Q35E - Organic Chemistry (Mcmurry)

Question

How many hydrogens does each of the following compounds have?

(a) ${\text{C}}_{\text{8}}{\text{H}}_{\text{?}}{\text{O}}_{\text{2}}$, has two rings and one double bond

(b)${\text{C}}_{\text{7}}{\text{H}}_{\text{?}}\text{N}$ , has two double bonds

(c)${\text{C}}_9{\text{H}}_{\text{?}}\text{NO}$ , has one ring and three double bonds

Step-by-Step Solution

Answer

(a)The number of hydrogens in the compound is 12.

(b)The number of hydrogens in the compound is 13

(c)The number of hydrogens in the compound is 13.

Step-by-Step solution Step 1: Degree of unsaturation

The formula used to evaluate the degree of unsaturation is:

$\mathbf{Degree}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{unsaturation}\mathbf{=}\frac{2C+2+N-H-X}{2}$

The double bonds and rings in a compound can be understood using the degree of unsaturation.

Step 2: Identifying the number of hydrogens in compound (a)

(a)The compound has three degrees of unsaturation. The number of hydrogens can be identified using the degree of unsaturation formula:

$\begin{array}{c}\text{Degree of unsaturation=}\frac{\text{2C+2+N-H-X}}{\text{2}}\\ 3=\frac{2\times 8+2+0-x-0}{2}\\ 3=\frac{18-x}{2}\end{array}$

On further solving, 

$\begin{array}{c}\text{18-x=6}\\ \text{x=18-6}\\ \text{=12}\end{array}$

Hence, the number of hydrogens in this compound is 12.

Step 3: Identification the number of hydrogens in compound (b)

(b)The compound has two double bonds. Hence, the degree of unsaturation is two. The number of hydrogens can be identified using the degree of unsaturation formula:

$\begin{array}{c}\text{Degree of unsaturation=}\frac{\text{2C+2+N-H-X}}{\text{2}}\\ 2=\frac{2\times 7+2+1-x-0}{2}\\ 2=\frac{17-x}{2}\end{array}$

On further solving, 

$\begin{array}{c}\text{17-x=4}\\ \text{ x=17-4}\\ \text{ =13}\end{array}$

Hence, the number of hydrogens in this compound is 13.

Step 4: Identifying the number of hydrogens in compound (c)

(c)The number of degrees of unsaturation in this compound is four. The number of hydrogens can be identified using the degree of unsaturation formula:

$\begin{array}{c}\text{Degree of unsaturation=}\frac{\text{2C+2+N-H-X}}{\text{2}}\\ 4=\frac{2\times 9+2+0-x-0}{2}\\ 4=\frac{20-x}{2}\end{array}$

On further solving, 

$\begin{array}{c}\text{20-x=8}\\ \text{ x=20-8}\\ \text{ =13}\end{array}$

Hence, the number of hydrogens in this compound is 13.