calculate the theoretical percentage of water for the following hydrates

💧 How to Calculate the Theoretical Percentage of Water in Hydrates

🧪 What Are Hydrates?

Hydrates are compounds that contain water molecules bound within their crystal structure. These water molecules are called "water of hydration." A common way to represent them is:

Salt · _n_H₂O
Where n = number of water molecules per formula unit.

Example:

• CuSO₄·5H₂O → Copper(II) sulfate pentahydrate
• MgSO₄·7H₂O → Magnesium sulfate heptahydrate

📐 Formula to Calculate Theoretical % of Water

Percent of Water=(Mass of Water in HydrateMolar Mass of the Entire Hydrate)×100\text{Percent of Water} = \left( \frac{\text{Mass of Water in Hydrate}}{\text{Molar Mass of the Entire Hydrate}} \right) \times 100Percent of Water=(Molar Mass of the Entire HydrateMass of Water in Hydrate​)×100

✅ Step-by-Step Example 1: CuSO₄·5H₂O

1. Find molar mass of each component:

• Cu = 63.55 g/mol
• S = 32.07 g/mol
• O₄ = 4 × 16.00 = 64.00 g/mol
• 5H₂O = 5 × (2 × 1.01 + 16.00) = 5 × 18.02 = 90.10 g/mol

2. Total molar mass of hydrate:

63.55+32.07+64.00+90.10=249.72 g/mol63.55 + 32.07 + 64.00 + 90.10 = 249.72 \text{ g/mol}63.55+32.07+64.00+90.10=249.72 g/mol

3. % Water:

\left( \frac{90.10}{249.72} \right) \times 100 = \textbf{36.07%}

✅ Example 2: MgSO₄·7H₂O

1. Mg = 24.31, S = 32.07, O₄ = 64.00
2. 7H₂O = 7 × 18.02 = 126.14 g/mol
3. Total molar mass = 24.31 + 32.07 + 64.00 + 126.14 = 246.52 g/mol
4. % Water:

\left( \frac{126.14}{246.52} \right) \times 100 = \textbf{51.17%}

❓ Common FAQs

1. Why calculate the theoretical % of water in a hydrate?

• To compare with experimental % and determine purity
• To identify unknown hydrates
• For lab analysis and chemical formulation

2. What if I only know the formula name?

You can look up the formula or molar masses online (e.g., Calcium chloride dihydrate = CaCl₂·2H₂O) and plug them into the formula above.

3. How to find molar masses?

Use a periodic table to sum:

• Atomic masses of all atoms in the salt
• Add the mass of water: 1 H₂O = 18.02 g/mol

4. Can the percentage of water be more than 50%?

Yes! In hydrates like Ba(OH)₂·8H₂O, water can make up more than 60% of the total mass.