What is the correct order of oxidation states of suphur in anions `So_(3)^(2-),S_(2)O_(4)^(2-)` and `S_(2)_(6)^(2-)` ?

Options

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

Answer

To determine the correct order of oxidation states of sulfur in the anions \( SO_3^{2-} \), \( S_2O_4^{2-} \), and \( S_2O_6^{2-} \), we will calculate the oxidation state of sulfur in each anion step by step.

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

1. The formula for the oxidation state can be expressed as:
\[ \text{Oxidation state of S} + 3 \times (\text{Oxidation state of O}) = \text{Charge on the ion} \]
2. The oxidation state of oxygen is typically \(-2\). Therefore, for \( SO_3^{2-} \):
\[ x + 3(-2) = -2 \]
3. Simplifying this gives:
\[ x - 6 = -2 \]
4. Solving for \( x \):
\[ x = -2 + 6 = +4 \]
5. Thus, the oxidation state of sulfur in \( SO_3^{2-} \) is \( +4 \).

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

1. For \( S_2O_4^{2-} \), the equation becomes:
\[ 2x + 4(-2) = -2 \]
2. Simplifying this gives:
\[ 2x - 8 = -2 \]
3. Solving for \( x \):
\[ 2x = -2 + 8 = 6 \implies x = +3 \]
4. Therefore, the oxidation state of sulfur in \( S_2O_4^{2-} \) is \( +3 \).

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

1. For \( S_2O_6^{2-} \), the equation is:
\[ 2x + 6(-2) = -2 \]
2. Simplifying this gives:
\[ 2x - 12 = -2 \]
3. Solving for \( x \):
\[ 2x = -2 + 12 = 10 \implies x = +5 \]
4. Thus, the oxidation state of sulfur in \( S_2O_6^{2-} \) is \( +5 \).

### Step 4: Summarize the oxidation states

Now we summarize the oxidation states we calculated:
- For \( SO_3^{2-} \): \( +4 \)
- For \( S_2O_4^{2-} \): \( +3 \)
- For \( S_2O_6^{2-} \): \( +5 \)

### Step 5: Determine the correct order

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

### Final Answer

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