How many isomers has the organic compound represented by the formula C$_3$H$_8$O ?

Analyze the question: C₃H₈O has a degree of unsaturation of 0, so it is fully saturated. That means there are no double bonds or rings. The possible isomers are therefore alcohols and ethers.

Concept: Structural isomers have the same molecular formula but different arrangements of atoms. For C₃H₈O, the functional groups possible are -OH (alcohol) and -O- (ether).

Solution:

1. Alcohols (R-OH) • Propan-1-ol: CH₃CH₂CH₂OH • Propan-2-ol: CH₃CH(OH)CH₃

2. Ethers (R-O-R') • Methoxyethane (ethyl methyl ether): CH₃-O-CH₂CH₃

Total: 2 alcohols + 1 ether = 3 isomers.

Check: Are there any others? An ether with 3 carbons can only split as 1 C + 2 C, so there is only one ether. The alcohol -OH can sit on a terminal carbon or the middle carbon, so there are only two alcohols. Nothing else fits the formula.

Answer: The compound has 3 structural isomers, which is option B.

Tip: For C₃H₈O, remember "2 alcohols + 1 ether = 3". Similarly, C₄H₁₀O has 7 isomers (4 alcohols + 3 ethers). Always calculate the degree of unsaturation first to know whether to look for rings or double bonds.