Which of the following a disproportional reactions?

Options

A. `Cr_(2)O_(7)^(2-)+2overset(ө)OHrarr2CrO_(4)^(2-)+H_(2)O`
B. `CrO_(4)^(2-)+2H^(o+)rarrCr_(2)O_(2)^(2-)+H_(2)O`
C. `CaCO_(3)+2H^(o+)rarrCa^(2)+H_(2)O+CO_(2)`
D. `Cu_(2)O+2H^(o+)rarrCu+Cu^(2+)+H_(2)O`

Explanation

To determine which of the given reactions is a disproportionation reaction, we need to understand what a disproportionation reaction is. A disproportionation reaction is a specific type of redox reaction where a single species is both oxidized and reduced, resulting in two different products.

### Step-by-Step Solution:

1. **Identify the Reactions**: We need to analyze each of the given reactions to check for disproportionation.

2. **Determine Oxidation States**: For each reaction, identify the oxidation states of the elements involved. This will help us see if any element is undergoing both oxidation (increase in oxidation state) and reduction (decrease in oxidation state).

3. **Analyze Each Reaction**:
- **First Reaction**: Check the oxidation states.
- Chromium (Cr) has an oxidation state of +6 in both cases.
- Hydrogen (H) has an oxidation state of +1 in both cases.
- Oxygen (O) has an oxidation state of -2 in both cases.
- **Conclusion**: No change in oxidation states; therefore, this is not a disproportionation reaction.

- **Second Reaction**: Check the oxidation states.
- Chromium (Cr) has an oxidation state of +6 in one case and +1 in another.
- Hydrogen (H) remains +1 in both cases.
- **Conclusion**: Only reduction occurs (Cr is reduced from +6 to +1), so this is not a disproportionation reaction.

- **Third Reaction**: Check the oxidation states.
- Calcium (Ca) has an oxidation state of +2 in both cases.
- **Conclusion**: No change in oxidation states; therefore, this is not a disproportionation reaction.

- **Fourth Reaction**: Check the oxidation states.
- Copper (Cu) has an oxidation state of +1 in one case, 0 in another, and +2 in another.
- Here, Cu is reduced from +1 to 0 and oxidized from +1 to +2.
- **Conclusion**: Since Cu is both oxidized and reduced, this is a disproportionation reaction.

4. **Final Answer**: The fourth reaction is a disproportionation reaction.