The oxidation numbers of the sulphur atoms in pcroxy- monosulphuric acid `(H_(2)SO_(5))` and peroxydisulphuric acid `(H_(2)S_(2)O_(8))` are respectively.

Options

A. `+8 and +7`
B. `+3 and +3`
C. `+6 and +6`
D. `+4 and +6`

Answer

To determine the oxidation numbers of the sulfur atoms in peroxy monosulfuric acid (H₂SO₅) and peroxydisulfuric acid (H₂S₂O₈), we will follow a systematic approach.

### Step 1: Analyze Peroxy Monosulfuric Acid (H₂SO₅)

1. **Identify the structure**: Peroxy monosulfuric acid contains one sulfur atom, five oxygen atoms, and two hydrogen atoms. The presence of the peroxy linkage indicates that there are two oxygen atoms connected by a single bond.

2. **Assign known oxidation states**:
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) typically has an oxidation state of -2, but in a peroxide linkage (O-O), it has an oxidation state of -1.

3. **Set up the equation**:
- Let the oxidation state of sulfur (S) be \( x \).
- The total contribution from two hydrogen atoms is \( 2(+1) = +2 \).
- The contribution from the five oxygen atoms is \( 3(-2) + 2(-1) = -6 - 2 = -8 \) (three O in double bonds and two O in the peroxy linkage).

4. **Calculate the overall charge**:
- The overall charge of the molecule is neutral (0).
- Therefore, we can set up the equation:
\[ x + 2 - 8 = 0 \]
\[ x - 6 = 0 \implies x = +6 \]

### Step 2: Analyze Peroxydisulfuric Acid (H₂S₂O₈)

1. **Identify the structure**: Peroxydisulfuric acid contains two sulfur atoms, eight oxygen atoms, and two hydrogen atoms. Each sulfur atom is connected to four oxygen atoms, including the peroxy linkage.

2. **Assign known oxidation states**:
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2, except for the two in the peroxy linkage which are -1.

3. **Set up the equation**:
- Let the oxidation state of each sulfur atom be \( y \).
- The total contribution from two hydrogen atoms is \( 2(+1) = +2 \).
- The contribution from the eight oxygen atoms is \( 6(-2) + 2(-1) = -12 - 2 = -14 \) (six O in double bonds and two O in the peroxy linkage).

4. **Calculate the overall charge**:
- The overall charge of the molecule is neutral (0).
- Therefore, we can set up the equation:
\[ 2y + 2 - 14 = 0 \]
\[ 2y - 12 = 0 \implies 2y = 12 \implies y = +6 \]

### Final Answer

The oxidation numbers of the sulfur atoms in peroxy monosulfuric acid (H₂SO₅) and peroxydisulfuric acid (H₂S₂O₈) are respectively +6 and +6.