Step 1: Understanding the Question:
The question asks which of the given fatty acids is most prone to oxidative degradation (rancidity).
Step 2: Key Concepts and Approach:
The rate of lipid oxidation depends directly on the number of double bonds (unsaturation) in the fatty acid chain.
The hydrogen atoms located on carbons adjacent to double bonds (especially the methylene carbons between two double bonds, called bis-allylic carbons) are easily abstracted by free radicals.
Step 3: Detailed Explanation:
• Analyzing the Structures:
* Palmitic Acid ($16:0$) and Stearic Acid ($18:0$) are saturated fatty acids. Since they have no double bonds, they are highly stable and resistant to oxidation.
* Oleic Acid ($18:1$) is a monounsaturated fatty acid with one double bond. It oxidizes slowly.
* Linolenic Acid ($18:3$) is a polyunsaturated fatty acid with three double bonds.
• Susceptibility to Oxidation:
The presence of multiple double bonds in linolenic acid introduces highly reactive bis-allylic methylene groups.
The $C-H$ bond dissociation energy at these sites is low, making it easy for free radicals to initiate lipid peroxidation.
• Relative Rates: Quantitatively, the relative rate of oxidation of $18:1$ (Oleic) : $18:2$ (Linoleic) : $18:3$ (Linolenic) is approximately $1 : 10 : 25$.
Step 4: Final Answer:
Linolenic acid has the highest susceptibility to oxidation because of its three double bonds.