Identify the correct sequence of increasing number of `pi`-bonds in the structure of the following molecules:
(I)`H_(2)S_(2)O_(6)` (II)`H_(2)S_(2)O_(3)` (III)`H_(2)S_(2)S_(5)`

Options

A. I, II and III
B. II, I and III
C. II, III and I
D. I, III and II

Explanation

To solve the problem of identifying the correct sequence of increasing number of π-bonds in the structures of the given molecules (I) H₂S₂O₆, (II) H₂S₂O₃, and (III) H₂S₂O₅, we will analyze each molecule step by step.

### Step 1: Analyze H₂S₂O₆ (Dithionic Acid)
- **Structure**: The structure of dithionic acid can be represented as HO-S(=O)-S(=O)-OH.
- **Pi Bonds**: In this structure, we can identify the double bonds:
- S=O (4 times) - Each double bond contains 1 π-bond.
- **Total π-bonds**: There are 4 π-bonds in H₂S₂O₆.

### Step 2: Analyze H₂S₂O₃ (Thiosulfuric Acid)
- **Structure**: The structure of thiosulfuric acid can be represented as HO-S(=O)-S(=O)-OH.
- **Pi Bonds**: In this structure, we can identify the double bonds:
- S=S (1 time) and S=O (2 times) - Each double bond contains 1 π-bond.
- **Total π-bonds**: There are 2 π-bonds in H₂S₂O₃.

### Step 3: Analyze H₂S₂O₅ (Disulfuric Acid)
- **Structure**: The structure of disulfuric acid can be represented as HO-S(=O)-S(=O)-OH.
- **Pi Bonds**: In this structure, we can identify the double bonds:
- S=O (3 times) - Each double bond contains 1 π-bond.
- **Total π-bonds**: There are 3 π-bonds in H₂S₂O₅.

### Step 4: Compare the Number of π-bonds
Now we can summarize the number of π-bonds in each molecule:
- H₂S₂O₆: 4 π-bonds
- H₂S₂O₃: 2 π-bonds
- H₂S₂O₅: 3 π-bonds

### Step 5: Arrange in Increasing Order
To arrange the molecules in increasing order of π-bonds:
1. H₂S₂O₃ (2 π-bonds)
2. H₂S₂O₅ (3 π-bonds)
3. H₂S₂O₆ (4 π-bonds)

### Final Answer
The correct sequence of increasing number of π-bonds is:
**H₂S₂O₃ < H₂S₂O₅ < H₂S₂O₆**.