The oxidation states of sulphur in the anions `SO_(3)^(2-), S_(2)O_(4)^(2-)`, and `S_(2)O_(6)^(2-)` follow the order

Options

A. `S_(2)O_(4)^(2-)ltSO_(3)^(2-)ltS_(2)O_(6)^(2-)`
B. `SO_(3)^(2-)ltS_(2)O_(4)^(2-)ltS_(2)O_(6)^(2-)`
C. `S_(2)O_(4)^(2-)ltS_(2)O_(6)^(2-) lt SO_(3)^(2-)`
D. `S_(2)O_(6)^(2-)ltS_(2)O_(4)^(2-)ltS_(2)O_(4)^(2-)ltSO_(3)^(2-)`

Explanation

To determine the oxidation states of sulfur in the anions \( SO_3^{2-} \), \( S_2O_4^{2-} \), and \( S_2O_6^{2-} \), we will follow these steps:

### Step 1: Determine the oxidation state of sulfur in \( SO_3^{2-} \)

1. Let the oxidation state of sulfur be \( x \).
2. The oxidation state of oxygen is \( -2 \).
3. The overall charge of the anion is \( -2 \).

The equation can be set up as follows:
\[ x + 3(-2) = -2 \]
\[ x - 6 = -2 \]
\[ x = -2 + 6 \]
\[ x = 4 \]

### Step 2: Determine the oxidation state of sulfur in \( S_2O_4^{2-} \)

1. Let the oxidation state of sulfur be \( x \).
2. There are 2 sulfur atoms, so their total contribution is \( 2x \).
3. The oxidation state of oxygen is \( -2 \), and there are 4 oxygen atoms.

The equation can be set up as follows:
\[ 2x + 4(-2) = -2 \]
\[ 2x - 8 = -2 \]
\[ 2x = -2 + 8 \]
\[ 2x = 6 \]
\[ x = 3 \]

### Step 3: Determine the oxidation state of sulfur in \( S_2O_6^{2-} \)

1. Let the oxidation state of sulfur be \( x \).
2. There are 2 sulfur atoms, so their total contribution is \( 2x \).
3. The oxidation state of oxygen is \( -2 \), and there are 6 oxygen atoms.

The equation can be set up as follows:
\[ 2x + 6(-2) = -2 \]
\[ 2x - 12 = -2 \]
\[ 2x = -2 + 12 \]
\[ 2x = 10 \]
\[ x = 5 \]

### Summary of Oxidation States

- For \( SO_3^{2-} \): Oxidation state of sulfur = \( 4 \)
- For \( S_2O_4^{2-} \): Oxidation state of sulfur = \( 3 \)
- For \( S_2O_6^{2-} \): Oxidation state of sulfur = \( 5 \)

### Conclusion

The order of oxidation states of sulfur in the anions is:
\[ S_2O_6^{2-} (5) > SO_3^{2-} (4) > S_2O_4^{2-} (3) \]