The tendency of `bF_(3), BCl_(3)` and `BBr_(3)` behave as Lewis acid decreases in the sequnece
(a)`BCl_(3) gt BF_(3) gt BBr_(3)`
(b)`BBr_(3) gt BCl_(3) gt BF_(3)`
(c)`BBr_(3) gt BF_(3) gt BCl_(3)`
(d)`BF_(3) gt BCl_(3) gt BBr_(3)`

Options

A. `BCl_(3) gt BF_(3) gt BBr_(3)`
B. `BBr_(3) gt BCl_(3) gt BF_(3)`
C. `BBr_(3) gt BF_(3) gt BCl_(3)`
D. `BF_(3) gt BCl_(3) gt BBr_(3)`

Explanation

To determine the sequence in which \( BF_3 \), \( BCl_3 \), and \( BBr_3 \) behave as Lewis acids, we need to analyze the properties of these compounds and how they relate to Lewis acidity.

### Step-by-Step Solution:

1. **Understanding Lewis Acids**:
- Lewis acids are defined as electron pair acceptors. They are typically electron-deficient species that can accept electrons from Lewis bases (electron pair donors).

2. **Analyzing the Boron Compounds**:
- All three compounds, \( BF_3 \), \( BCl_3 \), and \( BBr_3 \), are formed from boron and halogens. Boron has an incomplete octet and is electron-deficient, making it a Lewis acid.

3. **Comparing the Halogens**:
- The halogens (F, Cl, Br) differ in size and electronegativity:
- **Fluorine (F)**: Smallest size, highest electronegativity.
- **Chlorine (Cl)**: Larger than fluorine, lower electronegativity.
- **Bromine (Br)**: Largest size, lower electronegativity than both F and Cl.

4. **Effect of Size and Overlap**:
- As we move from fluorine to bromine, the size of the halogen increases. This affects the overlap between the orbitals of boron and the halogen:
- \( BF_3 \): Involves 2p-2p overlap (strong overlap).
- \( BCl_3 \): Involves 2p-3p overlap (weaker overlap).
- \( BBr_3 \): Involves 2p-4p overlap (even weaker overlap).

5. **Determining Lewis Acidity**:
- The strength of Lewis acidity decreases as the overlap decreases. Therefore:
- \( BBr_3 \) has the weakest overlap and thus behaves as the strongest Lewis acid.
- \( BCl_3 \) is next in line.
- \( BF_3 \) has the strongest overlap but is the least Lewis acidic due to the high electronegativity of fluorine, which holds onto its electrons more tightly.

6. **Conclusion**:
- The order of Lewis acidity is:
\[ BBr_3 > BCl_3 > BF_3 \]
- Thus, the correct answer is (b) \( BBr_3 > BCl_3 > BF_3 \).