The correct order of hydration enthalpies of alkali metal ions is:

Options

A. `Li^(+)gtNa^(+)gtK^(+)gtCs^(+)gtRb^(+)`
B. `Na^(+)gtLi^(+)gtK^(+)gtRb^(+)gtCs^(+)`
C. `Na^(+)gtLi^(+)gtK^(+)gtCs^(+)gtRb^(+)`
D. `Li^(+)gtNa^(+)gtRb^(+)gtCs^(+)gtK^(+)`

Answer

To determine the correct order of hydration enthalpies of alkali metal ions (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺), we need to consider the factors that influence hydration enthalpy.

### Step-by-step Solution:

1. **Understanding Hydration Enthalpy**:
- Hydration enthalpy is the amount of energy released when ions are surrounded by water molecules. It is a measure of the strength of interaction between the ion and water.

2. **Factors Affecting Hydration Enthalpy**:
- The hydration enthalpy depends on the charge-to-size ratio of the ions. A higher charge and a smaller ionic radius lead to a greater hydration enthalpy.
- For alkali metals, they all have a +1 charge, so we focus on their ionic sizes.

3. **Ionic Sizes of Alkali Metals**:
- The ionic sizes of alkali metals increase as we move down the group in the periodic table:
- Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺
- This means that lithium ion (Li⁺) is the smallest, and cesium ion (Cs⁺) is the largest.

4. **Comparing Hydration Enthalpies**:
- Since Li⁺ is the smallest ion, it has the highest charge-to-size ratio, leading to the greatest hydration enthalpy.
- As we move down the group, the size of the ions increases, and thus the hydration enthalpy decreases.

5. **Order of Hydration Enthalpies**:
- Based on the above analysis, the order of hydration enthalpies from highest to lowest is:
- Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺

### Final Answer:
The correct order of hydration enthalpies of alkali metal ions is:
**Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺**