`Li+N_(2) overset(Delta)rarrA overset(H_(2)O)rarr B+(C )` gas
Then the correctly matched pair for `A,B,C` are `:`

Options

A. `{:(,A,B,C),((1),LiN_(3),LiOH,NH_(3)):}`
B. `{:(,A,B,C),((2),LiN_(3),LiH,NO_(3)):}`
C. `{:(,A,B,C),((3),LiN,LiOH,NO_(2)):}`
D. `{:(,A,B,C),((4),Li_(3)N,LiOH,NH_(2)):}`

Explanation

To solve the question, we will break down the reactions step by step to identify the products A, B, and C.

### Step 1: Reaction of Lithium with Nitrogen
When lithium (Li) reacts with nitrogen gas (N₂) upon heating, it forms lithium nitride (Li₃N).

**Reaction:**
\[ 6 \text{Li} + \text{N}_2 \rightarrow 2 \text{Li}_3\text{N} \]

Here, we can see that for every 6 lithium atoms, 1 molecule of nitrogen gas reacts to produce 2 units of lithium nitride.

**Product A:**
- **A = Li₃N**

### Step 2: Hydrolysis of Lithium Nitride
Next, we need to consider the hydrolysis of lithium nitride (Li₃N) when it is treated with water (H₂O). The reaction can be represented as follows:

**Reaction:**
\[ \text{Li}_3\text{N} + 3 \text{H}_2\text{O} \rightarrow 3 \text{LiOH} + \text{NH}_3 \]

In this reaction, lithium nitride reacts with water to produce lithium hydroxide (LiOH) and ammonia gas (NH₃).

**Product B:**
- **B = LiOH**

**Gas C:**
- **C = NH₃**

### Summary of Products:
- **A = Li₃N**
- **B = LiOH**
- **C = NH₃**

### Final Answer:
The correctly matched pair for A, B, and C are:
- A: Li₃N
- B: LiOH
- C: NH₃