Animated Solution for Chemistry - Organic Chemistry: Geometrical isomerism is not shown by

Geometrical isomerism, a fascinating type of stereoisomerism, arises primarily due to the restricted rotation around a carbon-carbon double bond ($C=C$). Unlike single bonds, where atoms can spin freely like a wheel on an axle, the pi-bond in a double bond locks the atoms in a rigid planar structure. This rigidity means that the spatial arrangement of groups attached to these carbons is fixed, leading to different isomers if the groups are arranged differently.

However, not every molecule with a double bond exhibits geometrical isomerism. There is a strict mathematical and physical condition that must be met.

For an alkene of the general formula $abC=Ccd$ to show geometrical isomerism (often referred to as cis-trans isomerism), the two groups attached to each doubly bonded carbon atom must be different.

Mathematically, this is expressed as: $a eq b$ $c eq d$

If either $a=b$ or $c=d$, the molecule possesses a plane of symmetry or an axis of symmetry that makes any swapped arrangement superimposable on the original. In simpler terms, flipping identical groups doesn't create a new molecule!

Let's apply this golden rule to the given problem. We need to find the molecule that does not show geometrical isomerism.

Option (a): 1,1-dichloro-1-pentene Let's draw its structure: $\mathrm{C}{\mathrm{l}}_2\mathrm{C}=\mathrm{CH}-\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_3$. Focus on the first carbon atom ($C_1$). What groups are attached to it? We have two Chlorine ($\mathrm{Cl}$) atoms. Since $a=\mathrm{Cl}$ and $b=\mathrm{Cl}$, we clearly see that $a=b$. Because the two groups on the same carbon are identical, this molecule fails the essential condition. Therefore, it cannot show geometrical isomerism.

What about the others? If you draw 1,2-dichloro-1-pentene, 1,3-dichloro-2-pentene, and 1,4-dichloro-2-pentene, you will notice that in each case, both doubly bonded carbons have two different groups attached to them. Thus, they all exhibit geometrical isomerism.

Whenever you are asked to identify geometrical isomerism, your first instinct should be to zoom in on the double bond and inspect the groups on each carbon individually. If you spot identical twins on the same carbon, you've found your answer!