{4}.7H_{2}O} .\frac{1molH_{2}O}{18gH_{2}O}=0.369mol H_{2}O$