In which of the following compounds B-F bond length is shortest?

Options

A. `BF_(4)^(-)`
B. `BF_(3) barrNH_(3)`
C. `BF_(3)`
D. `BF_(3) barrN(CH_(3))_(3)`

Explanation

To determine which compound has the shortest B-F bond length, we need to analyze the bonding characteristics of each option provided.

### Step-by-Step Solution:

1. **Identify the Compounds**: The given compounds are:
- A) BF4^-
- B) F3B directing towards NH3
- C) BF3
- D) F3B directing towards N(CH3)3

2. **Analyze BF4^-**:
- In BF4^-, boron is surrounded by four fluorine atoms, forming single bonds.
- The bond length in BF4^- is relatively long due to the presence of single bonds.

3. **Analyze F3B directing towards NH3**:
- In this scenario, BF3 acts as a Lewis acid and can accept a lone pair from NH3.
- However, the B-F bonds in BF3 are still single bonds, so the bond length remains comparable to BF4^-.

4. **Analyze BF3**:
- BF3 has three fluorine atoms bonded to boron.
- Importantly, there is a possibility of p-pi backbonding due to the presence of a lone pair on fluorine.
- This backbonding can introduce some double bond character to the B-F bonds, which shortens the bond length compared to pure single bonds.

5. **Analyze F3B directing towards N(CH3)3**:
- Similar to the previous case, BF3 interacts with N(CH3)3, but the B-F bonds are still primarily single bonds.
- Thus, the bond lengths are not shorter than those in BF3.

6. **Compare Bond Lengths**:
- The bond lengths can be summarized as follows:
- BF4^-: Longest (single bonds)
- F3B (with NH3): Similar to BF4^- (single bonds)
- BF3: Shorter (due to double bond character from backbonding)
- F3B (with N(CH3)3): Similar to BF4^- (single bonds)

7. **Conclusion**:
- The compound with the shortest B-F bond length is **BF3** due to the presence of double bond character from p-pi backbonding.

### Final Answer:
The compound with the shortest B-F bond length is **C) BF3**.