Why is it hard, and costly to remove salt from water?
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Mixing salt and water is an exothermic reaction, a chemical reaction which releases energy (in this case, a tiny bit of heat is released).
In chemistry, doing the reverse of an exothermic reaction is called endothermic, which means it takes energy. So, separating salt and water is necessarily endothermic, that is to say, it requires energy.
From a practical standpoint, any reaction which requires energy is going to cost more and be harder to do than on which releases energy.
Every possible method of separating salt from water requires either immense power (heat for distillation) or immense pressure (reverse osmosis). Both of these require a large amount of energy.
Almost all chemistry is like this; performing a reaction one way releases energy (exothermic) and performing it the other way takes energy (endothermic). Combining iron and oxygen to form rust produces x units of energy. Separating the rust back into iron and oxygen would take x units of energy. (And due to conservation of energy, x is the same value given the same amount of material being converted.)
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