The oxidation reaction is defined as the reaction in which a chemical species loses electrons in a chemical reaction. It occurs when the oxidation number of a species increases.

A reduction reaction is defined as the reaction in which a chemical species gains electrons in a chemical reaction. It occurs when the oxidation number of a species decreases.

The given redox reaction follows:

$MnO_4^-(aq)+NO_2^-(aq)\rightarrow MnO_2(s)+NO_3^-(aq)$

To balance the given redox reaction in basic medium, there are few steps to be followed:

Writing the given oxidation and reduction half-reactions for the given equation with the correct number of electrons

Oxidation half-reaction: $NO_2^-+2OH^-\rightarrow NO_3^-+H_2O+2e^-$

Reduction half-reaction: $MnO_4^-+2H_2O+3e^-\rightarrow MnO_2+4OH^-$

Multiply each half-reaction by the correct number in order to balance charges for the two half-reactions

Oxidation half-reaction: $NO_2^-+2OH^-\rightarrow NO_3^-+H_2O+2e^-$ ( × 3)

Reduction half-reaction: $MnO_4^-+2H_2O+3e^-\rightarrow MnO_2+4OH^-$ ( × 2)

The half-reactions now become:

Oxidation half-reaction: $3NO_2^-+6OH^-\rightarrow 3NO_3^-+3H_2O+6e^-$

Reduction half-reaction: $2MnO_4^-+4H_2O+3e^-\rightarrow 2MnO_2+8OH^-$

Add the equations and simplify to get a balanced equation

Overall redox reaction: $3NO_2^-+2MnO_4^-+H_2O\rightarrow 3NO_3^-+2MnO_2+2OH^-$

As we can see that in the overall redox reaction, hydroxide ions are released in the solution. Thus, making it a basic solution

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