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In the conversion of $B{r^ - }$ to $Br{O_2}^ - $:
A.There is anodic oxidation in basic solution
B.Equivalent mass of $B{r^ - }$ is twenty (atomic weight of Br=80)
C.There is anodic oxidation is acidic medium
D.There is cathodic reduction in basic solution

Answer
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Hint: We can define redox reactions as chemical reactions in which transfer of electrons takes place between two reactants. We can identify the transfer of electrons by observing the change in oxidation states of the species that are reacting. Batteries (or) electrochemical cells are the examples of redox reactions.

Complete step by step answer:
When $B{r^ - }$ is converted into $Br{O_2}^ - $, the anodic oxidation would take place in the basic solution. Therefore, option (A) is correct.
Let us now calculate the oxidation number of bromine in $B{r^ - }$ and $Br{O_2}^ - $.
In $B{r^ - }$, the oxidation number of bromine is -1 and let us consider the oxidation number of bromine as x in $Br{O_2}^ - $.
Oxidation number = $x + 2\left( { - 2} \right) = - 1$
Oxidation number = $x - 4 = - 1$
Oxidation number = $x = - 1 + 4$
Oxidation number = $ + 3$
We can see that the oxidation number of bromine changes from -1 to +3. The net increase in the oxidation number of bromine is +4.
We can calculate the equivalent mass of $B{r^ - }$ by dividing the atomic mass of bromine to the net increase in oxidation number.
The atomic mass of bromine is 80, and the net increase in oxidation number +4.
Equivalent mass=$\dfrac{{80}}{4}$
Equivalent mass=20
We have calculated the equivalent mass of $B{r^ - }$ as 20.
Therefore, option (B) is correct.
During the conversion of $B{r^ - }$ to $Br{O_2}^ - $, there is an anodic oxidation whose acidic medium is incorrect because the anodic oxidation takes place on the basic medium.
Therefore, the option (C) is incorrect.
During the conversion of $B{r^ - }$ to $Br{O_2}^ - $, there is cathodic reduction in basic solution because the cathodic reduction takes place on the acidic medium.
Therefore, the option (D) is incorrect.

So, the correct answer is Option A,B .

Note:
We must know that respiration, photosynthesis, combustion, rusting are some examples of redox reactions. The species (molecule/ion) that accepts electrons are known as oxidizing agents and species (molecule/ion) that donates electrons are known as reducing agents. A substance that is oxidized acts as a reducing agent and substance that is reduced acts as oxidizing agent.