Question

How can I draw all the isomers with molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}$? (that contain a cyclobutane ring and there are seven) and how can I identify chiral compounds and achiral compounds?

Answer 1

Hint:We are given a compound having molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}$. To solve this we must know that the compounds having the same molecular formula but different structural formula are said to be isomers of each other and the phenomenon is known as isomerism.

Complete answer:
We know that the compounds having the same molecular formula but different structural formulas are said to be isomers of each other and the phenomenon is known as isomerism.
We are given a compound having molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}$.
We have to draw the isomers with molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}$ that contain a cyclobutane ring. Cyclobutane ring means a cyclic compound having four carbon atoms. Thus, the substituents to the ring can either be two methyl groups (which contain one carbon atom) or one ethyl group (which contain two carbon atoms). The methyl group is $ - {\text{C}}{{\text{H}}_{\text{3}}}$ and the ethyl group is $ - {\text{C}}{{\text{H}}_{\text{2}}} - {\text{C}}{{\text{H}}_{\text{3}}}$.
Thus, the isomers with molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}$ that contain a cyclobutane ring are as follows:

Thus, there are seven isomers with molecular formula ${{\text{C}}_{\text{6}}}{{\text{H}}_{{\text{12}}}}$ that contain a cyclobutane ring.
The two isomers are mirror images of each other and are known as enantiomers. Thus, trans-1,2-dimethyl cyclohexane exist as enantiomers.
Now, a compound which is asymmetric and cannot be superimposed on its mirror image is said to be chiral and this property is known as chirality.
The chirality in a molecule is due to the three-dimensional arrangement of molecules. A carbon atom is said to be chiral when it is bonded with four different substituents to it.
The chiral and a chiral isomers are as follows:

In ethylcyclobutane, there is an internal mirror plane. Thus, ethylcyclobutane is achiral.
In 1-1,dimethylcyclobutane, there is a mirror plane perpendicular to the ring and passing through carbon 1-carbon 3. Thus, 1-1,dimethylcyclobutane is achiral.
In cis-1,2-dimethylcyclobutane, there is a mirror plane perpendicular to the ring and passing through the midpoints of carbon 1-carbon 2 and carbon 3-carbon 4.
In trans-1,2-dimethylcyclobutane, there is no mirror plane. Thus, trans-1,2-dimethylcyclobutane is chiral.
In cis-1,3-dimethylcyclobutane, there is a mirror plane perpendicular to the ring and passing through carbon 1-carbon 3. Thus, cis-1,3-dimethylcyclobutane is achiral.
In trans-1,3-dimethylcyclobutane, there is a mirror plane perpendicular to the ring and passing through carbon 1-carbon 3. Thus, trans-1,3-dimethylcyclobutane is achiral.

Note:The compounds which are chiral in nature are optically active. The important condition for a compound to be optically active is that the compound should be asymmetric or it should have a chiral centre. Thus, the compound trans-1,2-dimethylcyclobutane is optically active.