What is the total number of acyclic ether isomers (including both...

The molecular formula is $\mathrm{C}_5\mathrm{H}_{12}\mathrm{O}$. The degree of unsaturation is $5 - \dfrac{12}{2} + 1 = 0$, which means the compounds are fully saturated and acyclic.

Acyclic ethers have the general formula $R-O-R'$. For a total of 5 carbon atoms, the possible combinations of alkyl groups are:
1. Methyl and Butyl ($1 + 4$ carbons)
2. Ethyl and Propyl ($2 + 3$ carbons)

For Methyl and Butyl ethers ($\mathrm{CH}_3-\mathrm{O}-\mathrm{C}_4\mathrm{H}_9$), the butyl group can be:
- n-butyl: $\mathrm{CH}_3-\mathrm{O}-\mathrm{CH}_2\mathrm{CH}_2\mathrm{CH}_2\mathrm{CH}_3$ (1 isomer)
- sec-butyl: $\mathrm{CH}_3-\mathrm{O}-\mathrm{CH}(\mathrm{CH}_3)\mathrm{CH}_2\mathrm{CH}_3$. The carbon atom bonded to the oxygen is chiral, so it exists as a pair of enantiomers (2 stereoisomers).
- isobutyl: $\mathrm{CH}_3-\mathrm{O}-\mathrm{CH}_2\mathrm{CH}(\mathrm{CH}_3)_2$ (1 isomer)
- tert-butyl: $\mathrm{CH}_3-\mathrm{O}-\mathrm{C}(\mathrm{CH}_3)_3$ (1 isomer)
Total for this category = $1 + 2 + 1 + 1 = 5$ isomers.

For Ethyl and Propyl ethers ($\mathrm{C}_2\mathrm{H}_5-\mathrm{O}-\mathrm{C}_3\mathrm{H}_7$), the propyl group can be:
- n-propyl: $\mathrm{C}_2\mathrm{H}_5-\mathrm{O}-\mathrm{CH}_2\mathrm{CH}_2\mathrm{CH}_3$ (1 isomer)
- isopropyl: $\mathrm{C}_2\mathrm{H}_5-\mathrm{O}-\mathrm{CH}(\mathrm{CH}_3)_2$ (1 isomer)
Total for this category = $1 + 1 = 2$ isomers.

Total number of acyclic ether isomers = $5 + 2 = 7$.

Answer: 7