To determine the role of hydrogen peroxide \((\text{H}_2\text{O}_2)\) in the given reactions, we need to analyze its behavior in both reactions in terms of oxidation and reduction.
Reaction (a): \(H_2O_2 + O_3 → H_2O + 2O_2\)
- In this reaction, hydrogen peroxide \((\text{H}_2\text{O}_2)\) reacts with ozone \((\text{O}_3)\) and forms water \((\text{H}_2\text{O})\) and oxygen gas \((\text{O}_2)\).
- To identify if \(H_2O_2\) acts as an oxidizing or reducing agent, we look at the changes in oxidation states:
- The oxygen in \(H_2O_2\) has an oxidation state of -1, and in \(\text{O}_2\), it is 0. This shows an increase in oxidation state, indicating oxidation of oxygen from \(H_2O_2\).
- Thus, \(H_2O_2\) is being oxidized, which means it acts as a reducing agent.
Reaction (b): \(H_2O_2 + Ag_2O → 2Ag + H_2O + O_2\)
- In this reaction, hydrogen peroxide \((\text{H}_2\text{O}_2)\) reacts with silver oxide \((\text{Ag}_2\text{O})\) to produce metallic silver, water, and oxygen gas.
- Analyzing the oxidation states:
- The oxidation state of silver in \(Ag_2O\) is +1, and it goes to 0 in the metallic form of silver \((\text{Ag})\). This decrease in oxidation state indicates a reduction process.
- For the reaction to have a reducing effect on Ag+, \(\text{H}_2\text{O}_2\) must donate electrons, indicating that it acts as a reducing agent.
From the above observations, it is clear that in both reactions \((\text{a})\) and \((\text{b})\), hydrogen peroxide \((\text{H}_2\text{O}_2)\) functions as a reducing agent.
Conclusion: The correct role of \(\text{H}_2\text{O}_2\) in the reactions is reducing in both (a) and (b). Therefore, the correct answer is:
Reducing in (a) and (b)