Least mobile ion is

Options

A. `[Be(H_(2)O)_(n)]^(+2)`
B. `[Na(H_(2)O)_(n)]^(+)`
C. `[Mg(H_(2)O)_(n)]^(+2)]`
D. `[Li(H_(2)O)_(n)]^(+)`

Answer

To determine the least mobile ion among the given options, we need to analyze the hydration energy and the charge-to-size ratio of the ions provided. Here’s a step-by-step solution:

### Step 1: Identify the Ions
The ions given in the question are:
- Beryllium \( \text{Be}^{2+} \)
- Sodium \( \text{Na}^+ \)
- Magnesium \( \text{Mg}^{2+} \)
- Lithium \( \text{Li}^+ \)

### Step 2: Understand Mobility of Ions
The mobility of an ion in solution is influenced by its hydration energy. Hydration energy is the energy released when water molecules surround an ion. Higher hydration energy generally means that the ion is more strongly attracted to water molecules, which can reduce its mobility.

### Step 3: Analyze Charge-to-Size Ratio
The charge-to-size ratio is crucial in determining hydration energy:
- **Charge**: Higher charge increases the attraction to water molecules.
- **Size**: Smaller ions have a higher charge-to-size ratio, leading to greater hydration energy.

### Step 4: Compare the Ions
- **Lithium \( \text{Li}^+ \)**: Small size, high charge-to-size ratio, high hydration energy.
- **Sodium \( \text{Na}^+ \)**: Larger than lithium, lower charge-to-size ratio, lower hydration energy than lithium.
- **Beryllium \( \text{Be}^{2+} \)**: Small size but has a +2 charge, which gives it a very high charge-to-size ratio and high hydration energy.
- **Magnesium \( \text{Mg}^{2+} \)**: Similar to beryllium, but larger in size, leading to lower hydration energy than beryllium.

### Step 5: Determine the Least Mobile Ion
Among these ions, lithium \( \text{Li}^+ \) has the highest hydration energy due to its small size and high charge-to-size ratio. This means it is surrounded by more water molecules, making it less mobile compared to the others.

### Conclusion
The least mobile ion among the given options is:
**Lithium \( \text{Li}^+ \) (or \( \text{Li(H}_2\text{O)}_n^+ \))**