The oxidation number of sulphur in `H_2S_2O_8 , H_2S_2O_4 , H_2S_2O_6` are respectively

Options

A. `+ 3, + 4, + 5`
B. `+ 5, + 4, + 3`
C. `+ 6, + 3, + 5`
D. `+ 3, + 5, + 4`

Explanation

To determine the oxidation number of sulfur in the compounds \( H_2S_2O_8 \), \( H_2S_2O_4 \), and \( H_2S_2O_6 \), we can follow these steps:

### Step 1: Write the general formula for oxidation state calculation
The oxidation state can be calculated using the formula:
\[ \text{Oxidation state of S} + \text{Oxidation state of O} + \text{Oxidation state of H} = \text{Total charge} \]

### Step 2: Calculate the oxidation state for \( H_2S_2O_8 \)
1. Identify the oxidation states:
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. Set up the equation:
\[ 2(+1) + 2x + 8(-2) = 0 \]
where \( x \) is the oxidation state of sulfur (S).

3. Solve the equation:
\[ 2 + 2x - 16 = 0 \\ 2x - 14 = 0 \\ 2x = 14 \\ x = +7 \]
Thus, the oxidation state of sulfur in \( H_2S_2O_8 \) is +7.

### Step 3: Calculate the oxidation state for \( H_2S_2O_4 \)
1. Set up the equation:
\[ 2(+1) + 2x + 4(-2) = 0 \]

2. Solve the equation:
\[ 2 + 2x - 8 = 0 \\ 2x - 6 = 0 \\ 2x = 6 \\ x = +3 \]
Thus, the oxidation state of sulfur in \( H_2S_2O_4 \) is +3.

### Step 4: Calculate the oxidation state for \( H_2S_2O_6 \)
1. Set up the equation:
\[ 2(+1) + 2x + 6(-2) = 0 \]

2. Solve the equation:
\[ 2 + 2x - 12 = 0 \\ 2x - 10 = 0 \\ 2x = 10 \\ x = +5 \]
Thus, the oxidation state of sulfur in \( H_2S_2O_6 \) is +5.

### Final Results:
The oxidation numbers of sulfur in the compounds are:
- For \( H_2S_2O_8 \): +7
- For \( H_2S_2O_4 \): +3
- For \( H_2S_2O_6 \): +5

### Summary:
- \( H_2S_2O_8 \): +7
- \( H_2S_2O_4 \): +3
- \( H_2S_2O_6 \): +5