Firstly let's briefly explain the difference between compounds and mixtures. Compounds are substances composed of many of the same molecule. Pure water, therefore, is an example of a compound as it is repeated molecules of H20. Mixtures are when two or more compounds are grouped together in a substance but retain their discrete molecular forms. For example, salty water is a mixture of pure water molecules and salt molecules. Mixtures can be separated without breaking molecular bonds, however compounds cannot.
If we take desalinization of sea water (salt water) for example. Sea water contains water molecules and salt molecules in a mixture. Pure water can be separated from the salt by passing the sea water through a very fine mesh at high pressure. The mesh acts like a sieve and does not let the salt molecules pass through, trapping them on one side and leaving pure water on the other side. This is called a reverse osmosis filter and is an example of separating two constituent molecules (compounds) from a mixture.
Separating water molecules themselves into their constituent atoms/molecules, however, does require bonds to be broken. In water the hydrogen and oxygen atoms are covalently bonded together. In order to separate them we must break these bonds and the application of energy through the process of electrolysis can achieve this. The result yields hydrogen gas at one electrode and oxygen gas at the other.
Notably, separating mixtures or compounds into their constituents requires energy in some form.
