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The order of stability of the following tautomeric compounds is:
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[A] I > II > III
[B] III > II> I
[C] II > I > III
[D] II > III > I

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Answer
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Hint: Tautomerism is a kind of isomerism. In this, there is an interconversion between the two possible chemical forms of the same species. There are sometimes tautomers which are more stable than the other one but an equilibrium is maintained between the forms.

Complete step by step answer:
We can define tautomers as the structural isomers of chemical compounds which they readily interconvert into each other. Generally, it’s the proton that relocates and thus there exists equilibrium between the two forms.
We call this process of interconverting of protons as tautomerization and the species undergoing the process are called the tautomers.
Here in the given compound we have keto – enol tautomerism. In this tautomerism, a compounds containing ketone groups i.e. –CO can undergo enol formation i.e. –CO converts to –COH even though Keto forms are considered more stable.
Now, let us see the structures given to us one by one.
In the third tautomer we have conjugated double bonds which give extra stability so III is the most stable.
Among the first and second tautomers, the first tautomer is the enol form and the second is the keto form. We know that keto is more stable than enol tautomer so structure II is more stable than structure I.
We can understand from the above discussion that the order of stability is III > II > I.
So, the correct answer is “Option B”.

Note: We should remember that tautomers are not similar to the canonical forms of resonance stabilised species. We can chemically distinguish tautomers and they can be identified by their different spectroscopic data. On the other hand resonance canonical structures do not physically exist and are just a hypothetical concept to understand theory of chemical compounds better.