Question

An alcohol has the formula \(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{OH}\). How many isomers can exist for this alcohol?

Short answer

The formula \(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{OH}\) can have three isomers.

Step-by-step solution

Identify the carbon chain

In this case, there are five carbon atoms. So, start with the longest and shortest chains. In this case, they are all of length 5 which gives us pentanols.

Location of the OH group

Find all the possible locations for the hydroxyl group (\(\mathrm{OH}\)). The \(\mathrm{OH}\) group can attach at the first, second, third, fourth or fifth carbon since there are five carbon atoms.

Find isomers

Figure out how many isomers can be formed from each position of the hydroxyl group. If the \(\mathrm{OH}\) group is at the first or fifth carbon, it results in only one possible structure. If it's in the second or fourth carbon, it also results in one structure because the molecule is symmetrical about the center. However, if the \(\mathrm{OH}\) group is at the third carbon, there are two possible structures: one with the \(\mathrm{OH}\) group on the end carbon (1-pentanol) and one with the \(\mathrm{OH}\) group in the middle of the carbon chain (2-methyl-2-butanol).

Count the isomers

By adding the number of isomers for each position, we can find the total number of isomers. In this case, there are three isomers.

Key concepts

Isomer Counting

When we talk about isomer counting, we're basically counting the different ways atoms can be arranged in a molecule while keeping the total number the same. For the alcohol with the formula \( \mathrm{C}_{5} \mathrm{H}_{11} \mathrm{OH} \), this involves seeing how many distinct ways we can arrange the carbon and hydroxyl groups.

• The total number of carbon atoms set the backbone structure.
• We consider different configurations based on where bonds are placed.

In the example, we need to decide on the locations where the hydroxyl (\( \mathrm{OH} \)) group can attach. Each potential placement leads to different isomers, but this kind of calculation requires checking each position methodically.
To break it down:• We find locations on the 5-carbon backbone.• Then we examine the symmetry because some placements will mirror each other, reducing the total count of unique isomers.

Alcohol Isomers

Alcohol isomers are different configurations of molecules that contain the same molecular formula but differ in the structure of their atoms.
In alcohol molecules, this is specifically about where the \( \mathrm{OH} \) group is attached to the carbon atoms.

• "Pentanols" as a category has isomers based on attachment points.
• For molecular formulas like \( \mathrm{C}_{5} \mathrm{H}_{11} \mathrm{OH} \), each connection point leads to a distinct structural isomer.

Each structure can vastly change the physical and chemical properties of the alcohol. For example, moving the \( \mathrm{OH} \) group from the end to the center changes polarity and boiling points. In the case of our example, arrangements include 1-pentanol and 2-methyl-2-butanol, creating variations even with the same number of carbon, hydrogen, and one hydroxyl group.

Hydroxyl Group Positioning

The position of the hydroxyl group (\( \mathrm{OH} \)) in an alcohol molecule significantly affects its structure and properties.
Here's why positioning is important:

• The "end" carbon position might create a straight-chained alcohol like 1-pentanol.
• A central carbon attachment, such as on the second or third carbon, provides more internal isomer variations.
• Symmetry around the carbon chain can reduce the number of distinguishable isomers, as in placing the \( \mathrm{OH} \) on the second and fourth carbons resulting in structurally identical alcohols.

Understanding these positions helps not only in visualizing molecular structure but in predicting how these molecules interact with others. Hence, knowing where the \( \mathrm{OH} \) group is attached can tell a lot about an alcohol's reactivity, boiling points, and even solubility in water.