Let's analyze the reaction:
\[ 2 \text{H}_2\text{O}_2 \to 2 \text{H}_2\text{O} + \text{O}_2 \]
Here’s a step-by-step explanation to determine the type of reaction:
1. **Identify Oxidation States**:
- In hydrogen peroxide (\(\text{H}_2\text{O}_2\)), hydrogen has an oxidation state of +1, and oxygen has an oxidation state of -1.
- In water (\(\text{H}_2\text{O}\)), hydrogen has an oxidation state of +1, and oxygen has an oxidation state of -2.
- In molecular oxygen (\(\text{O}_2\)), oxygen has an oxidation state of 0.
2. **Compare Oxidation States**:
- In \(\text{H}_2\text{O}_2\), the oxidation state of oxygen is -1.
- In \(\text{H}_2\text{O}\), the oxidation state of oxygen is -2.
- In \(\text{O}_2\), the oxidation state of oxygen is 0.
This shows that:
- Oxygen in \(\text{H}_2\text{O}_2\) (oxidation state -1) is being reduced to \(\text{H}_2\text{O}\) (oxidation state -2).
- Oxygen in \(\text{H}_2\text{O}_2\) (oxidation state -1) is being oxidized to \(\text{O}_2\) (oxidation state 0).
3. **Determine the Reaction Type**:
- **Redox Reaction**: A redox reaction involves the transfer of electrons between substances, leading to changes in oxidation states. In this reaction, both oxidation and reduction are occurring, so it is a redox reaction.
- **Hydrolysis Reaction**: This involves the reaction of a compound with water. This is not a hydrolysis reaction.
- **Solvolysis Reaction**: This is a type of reaction where a solvent reacts with a solute. This is not a solvolysis reaction.
- **Disproportionation Reaction**: This is a type of redox reaction where a single substance is both oxidized and reduced. In this case, oxygen is both oxidized and reduced, so it is also a disproportionation reaction.
Since the reaction fits the criteria for both a redox and a disproportionation reaction, the best classification among the provided options is:
**d.) Disproportionation.**