Find the oxidation number of sulphur in the following compounds: `H_(2)S,H_(2)SO_(4),S_(2)O_(4)^(2-),S_(2)O_(8)^(2-),HSO_(3)^(ө)`.

Explanation

To find the oxidation number of sulfur in the given compounds, we will follow a systematic approach for each compound. Let's go through them one by one.

### Step 1: Determine the oxidation number of sulfur in H₂S

1. **Write the equation for the oxidation number**: Let the oxidation number of sulfur be \( X \).
2. **Identify the oxidation numbers of hydrogen and sulfur**:
- Hydrogen (H) has an oxidation number of +1.
- The compound is neutral, so the sum of oxidation numbers equals 0.
3. **Set up the equation**:
\[ 2(+1) + X = 0 \]
\[ 2 + X = 0 \]
4. **Solve for \( X \)**:
\[ X = -2 \]

### Step 2: Determine the oxidation number of sulfur in H₂SO₄

1. **Write the equation for the oxidation number**: Let the oxidation number of sulfur be \( X \).
2. **Identify the oxidation numbers**:
- Hydrogen (H) = +1 (2 H atoms contribute +2)
- Oxygen (O) = -2 (4 O atoms contribute -8)
3. **Set up the equation**:
\[ 2(+1) + X + 4(-2) = 0 \]
\[ 2 + X - 8 = 0 \]
4. **Solve for \( X \)**:
\[ X - 6 = 0 \implies X = +6 \]

### Step 3: Determine the oxidation number of sulfur in S₂O₄²⁻

1. **Write the equation for the oxidation number**: Let the oxidation number of sulfur be \( X \).
2. **Identify the oxidation numbers**:
- Oxygen (O) = -2 (4 O atoms contribute -8)
- The overall charge of the ion is -2.
3. **Set up the equation**:
\[ 2X + 4(-2) = -2 \]
\[ 2X - 8 = -2 \]
4. **Solve for \( X \)**:
\[ 2X = 6 \implies X = +3 \]

### Step 4: Determine the oxidation number of sulfur in S₂O₈²⁻

1. **Write the equation for the oxidation number**: Let the oxidation number of sulfur be \( X \).
2. **Identify the oxidation numbers**:
- Oxygen (O) = -2 (8 O atoms contribute -16)
- The overall charge of the ion is -2.
3. **Set up the equation**:
\[ 2X + 8(-2) = -2 \]
\[ 2X - 16 = -2 \]
4. **Solve for \( X \)**:
\[ 2X = 14 \implies X = +7 \]

### Step 5: Determine the oxidation number of sulfur in HSO₃⁻

1. **Write the equation for the oxidation number**: Let the oxidation number of sulfur be \( X \).
2. **Identify the oxidation numbers**:
- Hydrogen (H) = +1
- Oxygen (O) = -2 (3 O atoms contribute -6)
- The overall charge of the ion is -1.
3. **Set up the equation**:
\[ 1 + X + 3(-2) = -1 \]
\[ 1 + X - 6 = -1 \]
4. **Solve for \( X \)**:
\[ X - 5 = -1 \implies X = +4 \]

### Summary of Oxidation Numbers
- **H₂S**: -2
- **H₂SO₄**: +6
- **S₂O₄²⁻**: +3
- **S₂O₈²⁻**: +7
- **HSO₃⁻**: +4