Which of the following properties of elements of alkaline earth metal does not increase with increasing atomic number ?

Options

A. Solubility of hydroxide
B. Reactivity with water
C. `I^(st)` Ionisation enthalpy
D. Stability of carbonate

Explanation

To solve the question regarding which property of alkaline earth metals does not increase with increasing atomic number, we can analyze the properties one by one.

### Step-by-Step Solution:

1. **Identify the Properties**: The properties we need to analyze are:
- Solubility of hydroxides
- Reactivity with water
- First ionization enthalpy
- Stability of carbonates

2. **Analyze Solubility of Hydroxides**:
- As we move down the group from beryllium (Be) to barium (Ba), the atomic size increases.
- Larger atomic size leads to decreased lattice energy due to the larger distance between ions.
- With decreased lattice energy, the solubility of hydroxides increases.
- **Conclusion**: Solubility of hydroxides increases down the group.

3. **Analyze Reactivity with Water**:
- Reactivity with water also increases down the group.
- This is because the ionization energy decreases as the atomic size increases, allowing metals to lose electrons more easily.
- **Conclusion**: Reactivity with water increases down the group.

4. **Analyze First Ionization Enthalpy**:
- The first ionization enthalpy decreases down the group.
- As the atomic size increases, the effective nuclear charge felt by the outermost electron decreases, making it easier to remove an electron.
- **Conclusion**: First ionization enthalpy decreases down the group.

5. **Analyze Stability of Carbonates**:
- The stability of carbonates increases down the group.
- Larger cations stabilize the carbonate ion due to better lattice formation.
- **Conclusion**: Stability of carbonates increases down the group.

6. **Final Comparison**:
- From the analysis:
- Solubility of hydroxides: Increases
- Reactivity with water: Increases
- First ionization enthalpy: Decreases
- Stability of carbonates: Increases
- The only property that does not increase with increasing atomic number is the **first ionization enthalpy**.

### Answer:
The property of alkaline earth metals that does not increase with increasing atomic number is **first ionization enthalpy**.

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