The solubility of alkali metal hydroxides follows the order:

Options

A. `LiOH lt NaOH lt KOH lt RbOH lt CsOH`
B. `LiOH gt NaOH gt KOH gt RbOH gt CsOH`
C. `LiOH gt CsOH gt RbOH gt NaOH gt KOH`
D. None of the above.

Explanation

To determine the order of solubility of alkali metal hydroxides, we follow these steps:

### Step 1: Understand the Factors Affecting Solubility
The solubility of alkali metal hydroxides (MOH) is influenced by two main factors:
1. **Polarity of the bond**: Higher polarity leads to increased solubility.
2. **Lattice enthalpy**: Lower lattice enthalpy also contributes to higher solubility.

### Step 2: Analyze the Cations
In alkali metal hydroxides, the cation is the alkali metal ion (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺). All these ions have a +1 charge, but they differ in size:
- Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺

### Step 3: Relate Size to Solubility
According to Fajans' rules:
- As the size of the cation increases, the polarizing power of the cation decreases.
- A smaller cation (like Li⁺) has a higher polarizing power, which can lead to a higher covalent character in the hydroxide, making it less soluble.
- Conversely, larger cations (like Cs⁺) have lower polarizing power, leading to a more ionic character and thus greater solubility.

### Step 4: Establish the Order of Solubility
Based on the above analysis:
- The order of solubility of alkali metal hydroxides will be inversely related to the size of the cation:
- LiOH < NaOH < KOH < RbOH < CsOH

Thus, the order of solubility is:
**LiOH < NaOH < KOH < RbOH < CsOH**

### Step 5: Conclusion
The order of solubility of alkali metal hydroxides follows the trend of increasing solubility with increasing size of the cation.

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