# 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.