Identifying Compounds Showing Cis-Trans Isomerism

Cis-trans isomerism, also known as geometric isomerism, is a type of stereoisomerism. It arises due to restricted rotation in a molecule, most commonly around a carbon-carbon double bond or within a cyclic structure. For a compound with a carbon-carbon double bond ($\text{C}=\text{C}$) to show cis-trans isomerism, each carbon atom involved in the double bond must be attached to two different groups.

Let's examine each given compound to see if it meets this condition:

• Compound 1: $(\text{H}_3\text{C})_2\text{C} = \text{CH} - \text{CH}_3$
• The first carbon of the double bond is bonded to two methyl groups ($\text{CH}_3$). Since the two groups attached to this carbon are the same ($\text{CH}_3$ and $\text{CH}_3$), this compound does not show cis-trans isomerism.

• Compound 2: $\text{H}_2\text{C} = \text{CCl}_2$
• The first carbon of the double bond is bonded to two hydrogen atoms ($\text{H}$). Since the two groups attached to this carbon are the same ($\text{H}$ and $\text{H}$), this compound does not show cis-trans isomerism.

• Compound 3: $\text{C}_6\text{H}_5(\text{H})\text{C} = \text{CH} - \text{CH}_3$
• Let's look at the groups attached to each carbon of the double bond:
• The first carbon ($\text{C}_6\text{H}_5(\text{H})\text{C}=$) is bonded to a phenyl group ($\text{C}_6\text{H}_5$) and a hydrogen atom ($\text{H}$). These are two different groups.
• The second carbon ($=\text{CH} - \text{CH}_3$) is bonded to a hydrogen atom ($\text{H}$) and a methyl group ($\text{CH}_3$). These are two different groups.
• Since both carbon atoms of the double bond are attached to two different groups, this compound can exist as cis and trans isomers. Therefore, it shows cis-trans isomerism.

Based on the analysis, only Compound 3 satisfies the condition for showing cis-trans isomerism.