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Why is potassium dichromate not a self indicator?

Answer
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Hint: Potassium dichromate is a strong oxidising agent, but not as strong as potassium permanganate, and potassium dichromate only works as an oxidising agent in acidic medium. It imparts yellowish colour as an indicator, but not as a self indicator.

Complete answer:
Potassium dichromate cannot function as a self indicator because of the colour the chromate ions ( Cr+3 ) give at the end of the reaction.
Generally, the dichromate solutions are orange, but they cannot act as self indicators. This happens due the reduction of dichromate ions into just chromium ions which gives out green colour. This does not help but hinders the visual detection of end points by dichromate colour.
Even if detection is possible, it cannot be accurate as we cannot accurately tell when the colour changes. Thus, using it as a self indicator will not be sufficient, an indicator has to be added so that it can be perfect.
On the contrary, potassium permanganate can be used as a self indicator.
This case does not occur in case of potassium permanganate that the colour variation can hinder. In potassium dichromate, it hinders only due to the reduction to chromium ions providing green colour.
Usually, the solution for which potassium dichromate is used as an indicator will provide
yellow colour, but here the colour change visualisation hinders due to chromate ions.

Note: Even though potassium is a weak oxidising agent in comparison to potassium permanganate, it is still widely used in redox titrations. One of the advantages of potassium dichromate over potassium permanganate is that it is available in high purity and is highly stable up to its melting point. The chemical formula of potassium dichromate is K2Cr2O7 and that of potassium permanganate is KMnO4 .