Question

The number of geometrical isomers of the following alkene \(\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{Cl}\) is

Short answer

There are 8 geometrical isomers.

Step-by-step solution

Identify double bonds for isomerism

The molecule given is a nonane with alternating double bonds starting with a chlorinated carbon at one end. Count the number of double bonds that can have geometrical (cis-trans) isomerism. These are each of the three non-terminal alkenes: between the first and second carbon, between the second-vthird carbon, and between the fourth-fifth carbon.

Determine possible configurations

Each of the identified double bonds can have two possible geometrical configurations (cis and trans). Thus, for each double bond, we have 2 possibilities.

Calculate total number of isomers

Since the configurations are independent of each other, we multiply the number of configurations for each double bond. This gives us a total of: \(2^3 = 8\) geometrical isomers.

Key concepts

Cis-Trans Isomerism

Cis-trans isomerism, also known as geometrical isomerism, is fascinating. It's a type of stereoisomerism seen specifically in certain alkenes. Alkenes are hydrocarbons with at least one carbon-carbon double bond. This isomerism occurs because of the rigidity of the double bond. Unlike single bonds, double bonds don't allow free rotation. This rigidity leads to the formation of two distinct configurations, namely 'cis' and 'trans'.

In a cis configuration, similar or identical groups are on the same side of the double bond. On the other hand, the trans configuration has similar groups on opposite sides of the double bond. This difference can significantly impact the physical and chemical properties of the molecules. Geometrical isomerism is crucial in chemistry, as it affects properties like boiling point, melting point, and solubility.

Example:

• Cis-2-butene has both methyl groups on the same side of the double bond.
• Trans-2-butene has the methyl groups on opposite sides.

Understanding cis-trans isomerism is vital for calculating and reasoning about the various isomers possible in a compound.

Double Bonds

Double bonds are a primary feature that allows geometrical isomerism to occur. In chemical terms, a double bond consists of one sigma bond and one pi bond. It's present between two carbon atoms. The presence of the double bond restricts the rotation around the carbon-carbon bond.

This constriction is why molecules like alkenes can form cis and trans isomers. In our nonane alkene example, the presence of multiple double bonds increases the number of possible isomers. Each double bond can exist in either a cis or trans form. Hence, for compounds with several double bonds, one can calculate the number of potential geometrical isomers by considering each bond's configuration independently.

For instance:

• Three double bonds provide a potential of 8 geometrical isomers as each double bond can independently adopt two forms (cis or trans).

The knowledge of double bonds is fundamental in predictively determining the geometry and variety of isomers a compound might have.

Geometrical Configurations

Geometrical configurations refer to the spatial arrangement of atoms around a double bond, leading to distinctive isomeric forms. Specifically, in alkenes, cis and trans configurations are the main options.

For each double bond in a molecule, it can independently adopt either a cis or a trans configuration. This peculiarity is why molecules with multiple double bonds can have numerous geometrical isomers. In the case of our nonane alkene with alternating double bonds, every single double bond can form two configurations.

To compute the total number of geometrical isomers, you multiply the number of configurations of each double bond. Mathematically, if a molecule has 'n' double bonds, the total possible geometrical isomers equals 2 raised to the power of 'n' ( $n$ ), which reflects the independent nature of these configurations.

This principle is crucial. It helps chemists and students conceptualize and visualize the vast array of possible forms a single compound might take based solely on how its atoms are spatially arranged.