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What is the role of hydrogen peroxide in the given two reactions
a) ${H_2}{O_2} + {O_3} \to {H_2}O + 2{O_2}$
b) ${H_2}{O_2} + A{g_2}O \to 2Ag + {H_2}O + {O_2}$
A. Oxidizing in (a) and reducing in (b)
B. Reducing in (a) and oxidizing in (b)
C. Reducing in both (a) and (b)
D. Oxidizing in both (a) and (b)

Answer
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Hint:Oxidizing agents are the compound which oxidizes the other compound and reduces itself in a redox reaction. Similarly reducing agents are the compound which reduces the other and itself gets oxidized.

Complete answer:
Redox reaction is a type of chemical reaction in which the oxidation states of atoms change. Earlier redox reactions were known for transferring the oxygen and hydrogen only. But redox reactions are actual transfer of electrons between chemical species.
The chemical species from which the electron has been removed is said to have been oxidized. So loss of electrons means an increase in oxidation state. On the other hand the species to which that electron has been added is said to have been reduced. So gain of electron means decrease in oxidation state.
In redox reaction one species is a reducing agent which reduces the other species and itself gets oxidized. The other is an oxidizing agent which oxidizes the other species, itself gets reduced.
In the reaction ${H_2}{O_2} + {O_3} \to {H_2}O + 2{O_2}$ Ozone ${O_3}$ is in zero oxidation state and then reduced to ${O^{2 - }}$ ion by hydrogen peroxide. Hence hydrogen peroxide here acting as reducing agent
In the reaction ${H_2}{O_2} + A{g_2}O \to 2Ag + {H_2}O + {O_2}$ $Ag$ is present in +2 oxidation state in $A{g_2}O$ and gets reduced to $Ag$ in zero oxidation state. Hence $A{g_2}O$ is getting reduced. Therefore hydrogen peroxide is acting as a reducing agent.

Hence the correct option will be A. hydrogen peroxide is acting as reducing agent in both the reactions.

Note:

The relative strengths of oxidizing and reducing agents determined by several reactions between them. Then the common oxidation-reduction half reactions have been organized into a table in which the strongest reducing agents are at one end and strong oxidizing agents on the other end.