The oxidation number of S in `H_2S_2O_8` is

Options

A. `+2`
B. `+4`
C. `+6`
D. `+7`

Explanation

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

### Step 1: Identify the structure of \( H_2S_2O_8 \)
The compound \( H_2S_2O_8 \) is known as peroxydisulfuric acid. It consists of two sulfur atoms, eight oxygen atoms, and two hydrogen atoms. The structure can be represented as:

- Each sulfur atom is bonded to oxygen atoms, and there is a peroxide linkage between them.

### Step 2: Assign oxidation states to known elements
- Hydrogen (H) typically has an oxidation state of +1.
- Oxygen (O) generally has an oxidation state of -2, except in peroxides where it has an oxidation state of -1.

### Step 3: Write the equation for the sum of oxidation states
Let the oxidation state of sulfur be \( x \). In \( H_2S_2O_8 \), we have:
- 2 hydrogen atoms contributing \( 2 \times (+1) = +2 \)
- 8 oxygen atoms contributing \( 8 \times (-2) = -16 \)
- There are 2 sulfur atoms contributing \( 2x \)

The overall charge of the molecule is neutral (0), so we can set up the equation:

\[ 2 + 2x - 16 = 0 \]

### Step 4: Solve for \( x \)
Rearranging the equation gives:

\[ 2x - 14 = 0 \]
\[ 2x = 14 \]
\[ x = 7 \]

### Step 5: Determine the oxidation number of sulfur
Since \( x = 7 \), the oxidation number of sulfur in \( H_2S_2O_8 \) is +7.

### Final Answer
The oxidation number of sulfur (S) in \( H_2S_2O_8 \) is +7.

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