Chemical Hydrates and Formula Calculations

A hydrate is an ionic compound whose crystals contain a fixed number of water molecules, called water of crystallization, and it is named by adding a Greek prefix and “hydrate” to the name of the anhydrous compound, as in copper(II) sulfate pentahydrate (CuSO₄·5H₂O). In brief: heating blue CuSO₄·5H₂O drives off the water and leaves white anhydrous CuSO₄; the water makes up 36.1% of the mass of the hydrate, and the number of water molecules x in an unknown hydrate is found from the ratio of moles of water to moles of salt.

Many common salts crystallize with water. Hydrates are important in construction, medicine, cooking and laboratory work. This article explains how hydrates are named and written, how to calculate formula masses and percent water, how to find the formula of a hydrate from experimental data, how hydrates are used as drying agents and in building materials, and gives a short history.

What is a hydrate?

In a hydrate, water molecules are part of the crystal structure, and they are held in definite positions around the cations or in the lattice. The ratio of water to salt is fixed: one formula unit of copper(II) sulfate pentahydrate has five water molecules. The water can be driven off by heating, which gives the anhydrous (“without water”) compound, and the change is often visible, as with the color change from blue to white for copper(II) sulfate and from pink to blue for cobalt(II) chloride. A hydrate is a pure compound with a fixed formula, not a mixture of a salt and water.

How are hydrates named?

The formula is written as the anhydrous salt, followed by a dot (·) and the number of water molecules: CuSO₄·5H₂O. The name is the name of the salt followed by the Greek prefix for the number of water molecules and the word “hydrate”: copper(II) sulfate pentahydrate. The prefixes are mono-, di-, tri-, tetra-, penta-, hexa-, hepta-, octa-, nona- and deca-.

Common hydrates

How do you calculate the percent water?

1. Find the molar mass of the whole hydrate by adding the mass of the anhydrous salt and the mass of the water: M(H₂O) = 18.015 g/mol.
2. Calculate the mass of the water: x × 18.015.
3. Percent water = (mass of water ÷ molar mass of the hydrate) × 100%.

How do you find the formula of a hydrate by experiment?

1. Weigh a clean, dry crucible. Add a sample of the hydrate and weigh again.
2. Heat gently, then strongly, to drive off all of the water. Cool in a desiccator and weigh again. Repeat until the mass is constant.
3. Calculate the mass of water lost (initial mass of hydrate − final mass of anhydrous salt).
4. Convert both masses to moles.
5. Divide the moles of water by the moles of salt, and round to the nearest whole number. This is x in the formula salt·xH₂O.

Worked examples

1. Formula mass of CuSO₄·5H₂O. CuSO₄: 63.55 + 32.07 + 4 × 16.00 = 159.62. Five waters: 5 × 18.015 = 90.08. Total: 249.70 g/mol.
2. Percent water. 90.08 ÷ 249.70 × 100% = 36.08%.
3. Mass for a solution. To prepare 250.0 mL of 0.100 mol/L CuSO₄ solution from the pentahydrate: moles = 0.100 × 0.2500 = 0.0250 mol. Mass = 0.0250 × 249.70 = 6.24 g. If you used 3.99 g (0.0250 × 159.62) of the anhydrous salt, the solution would be the same.
4. Finding x from data. A 4.92 g sample of hydrated magnesium sulfate, MgSO₄·xH₂O, is heated to constant mass and leaves 2.40 g of anhydrous MgSO₄. The mass of water is 4.92 − 2.40 = 2.52 g. Moles of MgSO₄ = 2.40 ÷ 120.37 = 0.01994 mol. Moles of H₂O = 2.52 ÷ 18.015 = 0.1399 mol. The ratio is 0.1399 ÷ 0.01994 = 7.02, which is 7. The formula is MgSO₄·7H₂O.
5. Percent water from data. In example 4, 2.52 ÷ 4.92 × 100% = 51.2%, in agreement with the table value.
6. Mass of anhydrous salt from a hydrate. How much anhydrous calcium chloride is in 10.0 g of CaCl₂·2H₂O? The fraction of CaCl₂ is 110.98 ÷ 147.01 = 0.7549, so the mass is 7.55 g.
7. Number of water molecules. 1.00 g of CuSO₄·5H₂O is 1.00 ÷ 249.70 = 0.004005 mol, which contains 5 × 0.004005 = 0.02002 mol of water, and 0.02002 × 6.022 × 10²³ = 1.21 × 10²² water molecules.

Where are hydrates used?

• Building: gypsum, CaSO₄·2H₂O, is heated to make plaster of Paris, CaSO₄·½H₂O. When mixed with water, it sets as gypsum again.
• Drying agents: anhydrous calcium chloride, magnesium sulfate and sodium sulfate absorb water to form hydrates. They are used to dry organic liquids in the laboratory, and in drying tubes and desiccators.
• Indicators of moisture: anhydrous cobalt(II) chloride, which is blue, turns pink on contact with water, and was used in humidity indicator cards. Anhydrous copper(II) sulfate turns from white to blue to test for water.
• Medicine and household: Epsom salt is used in baths and as a laxative, and washing soda is a cleaning agent.
• Heat storage: some hydrates, such as sodium sulfate decahydrate, absorb and release large amounts of heat as they melt and freeze, and are studied for thermal energy storage.

Related behavior: efflorescence and deliquescence

Some hydrates lose water to the air at room temperature, which is called efflorescence, and the crystals turn to a powder. Washing soda does this. Some anhydrous salts absorb so much water from humid air that they dissolve in it, which is called deliquescence. Calcium chloride and sodium hydroxide are examples. Salts that take up moisture are hygroscopic.

How were hydrates studied?

Early chemists observed that crystals of many salts lost their transparency and shape when heated and gave off water. The term “water of crystallization” was used in the 18th and 19th centuries. Joseph Louis Proust studied compounds such as copper sulfate and showed that the amount of water is fixed, which supported the law of definite proportions. Modern X-ray crystallography has shown how the water molecules are bonded to the ions in the crystal, for example four of the five water molecules in copper(II) sulfate pentahydrate are directly attached to the copper ion.

Which mistakes are common?

Mistake 1: Treating the dot as a multiplication sign

The dot in CuSO₄·5H₂O means “associated with”. The 5 applies only to H₂O, and the whole hydrate is one compound.

Mistake 2: Forgetting to include the water in the molar mass

The mass of the hydrate is much bigger than that of the anhydrous salt. Use the correct one for your calculation.

Mistake 3: Stopping the heating too early

Heat to constant mass, or some water will remain and the result for x will be too low.

Mistake 4: Heating too strongly

Some salts decompose at high temperatures, and the loss of mass includes other substances, which gives a result for x that is too high.