Question

Among the following, the formula of saturated fatty acid is:
(A) ${{\text{C}}_{{\text{17}}}}{{\text{H}}_{{\text{29}}}}{\text{COOH}}$
(B) ${{\text{C}}_{{\text{17}}}}{{\text{H}}_{{\text{35}}}}{\text{COOH}}$
(C) ${{\text{C}}_{{\text{17}}}}{{\text{H}}_{{\text{31}}}}{\text{COOH}}$
(D) ${{\text{C}}_{{\text{17}}}}{{\text{H}}_{{\text{33}}}}{\text{COOH}}$

Answer 1

First determine the general formula of saturated fatty acid. Then from the general formula of saturated fatty acid and the number of carbon atoms, determine the number of hydrogen atoms.

Complete answer:
A saturated fatty acid has two parts, a hydrocarbon part and the carboxylic functional group. The hydrocarbon part contains methylene groups and terminal methyl groups. The carboxylic functional group is $- {\text{COOH}}$. Write the general formula of saturated fatty acid as
${{\text{C}}_{\text{n}}}{{\text{H}}_{{\text{2n + 1}}}}{\text{COOH}}$,
In the above formula, n gives the number of carbon atoms that are not a part of the carboxylic group. In the hydrocarbon part of saturated fatty acid, when n number of carbon atoms are present, $2n + 1$ hydrogen atoms are present. Substitute $n = 17$ in the above general formula of saturated fatty acid and calculate the number of hydrogen atoms present in the hydrocarbon part of saturated fatty acid.
$2n + 1 = 2\left( {17} \right) + 1 = 34 + 1 = 35$
Hence, 17 carbon atoms are present in the hydrocarbon part of saturated fatty acid, 35 hydrogen atoms are present in the hydrocarbon part of saturated fatty acid.
So, the formula of saturated fatty acid is ${{\text{C}}_{{\text{17}}}}{{\text{H}}_{{\text{35}}}}{\text{COOH}}$

**Hence, the correct option is the option (B).

Note:**
There is another approach to solve the problem. When 17 carbon atoms are present, 16 methylene groups and one methyl group are present. One methyl group gives 3 hydrogen atoms in the hydrocarbon part of the saturated fatty acid. Whereas each methylene group gives 2 hydrogen atoms. So, the total number of hydrogen atoms in the hydrocarbon part of the saturated fatty acid will be $3 + 2\left( {16} \right) = 3 + 32 = 35$ .