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Hygroscopy is the ability of a substance to attract and hold water molecules from the surrounding environment.

Why are some compounds hygroscopic and others are not? What is it about their structures that allows them to hold water? Is it due to the atoms being arranged in a certain structure due to bonding?

How can you tell if a compound is more hygroscopic than another?

Mithoron
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bohnita
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Ions are hygroscopic because they form very stable, low energy hydrates, which are thermodynamically favorable over water vapor. I.E. salt attracts water vapor because the hydrated salt is lower energy than the water vapor. Other very porous materials are hygrosopic due to capillary action. Water vapor is attracted to the surface initially due to a variety of reasons, then the narrow channels in the porous material cause the water to spread out to lower their energy.

Matt Towns
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    Also, it is worth mentioning that formation of hydrates is a property of compound as a whole, rather than individual ions. See, for example: neither $\ce{NaCl}$ nor $\ce{CaCO_3}$ form hydrates, but both $\ce{Na_2CO_3}$ and $\ce{CaCl_2}$ do, the latter quite eagerly. – Ivan Neretin Sep 04 '15 at 14:58
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Some salts have high tendency to be hydrated, like Li salts. The reason is that their hydration energy is very high, meaning that when they are hydrated, lot of energy is released. Since lower energy is always more stable, such salts tend to show high hygroscopy.