Which of the following ions, will have maximum hydration energy

Options

A. `Sr^(2+)`
B. `Ba^(2+)`
C. `Ca^(2+)`
D. `Mg^(2+)`

Explanation

To determine which of the given ions will have the maximum hydration energy, we can follow these steps:

### Step 1: Understand Hydration Energy
Hydration energy is the energy released when ions are surrounded by water molecules. It is influenced by two main factors: the charge of the ion and the size (radius) of the ion. The formula for hydration energy can be expressed as:
\[ \text{Hydration Energy} \propto \frac{z^2}{r} \]
where \( z \) is the charge of the ion and \( r \) is the radius of the ion.

### Step 2: Identify the Ions
The ions given in the question are:
- Calcium ion (\( \text{Ca}^{2+} \))
- Strontium ion (\( \text{Sr}^{2+} \))
- Barium ion (\( \text{Ba}^{2+} \))

### Step 3: Analyze the Charge of the Ions
All three ions have the same charge of +2. Therefore, the charge factor \( z^2 \) is constant for all three ions.

### Step 4: Compare the Ionic Radii
The ionic radii increase as we move down the group in the periodic table. The order of ionic radii for the given ions is:
- Calcium ion (\( \text{Ca}^{2+} \)) < Strontium ion (\( \text{Sr}^{2+} \)) < Barium ion (\( \text{Ba}^{2+} \))

This means that \( \text{Ca}^{2+} \) has the smallest radius, while \( \text{Ba}^{2+} \) has the largest radius.

### Step 5: Apply the Hydration Energy Formula
Since hydration energy is inversely proportional to the radius, the ion with the smallest radius will have the highest hydration energy. Therefore:
- \( \text{Ca}^{2+} \) will have the highest hydration energy, followed by \( \text{Sr}^{2+} \) and then \( \text{Ba}^{2+} \).

### Conclusion
Thus, the ion with the maximum hydration energy among the given options is:
**Calcium ion (\( \text{Ca}^{2+} \))**.

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