Existence of which hydrated salt is most likely?

Options

A. `LiCl.2H_(2)O`
B. `NaCl.2H_(2)O`
C. `KCl.2H_(2)O`
D. `CsCl.2H_(2)O`

Explanation

To determine which hydrated salt is most likely to exist among the given options, we need to analyze the properties of the alkali metal ions involved in each salt. The options provided are:

1. LiCl·2H2O
2. NaCl·2H2O
3. KCl·2H2O
4. CsCl·2H2O

### Step-by-Step Solution:

**Step 1: Understand the nature of alkali metal ions.**
- Alkali metals (Group 1 elements) include lithium (Li), sodium (Na), potassium (K), rubidium (Rb), and cesium (Cs).
- As we move down the group from Li to Cs, the size of the metal ion increases, and the charge density decreases.

**Hint for Step 1:** Consider how the size and charge density of the metal ions affect their ability to interact with water molecules.

**Step 2: Consider hydration energy.**
- Hydration energy is the energy released when ions are surrounded by water molecules. Smaller ions with higher charge density have greater hydration energy.
- Lithium ion (Li⁺) is the smallest and has the highest charge density among the alkali metals, leading to a higher hydration energy compared to Na⁺, K⁺, and Cs⁺.

**Hint for Step 2:** Recall that smaller ions typically have stronger interactions with water due to their higher charge density.

**Step 3: Compare the hydration enthalpy of the ions.**
- The hydration enthalpy of Li⁺ is significantly higher than that of Na⁺, K⁺, and Cs⁺. This means that Li⁺ can stabilize more water molecules around it, making its hydrated salt more likely to exist.

**Hint for Step 3:** Look at the trend in hydration enthalpy for alkali metals and how it affects the stability of their hydrated salts.

**Step 4: Analyze the stability of the hydrated salts.**
- Since Li⁺ has the highest hydration energy, the hydrated salt LiCl·2H2O is more stable and more likely to exist compared to the other salts listed.

**Hint for Step 4:** Think about how the stability of a compound is influenced by the interactions between its ions and surrounding molecules.

**Step 5: Conclusion.**
- Based on the analysis, the hydrated salt that is most likely to exist is LiCl·2H2O.

### Final Answer:
The hydrated salt that is most likely to exist is **LiCl·2H2O**.