Water in hydrated salts often doesn’t just sit in between the salt ions.
Oxygen in water has two extra pairs of electrons that aren’t involved in bonding with hydrogens. Iron ion has free unfilled orbitals. The interaction between an electron pair and an unfilled orbital forms donor-acceptor bond and the energy of this bond is lower than the previous no bond state.
Photons with a particular amount of energy excite electrons to go from filled to unfilled orbitals, and after some time the excited electrons return to their previous orbitals and emit photons with exactly same energy as the difference between these orbitals. That is what influences the color of compounds.
As previously stated, some unfilled orbitals of iron formed new bonds with water and lowered their energy. Because of that we now have different dynamics of photon-electron interaction and subsequently the color of substance changes.
Other metals and other electron pair donors can also interact with each other in the similar manner and change their color accordingly. Anhydrous nickel chloride for example is yellow, hydrated nickel chloride is green and nickel chloride in ammonia solution is blue.
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