How do you deduce the formula of a hydrate?

You deduce the formula of a hydrate by determining the ratio of water molecules to the other compound in the hydrate.

To deduce the formula of a hydrate, you need to know the mass of the hydrate and the mass of the anhydrous compound (the compound without water). Hydrates are compounds that have water molecules chemically attached to them. The water is not just physically mixed in, but is actually part of the compound's structure. The formula of a hydrate is written as the formula of the anhydrous compound followed by a dot and then the number of water molecules per formula unit of the anhydrous compound.

To find this ratio, you first weigh the hydrate, then heat it to remove the water (this process is called dehydration), and weigh the anhydrous compound that remains. The difference in mass is the mass of the water. You then convert these masses to moles (using the molar mass of water and the anhydrous compound), and the ratio of moles of water to moles of anhydrous compound gives you the formula of the hydrate.

For example, if you start with 10.0 g of a hydrate and after heating you have 6.4 g of anhydrous compound, you know that 3.6 g of water was removed. If the molar mass of the anhydrous compound is 64 g/mol and the molar mass of water is 18 g/mol, you find that you have 0.1 mol of anhydrous compound and 0.2 mol of water. This gives a ratio of 2:1, so the formula of the hydrate is (anhydrous compound)•2H2O.

Remember, it's important to heat the hydrate gently and slowly to avoid splattering or decomposition, and to ensure all the water is removed.