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Why \[{\text{KMn}}{{\text{O}}_{\text{4}}}\] is not used as the primary standard?

Answer
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Hint: We need to know that in chemistry two main reactions play a major role. One is the oxidation reaction. Another is the reduction reaction. Oxidation reaction is nothing but addition of oxidation or removal of hydrogen or loss of electrons. Reduction is nothing but addition of hydrogen or removal of oxygen or gain of electrons in the reaction from reactant to product. For oxidation and reduction purposes using some reagents, reagents are called oxidising and reducing agents. The oxidising agent is nothing but the reagent is used for oxidation of reactant to give respect to the product.

Complete answer:
We need to know that the oxidation agent acts as an electron acceptor and the reducing agent acts as electron donor. In some cases, oxidation and reduction occur in the same reaction, these kinds of reactions are called redox reactions.
Hydrogen peroxide (\[{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}\]), Fenton’s reagent, oxygen (\[{{\text{O}}_{\text{2}}}\]) and ozone (\[{{\text{O}}_{\text{3}}}\]) are examples of common oxidising agent.
The molecular formula of potassium permanganate is \[{\text{KMn}}{{\text{O}}_{\text{4}}}\]. Potassium permanganate is one of the oxidising agents in chemistry. Potassium permanganate is not used as primary standard because is not able to release in \[{\text{Mn}}{{\text{O}}_{\text{2}}}\] in the reaction. Potassium permanganate is always in the stable form. The reason \[{\text{KMn}}{{\text{O}}_{\text{4}}}\] is also used as a colour indicator in analysis.
According to the above discussion, we conclude \[{\text{KMn}}{{\text{O}}_{\text{4}}}\] is not used as the primary standard.

Note:
We need to remember the oxidation of primary alcohol to give respect to aldehyde. If the oxidation of secondary alcohol to give respect to ketone product. The oxidation aldehyde gives carboxylic acid. Even oxidation of ketone is also given carboxylic acid. The oxidation of alkane to give primary alcohol and oxidation of alkene give secondary alcohol. The above discussed oxidation process all depends on oxidising agents. Some special oxidising agents are used for direct conversion of alcohol to oxidation. In some oxidation agents are used for direct conversion of alkane to aldehyde. In some cases, alkane directly converts to ketone.
Nitrogen dioxide (\[{\text{N}}{{\text{O}}_{\text{2}}}\]), dinitrogen tetroxide ( \[{{\text{N}}_{\text{2}}}{{\text{O}}_{\text{4}}}\]), sodium perborate acts as specific oxidising agent for alcohol.
Sodium bismuthate (\[{\text{NaBi}}{{\text{O}}_{\text{3}}}\]), lead dioxide (\[{\text{Pb}}{{\text{O}}_{\text{2}}}\]) and sodium dichromate (\[{\text{N}}{{\text{a}}_{\text{2}}}{\text{C}}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}\]) are some examples for carboxylic acid oxidation reaction.