The correct order of increasing hydration energy of the following conjugate bases of oxoacids of bromine is

Options

A. `BrO_(4)^(-) lt BrO_(3)^(-) lt BrO_(2)^(-)lt BrO^(-)`
B. `BrO_(4)^(-) lt BrO_(3)^(-) lt BrO^(-) lt BrO_(2)^(-)`
C. `BrO_(3)^(-)lt BrO_(4)^(-)ltBrO_(2)^(-) lt BrO^(-)`
D. `BrO^(-) lt BrO_(2)^(-) lt BrO_(3)^(-) lt BrO_(4)^(-)`

Answer

To determine the correct order of increasing hydration energy of the conjugate bases of the oxoacids of bromine (BrO⁻, BrO₂⁻, BrO₃⁻, and BrO₄⁻), we need to analyze how the size of these ions affects their hydration energy.

### Step-by-Step Solution:

1. **Understand Hydration Energy**: Hydration energy is the energy released when one mole of an ion is surrounded by water molecules. Smaller ions tend to have higher hydration energy because they can be surrounded more closely by water molecules.

2. **Identify the Ions**: The conjugate bases we are considering are:
- BrO⁻ (hypobromite)
- BrO₂⁻ (bromite)
- BrO₃⁻ (bromate)
- BrO₄⁻ (perbromate)

3. **Analyze the Size of Ions**: As the number of oxygen atoms attached to bromine increases, the size of the conjugate base increases due to the additional electron repulsion and the overall structure of the ion.
- BrO⁻ is the smallest ion.
- BrO₂⁻ is larger than BrO⁻.
- BrO₃⁻ is larger than BrO₂⁻.
- BrO₄⁻ is the largest ion.

4. **Determine the Order of Hydration Energy**: Since smaller ions have higher hydration energy, we can establish the order based on size:
- BrO⁻ (smallest) → highest hydration energy
- BrO₂⁻ → lower hydration energy than BrO⁻
- BrO₃⁻ → lower hydration energy than BrO₂⁻
- BrO₄⁻ (largest) → lowest hydration energy

5. **Final Order of Increasing Hydration Energy**: Therefore, the order of increasing hydration energy is:
- BrO₄⁻ < BrO₃⁻ < BrO₂⁻ < BrO⁻

### Conclusion:
The correct order of increasing hydration energy of the conjugate bases of oxoacids of bromine is:
**BrO₄⁻ < BrO₃⁻ < BrO₂⁻ < BrO⁻**