Complate the following reactions.
(i) `Cr_2O_7^(2-)+3SO_2+2H^(+)to2Cr^(3+)+"________"+H_2O`
(ii) `2MnO_4^(-)+5SO_3^(2-)+6H^(+)to2Mn^(2+)+"______"+3H_2O`
(iii) `Cr_2O_7^(2-)+6Fe^(2+)+14H^(+)to2Cr^(3+)+"_______"+7H_2O`

Options

A. `3SO_4^(2-),SO_2^(2-),Fe^(3+)`
B. `3SO_4^(2-),5CO_4^(2-),6Fe^(3+)`
C. `3SO_4^(2-),SO_2,K^(+)`
D. `S,SO_2,Fe^(3+)`

Answer

To complete the reactions given in the question, we will analyze each reaction step by step, focusing on the oxidation states and the species involved.

### Reaction (i):
**Given:**
\[ \text{Cr}_2\text{O}_7^{2-} + 3\text{SO}_2 + 2\text{H}^+ \to 2\text{Cr}^{3+} + \_\_\_\_\_ + \text{H}_2\text{O} \]

1. **Identify Oxidation States:**
- Chromium in \(\text{Cr}_2\text{O}_7^{2-}\) has an oxidation state of +6.
- Sulfur in \(\text{SO}_2\) has an oxidation state of +4.

2. **Determine Changes:**
- Chromium is reduced from +6 to +3.
- Sulfur is oxidized from +4 to +6.

3. **Products of Oxidation:**
- The oxidation of \(3\text{SO}_2\) to \(\text{SO}_4^{2-}\) (sulfate ion) occurs, which has sulfur in the +6 oxidation state.

4. **Complete the Reaction:**
- Therefore, the completed reaction is:
\[ \text{Cr}_2\text{O}_7^{2-} + 3\text{SO}_2 + 2\text{H}^+ \to 2\text{Cr}^{3+} + 3\text{SO}_4^{2-} + \text{H}_2\text{O} \]

### Reaction (ii):
**Given:**
\[ 2\text{MnO}_4^{-} + 5\text{SO}_3^{2-} + 6\text{H}^+ \to 2\text{Mn}^{2+} + \_\_\_\_\_ + 3\text{H}_2\text{O} \]

1. **Identify Oxidation States:**
- Manganese in \(\text{MnO}_4^{-}\) has an oxidation state of +7.
- Sulfur in \(\text{SO}_3^{2-}\) has an oxidation state of +4.

2. **Determine Changes:**
- Manganese is reduced from +7 to +2.
- Sulfur is oxidized from +4 to +6.

3. **Products of Oxidation:**
- The oxidation of \(5\text{SO}_3^{2-}\) to \(5\text{SO}_4^{2-}\) occurs.

4. **Complete the Reaction:**
- Therefore, the completed reaction is:
\[ 2\text{MnO}_4^{-} + 5\text{SO}_3^{2-} + 6\text{H}^+ \to 2\text{Mn}^{2+} + 5\text{SO}_4^{2-} + 3\text{H}_2\text{O} \]

### Reaction (iii):
**Given:**
\[ \text{Cr}_2\text{O}_7^{2-} + 6\text{Fe}^{2+} + 14\text{H}^+ \to 2\text{Cr}^{3+} + \_\_\_\_\_ + 7\text{H}_2\text{O} \]

1. **Identify Oxidation States:**
- Chromium in \(\text{Cr}_2\text{O}_7^{2-}\) has an oxidation state of +6.
- Iron in \(\text{Fe}^{2+}\) has an oxidation state of +2.

2. **Determine Changes:**
- Chromium is reduced from +6 to +3.
- Iron is oxidized from +2 to +3.

3. **Products of Oxidation:**
- The oxidation of \(6\text{Fe}^{2+}\) to \(6\text{Fe}^{3+}\) occurs.

4. **Complete the Reaction:**
- Therefore, the completed reaction is:
\[ \text{Cr}_2\text{O}_7^{2-} + 6\text{Fe}^{2+} + 14\text{H}^+ \to 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O} \]

### Summary of Completed Reactions:
1. \( \text{Cr}_2\text{O}_7^{2-} + 3\text{SO}_2 + 2\text{H}^+ \to 2\text{Cr}^{3+} + 3\text{SO}_4^{2-} + \text{H}_2\text{O} \)
2. \( 2\text{MnO}_4^{-} + 5\text{SO}_3^{2-} + 6\text{H}^+ \to 2\text{Mn}^{2+} + 5\text{SO}_4^{2-} + 3\text{H}_2\text{O} \)
3. \( \text{Cr}_2\text{O}_7^{2-} + 6\text{Fe}^{2+} + 14\text{H}^+ \to 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O} \)