Molar Mass of Hydrates: Formulas, Calculations and the Classic Heating Lab
How to read hydrate formulas like CuSO4·5H2O, calculate their molar mass and percent water, and find the formula of an unknown hydrate from lab data.
Many salts crystallize with water molecules built into their structure. These compounds are called hydrates, and the water is part of their formula and their mass. Leaving it out is one of the most common errors in solution preparation.
Reading a hydrate formula
In CuSO₄·5H₂O, the dot means "combined with": one unit of copper(II) sulfate with five molecules of water. The number before H₂O multiplies the entire water molecule. Other common hydrates:
- MgSO₄·7H₂O (Epsom salt)
- Na₂CO₃·10H₂O (washing soda)
- CaSO₄·2H₂O (gypsum)
- CoCl₂·6H₂O (cobalt(II) chloride hexahydrate)
In the molecular weight calculator you can type the dot as ·, *, or a period, for example CuSO4*5H2O or CuSO4.5H2O.
Calculating the molar mass
Add the anhydrous part and the water:
| Part | Calculation | g/mol |
|---|---|---|
| CuSO₄ | 63.546 + 32.06 + 4(15.999) | 159.60 |
| 5H₂O | 5 × 18.015 | 90.08 |
| CuSO₄·5H₂O | 249.68 | |
Why it matters in the lab
To make 250 mL of a 0.100 M copper sulfate solution, you need 0.0250 mol of CuSO₄. If your bottle contains the pentahydrate, weigh 0.0250 × 249.68 = 6.24 g. Using the anhydrous molar mass (159.60) would give 3.99 g, and your solution would be only about 64% as concentrated as intended. Always check the label for "anhydrous" or the hydrate formula. More on preparing solutions in molarity and solutions.
Percent water
Percent water = mass of water ÷ molar mass of hydrate × 100. For CuSO₄·5H₂O: 90.08 ÷ 249.68 = 36.1%.
Finding the formula of an unknown hydrate
The classic lab: heat a weighed sample until all water is driven off, then weigh the remaining anhydrous salt.
Example: 5.00 g of a magnesium sulfate hydrate leaves 2.44 g of anhydrous MgSO₄ after heating.
- Mass of water lost: 5.00 − 2.44 = 2.56 g
- Moles of MgSO₄: 2.44 ÷ 120.36 = 0.0203 mol
- Moles of water: 2.56 ÷ 18.015 = 0.142 mol
- Ratio: 0.142 ÷ 0.0203 = 7.0
The formula is MgSO₄·7H₂O. Dividing by the smaller number of moles to find a whole-number ratio is the same technique used for empirical formulas.
Lab tips
- Heat to constant mass: reweigh until two readings agree, so you know all the water is gone.
- Let the crucible cool in a desiccator before weighing; warm objects give low readings and dry salts absorb moisture from air.
- Copper sulfate turns from blue to white as it loses water, a useful visual check.
- Follow your lab's safety instructions and wear eye protection.
Further reading from official sources
- Atomic Weights and Isotopic Compositions – NIST Physical Measurement Laboratory
- Standard atomic weights – IUPAC Commission on Isotopic Abundances and Atomic Weights
