Question

(a) How many constitutional isomers are possible for a triglyceride containing one molecule each of palmitic acid, oleic acid, and stearic acid? (b) Which of these constitutional isomers are chiral?

Short answer

Answer: There are three possible constitutional isomers for a triglyceride containing one molecule each of palmitic acid, oleic acid, and stearic acid. None of these constitutional isomers are chiral.

Step-by-step solution

Understand the structure of the triglyceride and the fatty acids involved

A triglyceride molecule consists of a glycerol backbone (3 carbons) with three fatty acid chains (R groups) attached to the carbons through ester linkages. In this exercise, the triglyceride contains one molecule each of palmitic acid, oleic acid, and stearic acid. Palmitic acid (C16:0): 16-carbon saturated fatty acid Oleic acid (C18:1): 18-carbon monounsaturated fatty acid with one double bond (cis configuration) Stearic acid (C18:0): 18-carbon saturated fatty acid The isomers that can form will depend on how these fatty acid chains are attached to the glycerol backbone.

Calculate the total number of constitutional isomers

To determine the number of possible constitutional isomers, we need to look at the permutations of the three fatty acid chains on the glycerol backbone at three positions: 1st, 2nd, and 3rd carbons. There are 3! (3 factorial) ways to arrange these fatty acid chains: 3! = 3 × 2 × 1 = 6 However, the glycerol backbone has a symmetric structure, which means the isomers in which the chains are inverted will be identical. Therefore, we need to divide by 2 to account for the symmetry: Total number of constitutional isomers = 6 / 2 = 3 So, there are three possible constitutional isomers for the triglyceride containing palmitic acid, oleic acid, and stearic acid.

Identify the chiral isomers

A chiral isomer has a non-superposable mirror image, which is a result of an asymmetric carbon atom (a carbon atom with four different substituents). However, in the case of these triglycerides, there are no asymmetric carbon atoms in any of the three constitutional isomers, as all the attachment points have symmetrical attachments. Hence, none of the constitutional isomers is chiral. To summarize: (a) There are three possible constitutional isomers for a triglyceride containing one molecule each of palmitic acid, oleic acid, and stearic acid. (b) None of these constitutional isomers are chiral.