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FeCl3,FeSO4 and CuSO4 all are deliquescent solids.

Is there any way to predict this without knowing this fact? I am looking for a way to predict if a substance is deliquescent for my upcoming exams.

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There is no general rule, just partial empirical rules for particular anions, which can be memorized from textbooks.

There is theoretical reasoning why salts are soluble or not, concerning the energy of the crystal lattice, energy of ion hydration, entropy change etc. But easier way is to go for empirical rules and "chemical sense".

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