`BX_(3)+NH_(3) overset(B.T.) to BX_(3) *NH_(3)`+Heat of adduct formation `(DeltaH)`
The numberical value of `DeltaH` is found to be maximum for:

Options

A. `BF_(3)`
B. `BC l_(3)`
C. `B Br_(3)`
D. `BI_(3)`

Explanation

To solve the question regarding the heat of adduct formation (ΔH) for the reaction of boron trihalides (BX₃) with ammonia (NH₃), we need to analyze the stability of the adduct formed and the factors that influence ΔH. Here’s a step-by-step solution:

### Step 1: Understand the Reaction
The reaction involves boron trihalides (BX₃) reacting with ammonia (NH₃) to form an adduct (BX₃·NH₃) and release heat. The general reaction can be written as:
\[ \text{BX}_3 + \text{NH}_3 \rightarrow \text{BX}_3 \cdot \text{NH}_3 + \text{Heat} \]

**Hint:** Identify the reactants and products in the reaction.

### Step 2: Identify the Lewis Acid-Base Interaction
Boron trihalides (BX₃) act as Lewis acids because boron has an empty p-orbital that can accept a lone pair of electrons from a Lewis base, which in this case is ammonia (NH₃). The nitrogen atom in ammonia donates its lone pair to boron.

**Hint:** Recall the definitions of Lewis acids and bases.

### Step 3: Analyze the Stability of the Adduct
The stability of the adduct formed (BX₃·NH₃) is influenced by the ability of BX₃ to accept the lone pair from NH₃. The order of Lewis acidity for boron trihalides is:
\[ \text{BF}_3 < \text{BCl}_3 < \text{BrF}_3 < \text{BI}_3 \]
This means that BI₃ is the strongest Lewis acid among the boron trihalides.

**Hint:** Remember that the size of the halide and its electronegativity affect the Lewis acidity.

### Step 4: Consider the Size and Electron Density of Halides
As we move down the group from fluorine to iodine, the size of the halide increases, and the electron density decreases. This leads to reduced electron-electron repulsion between the lone pairs of electrons on NH₃ and the halide, making the adduct more stable.

**Hint:** Think about how size and electron density influence repulsion and stability.

### Step 5: Conclude on ΔH
Since the heat of adduct formation (ΔH) is related to the stability of the adduct, the more stable the adduct, the more heat is released. Therefore, the numerical value of ΔH will be maximum for BI₃, as it forms the most stable adduct due to the least electron repulsion.

**Hint:** Stability of the adduct correlates directly with the amount of heat released.

### Final Answer
The numerical value of ΔH is found to be maximum for **BI₃**.