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  • Total number of possible isomers (both structural as well as stereoisomers) of cyclic ethers of molecular formula $\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}$ is : (1) 11 (2) 6 (3) 8 (4) 10

Q.88) Total number of possible isomers (both structural as well as stereoisomers) of cyclic ethers of molecular formula $\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}$ is : (1) 11 (2) 6 (3) 8 (4) 10

A) 11

B) 6

C) 8

D) 10

 

Answers (1)

best_answer

Q.88) To find the total number of isomers (both structural and stereoisomers) of cyclic ethers with the molecular formula $\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}$, we can follow these steps:

Step 1: Determine the Degree of Unsaturation (DOU)
The formula for calculating the degree of unsaturation (DOU) is:

$$
\mathrm{DOU}=\frac{2 C+2+N-H-X}{2}
$$


Where:
- $\mathrm{C}=$ number of carbon atoms
- $\mathrm{H}=$ number of hydrogen atoms
- $\mathrm{N}=$ number of nitrogen atoms (not applicable here)
- X = number of halogens (not applicable here)

For $\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}$ :
- $\mathrm{C}=4$
- H = 8
$-\mathrm{N}=\mathrm{O}$
$-X=0$

Substituting the values:

$$
\mathrm{DOU}=\frac{2(4)+2+0-8-0}{2}=\frac{8+2-8}{2}=\frac{2}{2}=1
$$

 

This indicates that there is one degree of unsaturation, which suggests the presence of one ring.

Step 2: Identify Possible Cyclic Structures
Given that we have one degree of unsaturation, we can form cyclic ethers. We will consider both 3-membered, 4-membered, and 5-membered rings.

3-Membered Ring (Epoxide)
- Structure 1: A 3-membered ring with one ethyl group (C?H?) and one oxygen atom.
- Chirality: This structure can have a chiral center, leading to one enantiomer.

4-Membered Ring (Butyrolactone)
- Structure 2: A 4-membered ring with one methyl group (CH?) and one oxygen atom.
- Chirality: This structure can also have a chiral center, leading to one enantiomer.

5-Membered Ring (Tetrahydrofuran)
- Structure 3: A 5-membered ring with two methyl groups and one oxygen atom.
- Chirality: This structure does not have any chiral centers.

Step 3: Count the Isomers
1. 3-Membered Ring:
- 1 structure (chiral) + 1 enantiomer = 2 isomers

2. 4-Membered Ring:
- 1 structure (chiral) + 1 enantiomer = 2 isomers
- 1 achiral structure = 1 isomer
- Total = 2 + 1 = 3 isomers

3. 5-Membered Ring:
- 1 structure (achiral) = 1 isomer

Step 4: Total Isomers
Now, we sum all the isomers:
- From the 3-membered ring: 2
- From the 4-membered ring: 3
- From the 5-membered ring: 1

Total = 2 + 3 + 1 = 6 isomers

Final Answer
The total number of isomers (considering both structural and stereoisomers) of cyclic ethers with the molecular formula C?H?O is 6.

Hence, the correct answer is option (2).

 

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