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 and electron configuration in each of the given compounds. Let's break this down step by step.

### Step 1: Identify the Compounds
The compounds mentioned are:
1. BF4^-
2. BF3
3. BF3NH3

### Step 2: Draw the Lewis Structures
- **BF4^-**: Boron (B) is surrounded by four fluorine (F) atoms and has a negative charge. The boron atom has an octet (8 electrons) due to the four bonds with fluorine.

- **BF3**: Boron is bonded to three fluorine atoms. In this case, boron has only 6 electrons in its valence shell, making it electron-deficient.

- **BF3NH3**: In this compound, BF3 is coordinated with ammonia (NH3). The nitrogen in ammonia donates a lone pair to boron, completing its octet. Thus, boron has 8 electrons in this case as well.

### Step 3: Analyze the Bonding
- In **BF4^-**, the B-F bonds are formed without any back-bonding because boron has a complete octet. The bond lengths are relatively longer due to the lack of additional electron interactions.

- In **BF3**, the boron atom is electron-deficient and can participate in back-bonding with the fluorine atoms. This back-bonding involves the donation of electron density from the filled p-orbitals of fluorine to the empty p-orbital of boron, which shortens the B-F bond length.

- In **BF3NH3**, although boron has a complete octet due to the coordinate bond with ammonia, the back-bonding is less significant compared to BF3 because the electron donation from NH3 does not enhance the B-F bond strength as effectively as the back-bonding in BF3.

### Step 4: Conclusion
Based on the analysis, the compound with the shortest B-F bond length is **BF3** due to the presence of significant back-bonding, which effectively shortens the bond length.

### Final Answer
The compound in which the B-F bond length is shortest is **BF3**.

---