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Substance A, ${{C}_{5}}{{H}_{8}}$ is chiral when A is treated with ${{H}_{2}}/Pt$ B, ${{C}_{5}}{{H}_{10}}$ is produced, B is achiral. A can be:
(a)- 1-Methylcyclobutene.
(b)- 3-Methylcyclobutene
(c)- trans-1,2-dimethylcyclopropane
(d)- cyclopentane

Answer
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Hint: If all the atoms or groups attached to the carbon atom are different, such carbon is called asymmetric carbon or chiral carbon. If any of the atoms or groups is repeated then the carbon is achiral. Unsymmetrical alkenes react with ${{H}_{2}}/Pt$ to form alkanes.

Complete step by step answer:
Compounds which are non-superimposable on their mirror image are called chiral compounds and the carbon should have all the groups or atoms attached to it differently.
So, let us check all the options one by one:
(a)- 1-Methylcyclobutene
The structure of 1-Methylcyclobutene is given below:

seo images

for the compound to be chiral, it should have at least one chiral carbon. In 1-Methylcyclobutene there is no chiral carbon atom present.
Hence, this option is incorrect.

(b)- 3-Methylcyclobutene
The structure of 3-Methylcyclobutene is given below:
seo images

So, the 3-Methylcyclobutene has one chiral carbon atom i.e., the 3rd carbon atom. It is also an alkene, so it will react with ${{H}_{2}}/Pt$ to form an alkane.
So, 3-Methylcyclobutene will form 3-Methylcyclobutane.
The reaction is:
seo images

This option is correct.

(c)- trans-1,2-dimethylcyclopropane
Trans-1,2-dimethylcyclopropane is an alkane and alkane cannot react with ${{H}_{2}}/Pt$.
So, this option is also incorrect.

(d)- cyclopentane
Cyclopentane is an alkane and alkane cannot react with ${{H}_{2}}/Pt$.
So, this option is also incorrect.
Hence the A compound is 3-Methylcyclobutene and the B compound is 3-Methylcyclobutane.
So, the correct answer is “Option B”.

Note: If the compound at least has a chiral carbon atom, that compound should be considered as a chiral compound. The chiral carbon of the compound is also known as the stereocenter of that compound.