The solubility of alkli metals salts in water is due to the fact that the cations get hydrated by water molecules. The degree of hydration depends upon the size of the cation. If the trend of relative ionic radii is `Cs^(+) gt Rb^(+) gt K^(+) gt Na^(+) gt Li^(+) `.
What is the relative degree of hydration?

Options

A. `Cs_((aq))^(+) gt Pb_((aq))^(+) gt K_((aq))^(+) gt Na_((aq))^(+) gt Li_((aq))^(+)`
B. `Li_((aq))^(+) gt Na_((aq))^(+) gt K_((aq))^(+) gt Rb_((aq))^(+) gt Cs_((aq))^(+)`
C. `Na_((aq))^(+) gt K_((aq))^(+) gt Rb_((aq))^(+) gt Cs_((aq))^(+) gt Li_((aq))^(+)`
D. `Cs_((aq))^(+) gt Na_((aq))^(+) gt Li_((aq))^(+) gt K_((aq))^(+) gt Rb_((aq))^(+)`

Explanation

To determine the relative degree of hydration of alkali metal cations based on their ionic radii, we can follow these steps:

### Step 1: Understand the concept of hydration
Hydration refers to the process where water molecules surround and interact with ions. The degree of hydration depends on the size of the cation; smaller cations can attract water molecules more effectively due to their higher charge density.

### Step 2: Identify the trend of ionic radii
The trend of ionic radii for alkali metal cations is given as:
\[ \text{Cs}^+ > \text{Rb}^+ > \text{K}^+ > \text{Na}^+ > \text{Li}^+ \]
This means that lithium ion (\( \text{Li}^+ \)) is the smallest, while cesium ion (\( \text{Cs}^+ \)) is the largest.

### Step 3: Relate ionic size to charge density
Charge density is defined as the charge of the ion divided by its volume (or size). Since all alkali metal cations have the same charge (+1), the charge density is inversely proportional to the size of the cation. Therefore, the smaller the cation, the higher the charge density.

### Step 4: Rank the cations based on charge density
Based on the size trend:
- \( \text{Li}^+ \) has the highest charge density (smallest size)
- \( \text{Na}^+ \)
- \( \text{K}^+ \)
- \( \text{Rb}^+ \)
- \( \text{Cs}^+ \) has the lowest charge density (largest size)

### Step 5: Determine the relative degree of hydration
Since the degree of hydration is directly related to charge density, we can conclude the following:
- \( \text{Li}^+ \) will have the highest degree of hydration.
- \( \text{Na}^+ \) will have the next highest degree of hydration.
- \( \text{K}^+ \)
- \( \text{Rb}^+ \)
- \( \text{Cs}^+ \) will have the lowest degree of hydration.

### Final Ranking of Hydration
Thus, the relative degree of hydration from highest to lowest is:
\[ \text{Li}^+ > \text{Na}^+ > \text{K}^+ > \text{Rb}^+ > \text{Cs}^+ \]