If X,Y and Z are total number of `pi`-bond(s) in `H_(2)S_(2)O_(6),H_(2)SO_(3) and H_(2)S_(2)O_(7)` respectively then calculate vlaue of expression `|X+Y-Z|`.

Answer

To solve the problem, we need to determine the total number of π-bonds (or π-electrons) in the compounds H₂S₂O₆, H₂SO₃, and H₂S₂O₇. Let's break it down step by step.

### Step 1: Determine the structure of H₂S₂O₆ (Dithionic Acid)
1. **Structure**: Dithionic acid has the following structure:
- Two sulfur atoms (S) connected by a single bond.
- Each sulfur atom has two double-bonded oxygen atoms (O) and one hydroxyl group (OH).

The structure can be represented as:
```
O
||
HO-S-S-OH
||
O
```
2. **Count π-bonds**:
- Each double bond contributes one π-bond.
- There are 4 double bonds (2 from each sulfur).
- Thus, **X = 4**.

### Step 2: Determine the structure of H₂SO₃ (Sulfurous Acid)
1. **Structure**: Sulfurous acid has the following structure:
- One sulfur atom (S) with one double-bonded oxygen (O) and two hydroxyl groups (OH).

The structure can be represented as:
```
O
||
HO-S-OH
```
2. **Count π-bonds**:
- There is 1 double bond contributing one π-bond.
- Thus, **Y = 1**.

### Step 3: Determine the structure of H₂S₂O₇ (Pyrosulfuric Acid)
1. **Structure**: Pyrosulfuric acid has the following structure:
- Two sulfur atoms (S) connected by an oxygen bridge (O).
- Each sulfur atom has two double-bonded oxygen atoms (O) and one hydroxyl group (OH).

The structure can be represented as:
```
O
||
HO-S-O-S-OH
||
O
```
2. **Count π-bonds**:
- Each sulfur has 2 double bonds, contributing a total of 4 π-bonds.
- Thus, **Z = 4**.

### Step 4: Calculate the expression |X + Y - Z|
Now we can substitute the values we found:
- X = 4 (from H₂S₂O₆)
- Y = 1 (from H₂SO₃)
- Z = 4 (from H₂S₂O₇)

Now calculate:
\[ |X + Y - Z| = |4 + 1 - 4| = |1| = 1 \]

### Final Answer
The value of the expression |X + Y - Z| is **1**.

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