Problem 90 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

The molecular formula of a saturated compound is \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\). The formula permits the existence of two (a) functional isomers (b) position isomers (c) optical isomers (d) cis-trans isomers

Step-by-Step Solution

Answer

1,2-dichloroethane can have cis-trans isomers.

Step 1: Understanding the compound structure

The given compound is 1,2-dichloroethane, with the molecular formula \(\mathrm{C}_{2}\mathrm{H}_{4} \mathrm{Cl}_{2}\). It is saturated, meaning that it has single bonds only. We are going to determine what kind of isomers it can have.

Step 2: Analyzing potential for functional isomers

Functional isomers occur when compounds have the same molecular formula but different functional groups. Since 1,2-dichloroethane has only halogen atoms attached to an alkane core, and lacks other functional groups, functional isomers are not possible.

Step 3: Investigating position isomers

Position isomers arise when functional groups or substituents are located in different positions on the carbon chain. In 1,2-dichloroethane, moving the chlorine atoms to different carbons would result in similar compounds with no structural variation, so true position isomers cannot occur.

Step 4: Exploring optical isomers

Optical isomers, or enantiomers, appear when a molecule has a chiral center resulting in non-superimposable mirror images. The structure of 1,2-dichloroethane is symmetrical and does not contain any chiral centers. Thus, optical isomers are not possible.

Step 5: Determining cis-trans isomers

Cis-trans isomers, or geometric isomers, occur due to restricted rotation around a double bond or a ring. In alkanes, such as 1,2-dichloroethane, with two different substituents on each carbon, cis and trans forms can result. The molecule has two possible configurations with the chlorines being either on the same (cis) or opposite (trans) sides of the carbon-carbon bond.

Key Concepts

Saturated Compounds

Saturated compounds are a fundamental concept in organic chemistry. These compounds contain single covalent bonds between their carbon atoms, making them saturated with hydrogen atoms. This means they cannot accommodate more hydrogen because each carbon atom is bonded to the maximum number of hydrogen atoms it can.

• They are typically stable.
• They include alkanes and cycloalkanes.
• The molecular formula often follows \( C_nH_{2n+2} \).

Saturated compounds do not have functional isomer variants because there are no additional functional groups present to rearrange. The compound mentioned, 1,2-dichloroethane, is a clear example of a saturated compound with all single bonds.

Position Isomers

Position isomers are types of structural isomers where the position of a functional group or substituent in the compound can be varied. This can result in different isomers with the same molecular formula, although their chemical properties can vary. In the case of 1,2-dichloroethane:

• Cl atoms are attached to the first and second carbon in the carbon chain.
• Changing the position doesn't yield a new structure, hence no position isomers.

Understanding the potential for position isomers in a compound involves checking if moving a functional group results in a different compound with unique properties. For 1,2-dichloroethane, relocation of chlorine atoms within the two-carbon framework does not generate distinct isomers, confirming no possible position isomers.

Optical Isomers

Optical isomers, also known as enantiomers, are interesting forms of isomerism that deal with the 3D arrangement of atoms in molecules. They occur in compounds that have a chiral center, which makes them non-superimposable on their mirror image, similar to how your left hand is a mirror image of your right hand, but the two hands are not identical.
For optical isomers to exist:

• The molecule must have chirality, meaning at least one atom is bonded to four different substituents.
• They often exhibit different behaviors in polarized light.

In 1,2-dichloroethane: - The lack of a chiral center due to its symmetrical nature means optical isomers cannot form, as both halves of the molecule are identical.

Cis-Trans Isomers

Cis-trans isomers, also called geometric isomers, occur in compounds with restricted rotation, usually around a double bond or a ring. They result from different spatial arrangements of atoms.
For molecules like 1,2-dichloroethane:

• Although it's an alkane and generally flexible, restricted rotation is possible due to bulky substituents like chlorine atoms.
• Two possible configurations arise: 'cis' when substituents are on the same side, and 'trans' when they're on opposite sides.

The presence of these bulky groups in 1,2-dichloroethane is sufficient to allow for cis-trans isomerism, even without a double bond. This is particularly interesting as it highlights that not only alkenes can have geometric isomers, but also certain substituted alkanes.