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I understand that that energy is required to overcome intermolecular forces holding solute particles together in the crystal but I don't understand how this relates to lattice energies and its respective solubility in water

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When an ionic compound dissolves in water, the water molecules surround the individual ions. Since water is very polar, when water surrounds an ion there is a decrease in overall energy. However, to pull the ions apart in the first place, there has to be an energy increase to overcome the lattice energy. If the lattice energy (cost) is larger than the energy of solvation of the ions (gain) the compound won't dissociate, and it will be insoluble.

There is a large grey area where lattice energy and solvation energy are close, and for those compounds temperature has a big influence on solubility.

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