Lignoceric acid, CH₃ ― (CH₂)₂₂ ― COOH, is a C₂₄ fatty acid found in peanut oil in small amounts.
a. State the number of β oxidation cycles for the complete oxidation of lignoceric acid.

Verified step by step guidance

1. Step 1: Understand the structure of lignoceric acid. It is a fatty acid with the formula CH₃ ― (CH₂)₂₂ ― COOH, which means it has a total of 24 carbon atoms.
2. Step 2: Recall the process of β oxidation. In each cycle of β oxidation, two carbon atoms are removed from the fatty acid chain in the form of acetyl-CoA.
3. Step 3: Determine the number of β oxidation cycles required. Since lignoceric acid has 24 carbon atoms, the number of cycles can be calculated by dividing the total number of carbon atoms (24) by 2, and then subtracting 1 because the final two carbons are directly converted into acetyl-CoA without undergoing another cycle.
4. Step 4: Write the formula for the number of β oxidation cycles: \( \text{Number of cycles} = \frac{\text{Total carbon atoms}}{2} - 1 \). Substitute the value of 24 for the total carbon atoms.
5. Step 5: Perform the calculation using the formula to determine the number of β oxidation cycles for lignoceric acid.

Key Concepts

Beta Oxidation

Beta oxidation is a metabolic process that breaks down fatty acids into acetyl-CoA units, which can then enter the citric acid cycle for energy production. Each cycle of beta oxidation shortens the fatty acid chain by two carbon atoms and produces one molecule of acetyl-CoA, along with NADH and FADH2, which are used in the electron transport chain.

Fatty Acid Structure

Fatty acids are carboxylic acids with long hydrocarbon chains. The structure of lignoceric acid, a C24 fatty acid, indicates it has 24 carbon atoms, which influences the number of beta oxidation cycles it undergoes. The number of cycles is determined by the total number of carbon atoms in the fatty acid chain, as each cycle removes two carbon atoms.

Complete Oxidation

Complete oxidation of a fatty acid refers to the full breakdown of the fatty acid into carbon dioxide and water, releasing energy. For lignoceric acid, this involves multiple beta oxidation cycles followed by the entry of acetyl-CoA into the citric acid cycle, ultimately yielding ATP, the energy currency of the cell.