How to Calculate the Theoretical Percentage of Water in a Hydrate
A hydrate is an ionic compound that contains specific numbers of water molecules securely bound within its crystal structure. To calculate the theoretical percentage of water in a hydrate, you must divide the total molar mass of the water molecules by the total molar mass of the entire hydrate compound, and then multiply by 100.
- Mass of Water = Number of H₂O molecules (n) × 18.015 g/mol.
- Molar Mass of Hydrate = Molar mass of the anhydrous salt + Total mass of water.
Example: For Copper(II) sulfate pentahydrate (CuSO₄ · 5H₂O), the mass of water is 5 × 18.015 = 90.075 g/mol. The total molar mass of the hydrate is 159.61 + 90.075 = 249.685 g/mol.
In a laboratory setting, chemists often compare this calculated theoretical percentage against the experimental percentage (found by heating a hydrate sample to drive off the water and weighing the remaining anhydrous salt) to determine the purity of the sample or verify its empirical formula.
| Chemical Name | Chemical Formula | Theoretical % Water |
|---|---|---|
| Copper(II) sulfate pentahydrate | CuSO₄ · 5H₂O | 36.08% |
| Barium chloride dihydrate | BaCl₂ · 2H₂O | 14.75% |
| Magnesium sulfate heptahydrate (Epsom salt) | MgSO₄ · 7H₂O | 51.16% |
| Calcium sulfate dihydrate (Gypsum) | CaSO₄ · 2H₂O | 20.93% |
| Sodium carbonate decahydrate (Washing soda) | Na₂CO₃ · 10H₂O | 62.96% |
Frequently Asked Questions
What is the exact molar mass of water?
The exact molar mass of one molecule of water (H₂O) is 18.015 g/mol. This is calculated by adding the molar masses of two Hydrogen atoms (2 × 1.008 g/mol) and one Oxygen atom (1 × 15.999 g/mol).
What is an anhydrous salt?
An anhydrous salt is a hydrate that has lost all of its water molecules, typically through intense heating. "Anhydrous" literally means "without water." When calculating percent water, the molar mass of the anhydrous salt is the weight of the compound before you add the water weight.
Why do we calculate the theoretical percentage of water?
Calculating the theoretical percentage establishes a known baseline. When students or chemists perform experiments to dehydrate a salt, they can compare their actual, physical results (experimental yield) to the mathematical baseline (theoretical yield) to calculate their percent error and evaluate the accuracy of their experiment.