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LiI is soluble in water but LiF is not, why?

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Hint:. The Li is the third atom in the periodic table and possesses small atomic radii.
- The solubility depends on the lattice enthalpy of the compounds.

Complete step by step answer:
As in the question it has been asked to state the factors why LiI is soluble in water but the LiF is insoluble.
Here if we see both the elements the cation is the same i.e. the Li ion, so the difference in the property is due to the nature of anion and some of the effects governing the solubility.
Let’s first see the factors that affect the solubility of a substance.
- Solubility is related mainly to two terms i.e. lattice enthalpy of lattice energy and to the hydration enthalpy.
-Solubility of a product is directly proportional to the hydration energy i.e.
Solubility $\propto $ Hydration energy
-But solubility is inversely proportional to lattice energy.
$\text{Solubility}\propto \dfrac{\text{1}}{\text{Lattice}\,\text{energy}}$
So, $\text{Solubility}\propto \dfrac{\text{Hydration}\,\text{energy}}{\text{Lattice}\,\text{energy}}$
- As the hydration energy increases, the solubility increases and as the lattice energy decreases the solubility increases.

Now let’s see a brief idea of lattice energy and hydration energy.
Lattice energy - So lattice energy is always defined as that energy or enthalpy required to separate a mole of substance to its constituent ions.
Or if it terms of solid, we can say that the energy required to break the bonds between the ions that forms the lattice.
- Lattice energy mainly depends upon two factor-charge and size.
- As size decreases and charge increases, the lattice energy also increases and vice-versa.

Hydration energy – that energy released by the hydration of one mole of substance.
- Here in LiF, Li and F are having almost similar atomic radii; they are comparatively small in size, when compared with I in the LiI. As the size is very small, the lattice energy will be more since these ions are closely placed the electrostatic attraction between the ions will be more, whereas in LiI ,the I and Li atom have a huge difference in atomic size .The I atom is far larger than F and LiI is having low lattice enthalpy.
- And also in LiF, since they have high lattice enthalpy, their hydration energy will be very low and hence it is insoluble. But in LiI the lattice energy is having a small value and as lattice energy is having low value, the hydration enthalpy will be more, hence it is soluble in water.
- So we can conclude that the hydration energy and lattice energy are the two deciding factors for the reason why LiF is insoluble and LiI is soluble.

Note: The nature of the compounds also play a major role in the solubility of substance.
- The solubility of ionic compounds is more than the covalent compounds. Since ionic compounds are polar, water dissolves polar molecules more and the covalent compounds are nonpolar in nature.