Chapter 20, Problem 20.69QP

(a)

Interpretation Introduction

Interpretation: The questions based on the Table 20.4 are to be answered.

Concept introduction: Fats are the biomolecular compounds which are also known as triglycerides or lipids. It is one of the important macro nutrient found in our blood. Polyunsaturated triglycerides are the compounds comprises of double or triple bonds between the carbons.

Triglycerides are the tri-esters of fatty acid and glycerol. It is formed by the addition of glycerol with three fatty acids. Glycerol molecule comprises of three hydroxyl $\left(\text{OH}\right)$ groups. All lipids are water insoluble. These are the store houses of energy in the body. The fatty acids are of both types that are saturated and unsaturated. The unsaturated fatty acids are those which contain one or more $-\text{CH}=\text{CH}-$ double bonds in their chain.

To determine: The fat that consume more hydrogen in $1.0\text{kg}$ of oleic acid or $0.50\text{kg}$ of $\alpha -$ linolenic acid.

Answer to Problem 20.69QP

Solution

The fat that consumes more hydrogen is $0.50\text{kg}$ of $\alpha -$ linolenic acid.

Explanation of Solution

Explanation

The consumption of hydrogen is decided by the number of double or triple bonds. The molecular structure of oleic acid is given by following figure,

Figure 1

This contains a double bond at the carbon position $9$. From the molecular formula it is clear that for saturation of $18$ carbons $36$ hydrogen atoms are required. It means for saturation one molecule of hydrogen is required. In the molecular hydrogen form carbon –hydrogen ratio is represented as,

$\begin{array}{l}18:18\\ 1:1\end{array}$

This ratio indicates that for one mole carbon one mole of hydrogen is required. Then in the given oleic acid compound one mole hydrogen is required to make it saturated.

The given mass of oleic acid is $1\text{kg}$ that is $1000\text{g}$. The number of moles is calculated by the formula,

$\text{Number}\text{of}\text{moles}=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}$

Substitute the values in the above formula.

$\begin{array}{c}\text{Number}\text{of}\text{moles}=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}\\ =\frac{1000\text{g}}{282\text{g/mol}}\\ =3.55\text{mol}\end{array}$

Calculated moles of carbon are $3.55$. Therefore, required moles of hydrogen is calculated as,

$3.55\times 1=3.55\text{mol}$

The molecular structure of $\alpha -$ linolenic acid is given by following figure,

Figure 2

This contains three double bonds at the carbon positions $9,12,15$. From the molecular formula it is clear that for saturation of $18$ carbons $36$ hydrogen atoms are required. It means for saturation one molecule of hydrogen is required. In the molecular hydrogen form carbon –hydrogen ratio is represented as,

$\begin{array}{l}18:18\\ 1:1\end{array}$

This ratio indicates that for one mole carbon one mole of hydrogen is required. Then in the given $\alpha -$ linolenic acid compound three moles of hydrogen is required to make it saturated.

The given mass of oleic acid is $0.50\text{kg}$ that is $500\text{g}$. The number of moles is calculated by the formula,

$\text{Number}\text{of}\text{moles}=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}$

Substitute the values in the above formula.

$\begin{array}{c}\text{Number}\text{of}\text{moles}=\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}\\ =\frac{500\text{g}}{278\text{g/mol}}\\ =1.78\text{mol}\end{array}$

Calculated moles of carbon are $1.78$. Therefore, required moles of hydrogen is calculated as,

$1.78\times 3=5.34\text{mol}$

From the calculated value of moles of hydrogen it is clear that $0.50\text{kg}$ of $\alpha -$ linolenic acid consumes more hydrogen than $1.0\text{kg}$ of oleic acid.

(b)

Interpretation Introduction

To determine: The distinction between the two fatty acids; an explanation regarding the answer.

Answer to Problem 20.69QP

Solution

The distinction between the two fatty acids has been explained below.

Explanation of Solution

Explanation

The required moles of hydrogen for the two fatty acids are calculated in the part (a). On that basis the two fatty acids can be distinguished.

The hydrogenation reaction of $\alpha -$ linolenic acid as well as oleic acid is given in the following figure.

Figure 3

The above Figure 3 clearly explains the distinction between two fatty acids by determining the identity of their hydrogenation products.

Conclusion

1. a) The fat that consumes more hydrogen is $0.50\text{kg}$ of $\alpha -$ linolenic acid.
2. b) The distinction between the two fatty acids has been explained