Total number of possible isomers (both structural as well as stereoisomers) of cyclic ethers of molecular formula C₄H₈O is :

The correct answer is 10.

To determine the total number of possible cyclic ether isomers (both structural and stereoisomers) of molecular formula C₄H₈O, we can follow these step-by-step calculations and derivations:

Step 1: Calculate the Degree of Unsaturation (Double Bond Equivalent, DBE)
The formula for the degree of unsaturation is:
$DBE\; =\; C\; +\; 1\; -\; (H\; /\; 2)$
For C₄H₈O:
$DBE\; =\; 4\; +\; 1\; -\; (8\; /\; 2)\; =\; 1$
A DBE of 1 indicates the presence of either one double bond or one ring. Since the question specifies cyclic ethers, the oxygen atom must be a part of a single ring, and there are no double bonds in the molecule.

Step 2: Classify by Ring Size and Identify Isomers

1. Five-membered ring (Oxolane / Tetrahydrofuran ring)
The ring contains 1 oxygen atom and 4 carbon atoms:
- Tetrahydrofuran (THF): This molecule is symmetric and has no chiral centers.
Number of isomers = 1

2. Four-membered ring (Oxetane ring)
The ring contains 1 oxygen atom and 3 carbon atoms, with 1 methyl group substituent:
- 2-Methyloxetane: The methyl group is at the carbon adjacent to the oxygen atom. This carbon is chiral, yielding a pair of enantiomers (R and S configurations). (2 isomers)
- 3-Methyloxetane: The methyl group is at the 3-position. The molecule is symmetric and achiral. (1 isomer)
Number of isomers = 2 + 1 = 3

3. Three-membered ring (Oxirane / Epoxide ring)
The ring contains 1 oxygen atom and 2 carbon atoms, with 2 remaining carbon atoms as substituents:
- 2-Ethyloxirane: A single ethyl group substituent on the ring. The substituted carbon is chiral, yielding a pair of enantiomers. (2 isomers)
- 2,2-Dimethyloxirane: Two methyl groups on the same ring carbon. The molecule has no chiral center and is achiral. (1 isomer)
- 2,3-Dimethyloxirane: One methyl group on each ring carbon. This molecule has 2 chiral centers:
  • cis-2,3-dimethyloxirane: Possesses a plane of symmetry, making it a meso compound (achiral). (1 isomer)
  • trans-2,3-dimethyloxirane: Lacks a plane of symmetry, existing as a pair of enantiomers. (2 isomers)
Number of isomers = 2 + 1 + 3 = 6

Step 3: Calculate the Total Number of Isomers
Summing all the structural and stereoisomers:
$Total\; =\; 1\; (five-membered)\; +\; 3\; (four-membered)\; +\; 6\; (three-membered)\; =\; 10$
Thus, there are a total of 10 cyclic ether isomers for C₄H₈O.