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 lt II lt III`
B. `II lt III lt I`
C. `II lt I lt III`
D. `I lt III lt II`

Answer

To determine the correct sequence of increasing number of π-bonds in the given molecules (I) H₂S₂O₆, (II) H₂S₂O₃, and (III) H₂S₂S₅, we will analyze the structures of each compound and count the π-bonds.

### Step 1: Analyze H₂S₂O₆
1. **Draw the structure**: The structure consists of two sulfur (S) atoms, each bonded to two oxygen (O) atoms through double bonds, and two hydrogen (H) atoms bonded to the terminal oxygens.
2. **Count the π-bonds**:
- Each double bond consists of one σ-bond and one π-bond.
- In H₂S₂O₆, there are four double bonds (two S=O bonds from each sulfur).
- Therefore, the number of π-bonds = 4.

### Step 2: Analyze H₂S₂O₃
1. **Draw the structure**: The structure consists of two sulfur atoms, each bonded to one oxygen atom through a double bond and one hydrogen atom bonded to the terminal oxygen.
2. **Count the π-bonds**:
- In H₂S₂O₃, there are two double bonds (S=O).
- Therefore, the number of π-bonds = 2.

### Step 3: Analyze H₂S₂S₅
1. **Draw the structure**: The structure consists of two sulfur atoms bonded to one sulfur atom through a double bond and each sulfur bonded to two oxygen atoms through double bonds.
2. **Count the π-bonds**:
- In H₂S₂S₅, there are three double bonds (two S=O and one S=S).
- Therefore, the number of π-bonds = 3.

### Step 4: Summarize the findings
- H₂S₂O₆ has 4 π-bonds.
- H₂S₂O₃ has 2 π-bonds.
- H₂S₂S₅ has 3 π-bonds.

### Step 5: Arrange in increasing order
- The increasing order of π-bonds is:
- H₂S₂O₃ (2 π-bonds) < H₂S₂S₅ (3 π-bonds) < H₂S₂O₆ (4 π-bonds).

### Final Answer
The correct sequence of increasing number of π-bonds is:
**H₂S₂O₃ < H₂S₂S₅ < H₂S₂O₆**