7-67 - Organic Chemistry (Mcmurry)

Question

Calculate the degree of unsaturation in each of the following formulas:

1. Cholesterol ${\mathrm{C}}_{27}{\mathrm{H}}_{46}\mathrm{O}$,  
2. DDT ${\mathrm{C}}_{14}{\mathrm{H}}_9{\mathrm{Cl}}_5$, 
3. Prostaglandin E₁ , ${\mathrm{C}}_{20}{\mathrm{H}}_{34}{\mathrm{O}}_5$
4. Caffeine, ${\mathrm{C}}_8{\mathrm{H}}_{10}{\mathrm{N}}_4{\mathrm{O}}_2$
5. Cortisone ,${\mathrm{C}}_{21}{\mathrm{H}}_{28}{\mathrm{O}}_5$ 
6. Atropine, ${\mathrm{C}}_{17}{\mathrm{H}}_{23}{\mathrm{NO}}_3$

Step-by-Step Solution

Answer

1. There are 5 degrees of unsaturation in cholesterol.
2. There are 8 degrees of unsaturation in DDT.
3. There are 4 degrees of unsaturation in Prostaglandin .
4. There are 6 degrees of unsaturation in caffeine. 
5. There are 8 degrees of unsaturation in cortisone.

6. There are 7 degrees of unsaturation in atropine.

Degree of unsaturation

The degree of unsaturation helps determine the total number of double bonds and rings present in a molecule. By determining the degrees of unsaturation, the structure of a molecule can be drawn.

The degree of unsaturation in cholesterol

(a)

1. The degree of unsaturation of cholesterol is calculated by the formula given below,

$$\begin{gathered} Degree of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2} \\ =\frac{2\left(27\right)-46-0+0+2}{2} \\ =\frac{10}{2}=5 \end{gathered}$$ 

                  Thus, there are 5 degrees of unsaturation in cholesterol.

Degree of unsaturation

The degree of unsaturation is determined by counting the number of C, H, halogen atoms, and nitrogen atoms present in a molecule. From a chemical formula, we can determine the structure by calculating the degree of unsaturation.

The degree of unsaturation in DDT

(b)  The degree of unsaturation in DDT with chemical formula  is calculated by the formula given below,

 $$\begin{gathered} Degree of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2} \\ =\frac{2\left(14\right)-9-5+0+2}{2} \\ =\frac{16}{2}=8 \end{gathered}$$

Here, X is a chlorine atom.

 

Thus, there are 8 degrees of unsaturation in DDT.

Unsaturation number

The unsaturation number is the number of double bonds (pi bonds) and rings present in a compound. The other names for unsaturation number are degrees of unsaturation and double bond equivalents.

The degree of unsaturation in Prostaglandin E 1

(c) The degree of unsaturation in Prostaglandin  with chemical formula  is calculated by the formula shown below,

$$\begin{gathered} Degrees of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2} \\ =\frac{2\left(20\right)-34-0+0+2}{2} \\ =\frac{8}{2}=4 \end{gathered}$$ 

Here, O is ignored in this formula.

 

Thus, there are 4 degrees of unsaturation in Prostaglandin .

Double bond equivalents

The double bond equivalent is the other name for the degree of unsaturation. This term calculates the number of double bonds and pi bonds in the chemical formula. The formula is, 

$Degrees\mathit{ }of\mathit{ }unsaturation=\frac{2\left(C\right)-H-X+N+2}{2}$

The degree of unsaturation in caffeine

(d) 

The degree of unsaturation in caffeine with chemical formula  is calculated by the formula shown below. The O in the formula is ignored in the formula.

$$\begin{gathered} Degrees of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2} \\ =\frac{2\left(8\right)-10-0+4+2}{2} \\ =\frac{12}{2}=6 \end{gathered}$$

 

Formula for degree of unsaturation

The degree of unsaturation is having a very simple formula to calculate how many double bonds or rings present in a molecule. In the formula, C is for carbon, H is for hydrogen, X is for halogen, N is for nitrogen.

$Degrees of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2}$

The degree of unsaturation in cortisone

(e) The degree of unsaturation in cortisone having chemical formula  is calculated by the formula shown below. The O is not counted in the formula.

$$\begin{gathered} Degrees of Unsaturation =\frac{2\left(C\right)-H-X+N+2}{0} \\ =\frac{2\left(21\right)-28-0+0+2}{2} \\ =\frac{16}{2}=8 \end{gathered}$$

Unsaturated compounds

The unsaturated compounds have double bonds (pi bonds) or triple bonds in their compounds. The number of double bonds is calculated by the degree of unsaturation formula given below.

$Degree of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2}$

The degree of unsaturation in atropine

The degree of unsaturation in atropine having chemical formula  is calculated as follows,

$$\begin{gathered} Degree of unsaturation=\frac{2\left(C\right)-H-X+N+2}{2} \\ =\frac{2\left(17\right)-23-0+1+2}{2} \\ =\frac{14}{2}=7 \end{gathered}$$