All the boron trihalides except `BI_(3)` may be prepared by direction between the elements. Boron trihalides consist of trigonal-planar `BX_(3)` molecules. Unlike the halides of the other elements in the group they are monomeric in the gas, liquid and solid states, `BF_(3)` and `BCl_(3)` are gases, `BBr_(3)` is a volatile liquid and `BI_(3)` is a solid. Boron trihalides are Lewis acids because they form simple Lewis complexes with suitable bases, as in the reaction:
`BF_(3)(g)+NH_(3)(g)toF_(3)B-NH_(3)(s)`
However, boron chlorides, bromides and iodides are susceptible (sensitive) to protolysis by mild proton sources such as water, alcohols and even amines, for example `BCl_(3)` undergoes rapid hydrolysis:
`BCl_(3)(g)+3H_(2)O(l)toB(OH)_(3)(aq)+3HCl (aq)`
It is supposed that the first step in the above reaction is the formation of the complex `Cl_(3)B larr OH_(2)` which then eliminates `HCl` and reacts with water.
Which of the follwoing is the best order of Lewis acid strength of `BF_(3),BCl_(3)` and `BBr_(3)` ?

Options

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

Answer

To determine the best order of Lewis acid strength among the boron trihalides \( BF_3, BCl_3, \) and \( BBr_3 \), we can analyze the factors affecting their Lewis acidity based on the information provided.

### Step-by-Step Solution:

1. **Understanding Lewis Acids**:
- Lewis acids are substances that can accept an electron pair. The strength of a Lewis acid depends on the ability of the central atom (in this case, boron) to accept electrons.

2. **Back Bonding Concept**:
- In boron trihalides, back bonding occurs when the lone pair of electrons from the halogen atoms overlaps with the empty p-orbital of boron. This back bonding stabilizes the molecule and reduces the electron deficiency of boron.

3. **Effect of Halogen Size**:
- As we move down the group from fluorine to iodine, the size of the halogen atoms increases. Larger halogens (like bromine and iodine) have less effective overlap with the boron’s p-orbital, leading to weaker back bonding.

4. **Order of Back Bonding**:
- The extent of back bonding is strongest with fluorine and weakest with iodine. Therefore, the order of back bonding strength is:
\[ F > Cl > Br > I \]

5. **Impact on Lewis Acidity**:
- Since stronger back bonding decreases the electron deficiency of boron, it makes it a weaker Lewis acid. Conversely, lesser back bonding means boron remains more electron deficient, making it a stronger Lewis acid.
- Thus, the order of Lewis acid strength is inversely related to the extent of back bonding:
\[ BF_3 < BCl_3 < BBr_3 \]

6. **Conclusion**:
- Based on the above analysis, the correct order of Lewis acid strength for the boron trihalides is:
\[ BF_3 < BCl_3 < BBr_3 \]

### Final Answer:
The best order of Lewis acid strength of \( BF_3, BCl_3, \) and \( BBr_3 \) is:
\[ BF_3 < BCl_3 < BBr_3 \]