Question

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : Saponification value of ghee is relatively higher than most of the vegetable oils.
Reason (R) : The average molecular weight of the fatty acids in ghee is high and hence, ghee has a higher saponification value.
In light of the above statements, choose the correct answer from the options given below.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Hint:

Remember this fundamental inverse relationship in fat chemistry:
\[ \text{Saponification Value} \propto \frac{1}{\text{Average Molecular Weight of Fatty Acids}} \] Because milk fat (ghee) is rich in volatile, short-chain fatty acids like butyric acid ($\text{C}_4$), it has a lower average molecular weight and a higher saponification value than vegetable oils.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The saponification value (SV) is defined as the number of milligrams of potassium hydroxide ($\text{KOH}$) required to saponify 1 gram of fat or oil.
This value is an indicator of the average molecular weight (or chain length) of the fatty acids present in the triacylglycerols of the fat.

Step 2: Detailed Explanation:
Let us analyze Assertion (A):
Ghee (milk fat) has a saponification value that typically ranges from $220$ to $233\text{ mg KOH/g}$.
In contrast, most common vegetable oils (such as mustard, groundnut, sunflower, and soybean oils) have lower saponification values, usually ranging from $180$ to $195\text{ mg KOH/g}$.
Therefore, Assertion (A) is correct.
Now let us analyze Reason (R):
The saponification value is inversely proportional to the mean molecular weight of the fatty acids in the fat.
Each triacylglycerol molecule requires three molecules of $\text{KOH}$ for complete hydrolysis, regardless of the size of its constituent fatty acids:
\[ \text{Triacylglycerol} + 3\text{KOH} \rightarrow \text{Glycerol} + 3\text{Potassium Soap} \] A fat containing short-chain fatty acids has a lower average molecular weight.
This means that 1 gram of this fat will contain more individual triacylglycerol molecules than 1 gram of a fat made of long-chain fatty acids.
As a result, more molecules of $\text{KOH}$ are required to saponify 1 gram of the short-chain fat, yielding a higher saponification value.
Ghee is unique because it contains a high concentration of short-chain and medium-chain fatty acids (such as butyric, caproic, and caprylic acids), giving its fatty acids a low average molecular weight.
This low average molecular weight is the reason ghee has a high saponification value.
The statement in Reason (R) that the molecular weight is high is incorrect.

Step 3: Final Answer:
Assertion (A) is true, but Reason (R) is false.