Question

The low solubility of LiF and that of CsI in water are respectively due to which property of the alkali metal ions?
[A] Higher hydration enthalpy of $L{{i}^{+}}$, higher lattice enthalpy of $C{{s}^{+}}$
[B] Smaller hydration enthalpy of $L{{i}^{+}}$, higher lattice enthalpy of $C{{s}^{+}}$
[C] Smaller lattice enthalpy of $L{{i}^{+}}$, higher hydration enthalpy of $C{{s}^{+}}$
[D] Higher lattice enthalpy of $L{{i}^{+}}$, smaller hydration enthalpy of $C{{s}^{+}}$

Answer 1

Hint: Solubility of ionic compounds depends upon their lattice energy and hydration energy. If hydration energy is higher than lattice energy, it will be soluble in water and if not it is insoluble. Hydration energy is directly proportional to charge and inversely proportional to the size of the ion.

Complete answer: Firstly, let us discuss the insolubility of LiF in water.
In aqueous medium, the solubility of the compounds depends upon their hydration energy as well as lattice energy. We define hydration energy as the energy liberated upon dissolution of the compound in water and lattice energy is the energy which bounds the crystal lattice of an atom.
If the lattice energy of a compound is higher than the hydration energy, the compound will be insoluble in water and if lattice energy lower than the hydration energy, the compound will be soluble in water.
In LiF, as we know fluorine is small in size and highly electronegative and lithium is electropositive. This will make the LiF compound very stable thus resulting in higher lattice energy. Dissolving in water will not help LiF in gaining any extra stability.
Therefore, LiF is insoluble in water due to the higher lattice enthalpy of $L{{i}^{+}}$.
Now for CsI, as we know hydration energy is directly proportional to charge and inversely proportional to size. On dissolution in water, CsI will dissociate into $C{{s}^{+}}\text{ and }{{\text{I}}^{-}}$. Both these ions are larger in size thus, their hydration energy will decrease. And as we know, solubility of an ionic compound depends upon its lattice energy as well as hydration energy and as CsI has lower hydration energy therefore it is insoluble in water.
Therefore, CsI is insoluble in water due to the lower hydration energy of $C{{s}^{+}}$.

Therefore, the correct answer is option [D] Higher lattice enthalpy of $L{{i}^{+}}$, smaller hydration enthalpy of $C{{s}^{+}}$.

Note:
We can also answer this question by the concept of Hard-Soft Acid-Base (HSAB) Theory. According to this, hard-hard and soft-soft centres are stable and hard-soft pairs are unstable. For example, $L{{i}^{+}}$is a hard acid and ${{I}^{-}}$is a soft base, as their pair is hard-soft therefore they dissolve in water to gain stability whereas LiF does not as they are hard-hard centres.