Question

Predict and explain the relative solubilities in water of \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CO}_{2} \mathrm{H}\) and \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{5} \mathrm{CO}_{2} \mathrm{H}\).

Short answer

\(\mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H}\) is more soluble in water than \(\mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H}\).

Step-by-step solution

Understand molecules structure

Both given molecules, \(\mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H}\) and \(\mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H}\) are carboxylic acids. They have both polar (carboxyl group -COOH) and nonpolar (alkyl group - R) parts. But the length of the nonpolar part varies, which is 2 and 5 respectively.

Principle of Solubility

The principle of solubility is 'like dissolves like', which means polar substances dissolve in polar solvents (like water), and nonpolar substances dissolve in nonpolar solvents. Here, water is a polar solvent.

Predict Relative solubilities

\(\mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H}\) will be more soluble in water as compared to \(\mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H}\). This is because \(\mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H}\) have a shorter nonpolar part (or alkyl group) than \(\mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H}\) . Hence, it is comparatively more polar and dissolves better in water.

Key concepts

Polarity

Understanding polarity is crucial when predicting the solubility of different substances. A molecule is considered polar when it has a significant difference in the electronegativities of its atoms, causing an uneven distribution of charge. This results in a molecule with a positive end and a negative end, much like a magnet.
In chemistry, water is the classic example of a polar solvent due to its bent structure and the presence of highly electronegative oxygen atoms that pull electrons towards them. Hence, water has a partial negative charge near the oxygen and partial positive charges near the hydrogens. Because of these charges, water can dissolve other polar substances effectively, adhering to the principle of "like dissolves like."
Regarding the molecules \( \mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H} \) and \( \mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H} \), the polarity is influenced by the presence of the -COOH group, which is highly polar, and the length of the alkyl chain, which is nonpolar. A shorter nonpolar chain means that the molecule is more polar overall, making it more soluble in water.

Alkyl Group

Alkyl groups are fascinating structural components in organic chemistry, consisting solely of carbon and hydrogen atoms, typically arranged in a chain. These groups are characterized by single bonds and are derived from alkanes by removal of a hydrogen atom.
Alkyl groups are decidedly nonpolar because the carbon-carbon and carbon-hydrogen bonds share electrons relatively equally. This nonpolarity means that they do not interact well with polar substances like water. Thus, increasingly long alkyl chains reduce the overall polarity of a molecule.
In the context of the exercise, a molecule with a shorter alkyl chain, \( \mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H} \), is more soluble in water than one with a longer chain, such as \( \mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H} \). This is because the latter has a larger nonpolar portion that does not interact favorably with water molecules, thereby decreasing its solubility.

Carboxylic Acid

Carboxylic acids are a vital group of organic compounds characterized by the -COOH (carboxyl) group. This functional group consists of a carbon atom double-bonded to an oxygen atom, and single-bonded to an -OH group, creating a significant polar region in the molecule.
The polar nature of the carboxylic group allows carboxylic acids to engage in hydrogen bonding with water molecules, enhancing their solubility. Hydrogen bonding is a strong dipole-dipole attraction that occurs when the hydrogen atom from a polar group interacts with an electronegative atom, such as oxygen in water. This molecular interaction is key to dissolving carboxylic acids effectively in polar solvents.
The exercise highlights how the size of the alkyl chain attached to the carboxylic acid affects solubility. While the carboxylic group promotes solubility through hydrogen bonding, an elongated alkyl chain increases nonpolarity, subsequently reducing water solubility. Hence, \( \mathrm{CH}_3(\mathrm{CH}_2)_2\mathrm{CO}_2\mathrm{H} \) is more soluble than \( \mathrm{CH}_3(\mathrm{CH}_2)_5\mathrm{CO}_2\mathrm{H} \) due to its shorter alkyl linkage.