The oxidation number of sulphur in `H_(2)S_(2)O_(8)` is:

Options

A. `+2`
B. `+6`
C. `+7`
D. `+14`

Explanation

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

### Step 1: Assign known oxidation states
In \( H_2S_2O_8 \):
- Hydrogen (H) has an oxidation state of +1.
- Oxygen (O) typically has an oxidation state of -2, but in peroxides, it has an oxidation state of -1.

### Step 2: Identify the number of each atom in the compound
The formula \( H_2S_2O_8 \) contains:
- 2 Hydrogen atoms
- 2 Sulfur atoms
- 8 Oxygen atoms

### Step 3: Set up the equation for oxidation states
Let the oxidation state of sulfur be \( x \). The total oxidation state for the compound must equal 0 (since it is neutral).

The equation can be set up as follows:
\[ 2 \times (+1) + 2x + 8 \times (-2) = 0 \]

### Step 4: Simplify the equation
Substituting the known values into the equation:
\[ 2 + 2x - 16 = 0 \]
This simplifies to:
\[ 2x - 14 = 0 \]

### Step 5: Solve for \( x \)
Rearranging the equation gives:
\[ 2x = 14 \]
\[ x = 7 \]

### Step 6: Analyze the result
The calculated oxidation state of sulfur is +7. However, this seems unusual since sulfur typically does not exceed +6 in its common oxidation states.

### Step 7: Consider the structure of the compound
The structure of \( H_2S_2O_8 \) includes peroxo linkages (O-O bonds) which affect the oxidation states of the sulfur atoms. In this case, the oxygen atoms in the peroxide linkages have an oxidation state of -1.

### Step 8: Re-evaluate the oxidation state of sulfur
Taking into account the peroxide linkages, we can recalculate the oxidation state of sulfur:
- For the 6 oxygen atoms that are not in the peroxide, the oxidation state is -2.
- For the 2 oxygen atoms in the peroxide, the oxidation state is -1.

Thus, the equation becomes:
\[ 2 \times (+1) + 2x + 6 \times (-2) + 2 \times (-1) = 0 \]
This simplifies to:
\[ 2 + 2x - 12 - 2 = 0 \]
\[ 2x - 12 = 0 \]
\[ 2x = 12 \]
\[ x = 6 \]

### Conclusion
The oxidation number of sulfur in \( H_2S_2O_8 \) is +6.

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