Question

Acetic acid is miscible with water. Would you expect carboxylic acids with the general formula \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{n} \mathrm{COOH}\) to become more or less water soluble as \(n\) increases? Explain.

Short answer

As \( n \) increases, the solubility of carboxylic acids in water decreases due to the longer hydrophobic hydrocarbon chain.

Step-by-step solution

- Understand the Structure

Carboxylic acids have the general formula \(\text{CH}_{3}(\text{CH}_{2})_{n}\text{COOH}\). They consist of a hydrocarbon chain \( \text{CH}_{3}(\text{CH}_{2})_{n} \) and a carboxyl group \(\text{COOH}\).

- Analyze Solubility Factors

The solubility of carboxylic acids in water is influenced by the hydrophilic carboxyl group \( \text{COOH} \) and the hydrophobic hydrocarbon chain \( \text{CH}_{3}(\text{CH}_{2})_{n} \).

- Assessing the Effect of Increasing Chain Length

As \( n \) increases, the length of the hydrocarbon chain \( \text{CH}_{3}(\text{CH}_{2})_{n} \) increases, making the molecule more hydrophobic overall.

- Predicting Solubility Changes

The increased hydrophobic character due to a longer hydrocarbon chain reduces the overall solubility of the carboxylic acid in water. Therefore, as \( n \) increases, the solubility of the carboxylic acid in water decreases.

- Conclusion

Carboxylic acids with the general formula \( \text{CH}_{3}(\text{CH}_{2})_{n}\text{COOH} \) are less water soluble as \( n \) increases because the hydrophobic hydrocarbon chain becomes longer, outweighing the solubility contribution of the hydrophilic carboxyl group.

Key concepts

Carboxyl Group

The carboxyl group \(\text{COOH}\) is a key functional group in organic chemistry, specifically in carboxylic acids. This group consists of a carbon atom double-bonded to an oxygen atom and singly bonded to a hydroxyl group \( -\text{OH} \). This structure makes the carboxyl group polar due to the electronegativity difference between oxygen and hydrogen. The polar nature of the carboxyl group enables it to form hydrogen bonds with water molecules. Because of these hydrogen bonds, the carboxyl group is hydrophilic (water-loving) and greatly enhances the solubility of carboxylic acids in water.

Hydrocarbon Chain

In the general formula \text{CH}_{3}(\text{CH}_{2})_{n}\text{COOH}\, the \(\text{CH}_{3}(\text{CH}_{2})_{n}\) represents the hydrocarbon chain. This chain is made up of carbon and hydrogen atoms, and its length increases with the value of \( n \). The hydrocarbon chain is non-polar, making it hydrophobic (water-fearing). This means it does not mix well with polar molecules like water. As \( n \) increases, the length of the hydrocarbon chain also increases, contributing to the molecule's overall hydrophobic character. Therefore, a longer hydrocarbon chain will decrease the solubility of the carboxylic acid in water due to the increased influence of hydrophobic interactions.

Water Solubility

Water solubility is determined by a molecule's ability to interact with water molecules through polar interactions or hydrogen bonding. In carboxylic acids, the \(\text{COOH}\) group is polar and forms hydrogen bonds with water, enhancing solubility. However, the hydrocarbon chain, \(\text{CH}_{3}(\text{CH}_{2})_{n}\), is non-polar and does not interact favorably with water. As \( n \) increases and the hydrocarbon chain lengthens, the hydrophobic character of the molecule becomes more dominant, outweighing the hydrophilic effect of the carboxyl group. This results in a decrease in the solubility of carboxylic acids in water as the hydrocarbon chain lengthens. Therefore, longer-chain carboxylic acids are less soluble in water compared to their shorter-chain counterparts.