Compound `(X)` on reduction with `LiAlH_(4)` gives a hydride `(Y)` containing `21.72 %` hydrogen along with other products. The compound `(Y)` reacts with air explosively resulting in formation of boron trioxide. Identify `(X)` and `(Y)`.
Give balanced reactions involved in the formation of `(Y)` and its reaction with air. Give the structure of `(Y)`.

Explanation

To solve the problem, let's break it down step by step:

### Step 1: Identify Compound (Y)
We know that compound (Y) contains 21.72% hydrogen. To find the molecular formula of (Y), we can use the percentage composition to determine the ratio of hydrogen to boron.

1. **Calculate the molar mass of (Y)**:
- Let the molar mass of (Y) be \( M \).
- Given that hydrogen contributes 21.72% of the mass, we can set up the equation:
\[ \frac{2 \times 1.008}{M} \times 100 = 21.72 \]
where \( 2 \) is the number of hydrogen atoms in diborane (B2H6).

2. **Solve for M**:
\[ \frac{2.016}{M} \times 100 = 21.72 \implies M = \frac{2.016 \times 100}{21.72} \approx 9.28 \text{ g/mol} \]
Since this is not a whole number, we need to consider the molecular formula of diborane, which is known to be \( B_2H_6 \).

### Step 2: Identify Compound (X)
Now, we need to identify compound (X) that reacts with lithium aluminum hydride (LiAlH4) to form (Y).

1. **Reaction of (X) with LiAlH4**:
- The reaction of boron trichloride (BCl3) with LiAlH4 produces diborane (B2H6) along with aluminum chloride (AlCl3) and lithium chloride (LiCl).
- Therefore, we can identify compound (X) as \( BCl_3 \).

### Step 3: Write the balanced reaction for the formation of (Y)
The balanced reaction for the formation of diborane (Y) from boron trichloride (X) is:
\[ 4 \, BCl_3 + 6 \, LiAlH_4 \rightarrow 2 \, B_2H_6 + 3 \, AlCl_3 + 3 \, LiCl \]

### Step 4: Write the reaction of (Y) with air
Diborane (Y) reacts explosively with oxygen in the air to form boron trioxide (B2O3) and water (H2O). The balanced reaction is:
\[ 2 \, B_2H_6 + 7 \, O_2 \rightarrow 4 \, B_2O_3 + 6 \, H_2O \]

### Step 5: Structure of (Y)
The structure of diborane (B2H6) can be represented as follows:
```
H H
\ /
B - B
/ \
H H
```
In this structure, two boron atoms are bonded to each other, and each boron atom is also bonded to three hydrogen atoms, with two of the hydrogen atoms forming bridging bonds between the boron atoms.

### Summary
- **Compound (X)**: \( BCl_3 \)
- **Compound (Y)**: \( B_2H_6 \)
- **Balanced reaction for formation of (Y)**:
\[ 4 \, BCl_3 + 6 \, LiAlH_4 \rightarrow 2 \, B_2H_6 + 3 \, AlCl_3 + 3 \, LiCl \]
- **Reaction of (Y) with air**:
\[ 2 \, B_2H_6 + 7 \, O_2 \rightarrow 4 \, B_2O_3 + 6 \, H_2O \]
- **Structure of (Y)**: Diborane (B2H6) has a unique structure with bridging hydrogen atoms.