How to Calculate Hydrates

By John Brennan
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Salts known as hydrates contain molecules of water incorporated into their crystal structures. If you heat a hydrated salt, you can cause the water it contains to evaporate; the resulting crystal is called anhydrous, meaning without water. The difference in mass between the anhydrous and hydrated salt gives you the information you need to find the percentage of water in the hydrate. If you've already conducted this experiment and know the mass of both the hydrated and anhydrous salts, the calculations are simple.

Subtract the mass of the anhydrous salt from that of the hydrated salt. For example, if you have a sample of copper (II) sulfate that weighed 25 grams before you heated it and 16 grams afterward, subtract 16 from 25 to get 9 grams.

Divide this difference by the mass of the hydrated salt. Continuing the example, we would divide 9 grams by 25 grams to get 36 percent. This is the percentage of water in the hydrate, so it's the first thing you might need to calculate; however, we can calculate some other information as well.

Determine the molar mass of the anhydrous salt using the periodic table. The periodic table lists the molar mass of each element. Multiply the molar mass of each element in your compound by the number of times it appears in your compound to get the molar mass of the compound.

For example, the chemical formula of anhydrous copper (II) sulfate is Cu(SO4). The molar mass of this compound is equal to the molar mass of copper plus the molar mass of sulfur plus four times the molar mass of oxygen (since there are four oxygen atoms in the molecule). If we look up the molar masses of each on the periodic table, we find the following:

63.55 + 32.06 + (4 x 16) = 159.61 grams per mole

Divide the mass of your anhydrous (heated) salt sample by the molar mass of the anhydrous compound to get the number of moles of compound present. In our example, 16 grams / 160 grams per mole = 0.1 moles.

Divide the mass of water lost when you heated the salt by the molar mass of water, roughly 18 grams per mole. In our example, we lost 9 grams of water; if we divide 9 by 18, we get 0.5 moles of water lost.

Divide the number of moles of water lost by the number of moles of anhydrous salt to get the ratio of water molecules to formula units. In our example, 0.5 moles of water / 0.1 moles copper sulfate = 5:1 ratio. This means that for every unit of CuSO4 present, we have 5 molecules of water.

About the Author

Based in San Diego, John Brennan has been writing about science and the environment since 2006. His articles have appeared in "Plenty," "San Diego Reader," "Santa Barbara Independent" and "East Bay Monthly." Brennan holds a Bachelor of Science in biology from the University of California, San Diego.