What is the formula for the hydrate of the given compound?

Question: An 82.0 g sample of hydrated magnesium sulfate (MgSO₄) is heated to a constant mass of 40.1 grams. What is the formula for the hydrate? Answer: The formula for the hydrate is MgSO₄ • 7H₂O.

Explanation:

To determine the formula for the hydrate, we need to calculate the moles of the anhydrous compound and the moles of water in the sample.

1. Calculate Moles of Anhydrous Compound (MgSO₄):

The molar mass of MgSO₄ is:

Mg: 24.31 g/mol

S: 32.07 g/mol

O: 16.00 g/mol (x4)

Total molar mass of MgSO₄: 24.31 + 32.07 + (16.00 x 4) = 120.37 g/mol

Next, calculate the moles of MgSO₄ with the given mass of 40.1 g:

Moles of MgSO₄ = Mass of MgSO₄ / Molar mass of MgSO₄ = 40.1 g / 120.37 g/mol = 0.333 mol

2. Calculate Moles of Water:

Mass of water lost = 82.0 g - 40.1 g = 41.9 g

Moles of water = Mass of water / Molar mass of water = 41.9 g / 18.02 g/mol = 2.32 mol

3. Determine Hydrate Formula:

Ratio = Moles of anhydrous compound / Moles of water = 0.333 mol / 2.32 mol ≈ 1:7

Based on the ratio, the formula for the hydrate is MgSO₄ • 7H₂O.

Therefore, the correct formula for the hydrate of the given compound is MgSO₄ • 7H₂O.

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