Step 1: Concept
$\beta$-oxidation is the metabolic pathway by which fatty acyl-CoA molecules are broken down in the mitochondria to generate acetyl-CoA, NADH, and $\text{FADH}_{2}$. Each cycle cleaves a two-carbon unit from the carboxyl end of the fatty acid chain.
Step 2: Meaning
Oleic acid is a monounsaturated fatty acid containing 18 carbon atoms and a single double bond at carbon position 9 ($18:1\,\Delta^{9}$). Complete oxidation means chopping the entire chain into 2-carbon acetyl-CoA pieces.
Step 3: Analysis
* For a straight-chain saturated fatty acid with $n$ carbon atoms, the number of $\beta$-oxidation cycles required is calculated using the formula:
$$\text{Cycles} = \frac{n}{2} - 1$$
* For an 18-carbon fatty acid chain:
$$\text{Cycles} = \frac{18}{2} - 1 = 9 - 1 = 8\text{ cycles}$$
* The presence of the single double bond in oleic acid requires an auxiliary enzyme (enoyl-CoA isomerase) to shift the bond position during the pathway, but it does not alter the absolute total number of cleavage cycles required to split the 18 carbons into 9 fragments of acetyl-CoA.
Step 4: Conclusion
Therefore, exactly 8 cycles of cleavage are needed to completely oxidize the activated oleic acid chain into 9 individual acetyl-CoA units.
Final Answer: (C)