Question

Linoleic acid is an essential fatty acid found in many vegetable oils, such as soy, peanut, and cottonseed. A key structural feature of the molecule is the cis orientation around its two double bonds, where \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2}\) represent two different groups that form the rest of the molecule. (a) How many different compounds are possible, changing only the cis-trans arrangements around these two double bonds? (b) How many are possible for a similar compound with three double bonds?

Short answer

4 isomers for linoleic acid (two double bonds); 8 isomers for three double bonds.

Step-by-step solution

- Understanding cis-trans Isomerism

Cis-trans isomerism (geometric isomerism) occurs due to the rigidity of double bonds. Each double bond can be either in the 'cis' (same side) or 'trans' (opposite side) arrangement.

- Determine the number of double bonds

For part (a), linoleic acid has two double bonds. For part (b), the question specifies a compound with three double bonds.

- Calculate the number of isomers for two double bonds

Each double bond can be either 'cis' or 'trans'. With two double bonds, there are 2 choices (cis or trans) per double bond. Thus, the total number of possible isomers is calculated as 2^2 = 4.

- Calculation for three double bonds

Similarly, for a molecule with three double bonds, each of which can independently be 'cis' or 'trans', the number of possible configurations is 2^3 = 8.

- Summarize results

For linoleic acid with two double bonds, the number of possible isomers is 4. For a similar compound with three double bonds, the number of possible isomers is 8.

Key concepts

Essential Fatty Acids

Essential fatty acids (EFAs) are critical nutrients that our bodies need to function but cannot produce on their own. Hence, they must be obtained through diet. The two primary essential fatty acids are linoleic acid and alpha-linolenic acid. These EFAs play several crucial roles in our bodies:

• They are components of cell membranes, affecting fluidity and flexibility.


• They are precursors to bioactive compounds like prostaglandins, which are involved in inflammation and other physiological processes.


• They contribute to the proper functioning of the nervous system and brain development.

Linoleic acid, found in vegetable oils like soybean, peanut, and cottonseed oil, is a type of omega-6 fatty acid. Including essential fatty acids in your diet helps maintain healthy skin, support the immune system, and regulate blood pressure. Given their importance, it's easy to see why understanding their structure and function is beneficial.

Double Bonds

Double bonds are a defining feature in unsaturated fatty acids, and they significantly impact the chemical properties of molecules. A double bond consists of two pairs of shared electrons between two atoms, making it stronger than a single bond. However, this also brings rigidity to the molecule, preventing free rotation around the bond.
This rigidity leads to different spatial arrangements of the atoms or groups attached to the double-bonded carbons, commonly referred to as cis and trans isomers. For every double bond present in a chain, we can have:

• Cis configuration: Both hydrogen atoms attached to the double-bonded carbons are on the same side, creating a bend in the molecule.


• Trans configuration: The hydrogen atoms are on opposite sides, making the molecule more linear.

Double bonds also create sites of reactivity in a molecule and influence its physical properties, such as melting point and solubility. Knowing if a fatty acid has one or more double bonds can tell us a lot about its behavior and biological role.

Geometric Isomerism

Geometric isomerism, also known as cis-trans isomerism, is a specific type of stereoisomerism. This occurs due to the presence of double bonds or rings, where rotation around the bond isn't possible. Each double bond in a molecule can exhibit either a 'cis' or 'trans' arrangement:

• 'Cis' Isomers: Groups are on the same side of the double bond. These create a kink or bend in the molecule. An example is linoleic acid, which has two 'cis' double bonds.


• 'Trans' Isomers: Groups are on opposite sides of the double bond. These make the molecule more straight and rigid.

The presence and arrangement of geometric isomers significantly affect the chemical and physical properties of a molecule. For instance:

• They can influence the melting point: 'Cis' isomers typically have lower melting points compared to 'trans' isomers due to their less compact structure.


• They affect the biological function: Each configuration might interact differently with enzymes or other molecules in the body.

Understanding geometric isomerism helps in predicting and explaining how molecules will behave in biological systems and industrial applications.