The correct set of oxidation numbers of sulphur atoms in `H_(2)S_(2)O_(3)` is/are:

Options

A. `+6,-2`
B. `+4,-2`
C. `+2,+4`
D. `+5,-1`

Answer

To determine the correct set of oxidation numbers of sulfur atoms in \( H_2S_2O_3 \), we can follow these steps:

### Step 1: Identify the structure of \( H_2S_2O_3 \)
The molecular formula \( H_2S_2O_3 \) indicates that there are 2 sulfur (S) atoms, 2 hydrogen (H) atoms, and 3 oxygen (O) atoms. The structure can be visualized as follows:
- Two sulfur atoms are connected to each other.
- Each sulfur atom is bonded to oxygen atoms, with one of the oxygen atoms double-bonded to one of the sulfur atoms.
- The hydrogen atoms are bonded to the sulfur atoms.

### Step 2: Assign oxidation states to hydrogen and oxygen
- Hydrogen (H) typically has an oxidation state of +1.
- Oxygen (O) typically has an oxidation state of -2, except in peroxides or when bonded to fluorine.

### Step 3: Set up the oxidation state equation
Let the oxidation state of sulfur be represented as \( x \). The overall charge of the molecule is neutral (0). The equation can be set up as follows:

\[ 2 \times (+1) + 2x + 3 \times (-2) = 0 \]

### Step 4: Simplify the equation
Substituting the values into the equation gives:

\[ 2 + 2x - 6 = 0 \]

### Step 5: Solve for \( x \)
Rearranging the equation:

\[ 2x - 4 = 0 \]
\[ 2x = 4 \]
\[ x = +2 \]

### Step 6: Determine the oxidation states of both sulfur atoms
From the structure, we can see that one sulfur atom is bonded to two oxygen atoms (one double-bonded and one single-bonded) and the other sulfur atom is bonded to one oxygen atom (single-bonded) and one hydrogen atom.

1. The first sulfur atom (let's call it S1) is bonded to one double-bonded oxygen and one single-bonded oxygen, which gives it an oxidation state of +6.
2. The second sulfur atom (let's call it S2) is bonded to one hydrogen and one single-bonded oxygen, which gives it an oxidation state of -2.

### Conclusion
The oxidation states of sulfur in \( H_2S_2O_3 \) are +6 for one sulfur atom and -2 for the other sulfur atom.

### Final Answer
The correct set of oxidation numbers of sulfur atoms in \( H_2S_2O_3 \) is +6 and -2.

---