Q34 - Organic Chemistry (Mcmurry)

Question

Question: Calculate the degree of unsaturation in the following formulas, and

draw five possible structures for each:

$$\begin{gathered} {\mathbf{\text{(a) C}}}_{\mathbf{\text{10}}}{\mathbf{\text{H}}}_{\mathbf{\text{16}}} \\ {\mathbf{\text{(b) C}}}_{\mathbf{\text{8}}}{\mathbf{\text{H}}}_{\mathbf{\text{8}}}\mathbf{\text{O }} \\ {\mathbf{\text{(c) C}}}_{\mathbf{\text{7}}}{\mathbf{\text{H}}}_{\mathbf{\text{10}}}{\mathbf{\text{Cl}}}_{\mathbf{\text{2}}} \\ {\mathbf{\text{(d) C}}}_{\mathbf{\text{10}}}{\mathbf{\text{H}}}_{\mathbf{\text{16}}}{\mathbf{\text{O}}}_{\mathbf{\text{2}}} \\ {\mathbf{\text{(e) C}}}_{\mathbf{5}}{\mathbf{\text{H}}}_{\mathbf{9}}{\mathbf{\text{NO}}}_{\mathbf{\text{2}}} \\ {\mathbf{\text{(f)C}}}_{\mathbf{8}}{\mathbf{\text{H}}}_{\mathbf{10}}\mathbf{\text{ClNO }} \end{gathered}$$

Step-by-Step Solution

Answer

Answer

(a)The degree of unsaturation for is three C₁₀H₁₆.

(b)The degree of unsaturation for this compound is five.               

(c)The degree of unsaturation for this compound is two

(d) The degree of unsaturation for this compound is three. 

(e) The degree of unsaturation for this compound is two.

(f) The degree of unsaturation for this compound is two.

Step 1: Degree of unsaturation

 

Unsaturated molecules are molecules comprising rings or double bonds. The formula to evaluate degree of unsaturation is:

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

Where C, N, H, and X denote the number of carbon, nitrogen, hydrogen and halogen.

Step 2: Degree of unsaturation and five possible structures for compound a

The degree of unsaturation  C₁₀H₁₆in can be given as:

 $$\begin{gathered} \text{Degree of unsaturation = }\frac{\text{2C + 2 + N - H - X}}{\text{2}} \\ =\frac{2\times 10+2+0-16-0}{2} \\ =\frac{22-16}{2} \\ =3 \end{gathered}$$

The number of degrees of unsaturation for this compound is 3.

The five possible structures can be given as: 

Five possible structures of compound a

 

Step 3: Degree of unsaturation and five possible structures for compound b

The degree of unsaturation C₈H₈O₈ in can be given as:

$$\begin{gathered} \text{Degree of unsaturation = }\frac{\text{2C + 2 + N - H - X}}{\text{2}} \\ =\frac{2\times 8+2+0-8-0}{2} \\ =\frac{18-8}{2} \\ =5 \end{gathered}$$

Hence, the given compound has five degrees of unsaturation.

 

The five possible structures can be given as:

Five possible structures of compound b

 

Step 5: Degree of unsaturation and five possible structures for compound d

The degree of unsaturation C₁₀H₁₆O₂ in can be given as:

 $$\begin{gathered} \text{Degree of unsaturation = }\frac{\text{2C + 2 + N - H - X}}{\text{2}} \\ =\frac{2\times 10+2+0-16-0}{2} \\ =\frac{6}{2} \\ =3 \end{gathered}$$

 

The degree of unsaturation for this compound is three.

The five possible structures for this compound can be 

Five possible structures of compound d

Step 6: Degree of unsaturation and five possible structures for compound e

 

 

(e)The degree of unsaturation in can be given as:

 $$\begin{gathered} \text{Degree of unsaturation = }\frac{\text{2C + 2 + N - H - X}}{\text{2}} \\ =\frac{2\times 5+2+1-9-0}{2} \\ =\frac{4}{2} \\ =2 \end{gathered}$$

 

The degree of unsaturation ${\text{C}}_5{\text{H}}_9{\text{NO}}_{\text{2}}$for this compound is two.

The five possible structures for this compound can be given as:

Five possible structures of compound e

Step 2: Degree of unsaturation and five possible structures for compound f

 

 

(f)The degree of unsaturation ${\text{C}}_8{\text{H}}_{10}\text{ClNO}$in can be given as:

$$\begin{gathered} \text{Degree of unsaturation = }\frac{\text{2C + 2 + N - H - X}}{\text{2}} \\ =\frac{2\times 8+2+1-10-1}{2} \\ =\frac{8}{2} \\ =4 \end{gathered}$$

The compound has four degrees of unsaturation.

 

The five possible structures of the compound can be given as:

 

 

 

Five possible structures of compound f