The solubility of benzoic acid \(\left(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) is \(0.34 \mathrm{g} / 100 \mathrm{mL}\) in water at \(25^{\circ} \mathrm{C}\) and is \(10.0 \mathrm{g} / 100 \mathrm{mL}\) in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) at \(25^{\circ} \mathrm{C}\). Rationalize this solubility behavior. (Hint: Benzoic acid forms a dimer in benzene.) Would benzoic acid be more or less soluble in a 0.1-M NaOH solution than it is in water? Explain.

To rationalize the solubility behavior of benzoic acid in water and benzene, we need to understand the characteristics of each solvent and how they influence the solubility of benzoic acid. Water is a polar solvent, and benzene is a non-polar solvent. According to the rule "like dissolves like," polar solutes are more soluble in polar solvents, and non-polar solutes are more soluble in non-polar solvents. Benzoic acid has polar -COOH and non-polar -C6H5 functional groups, so it has both polar and non-polar character. In water, the polar -COOH group forms hydrogen bonds with water molecules, which increases its solubility. However, the non-polar -C6H5 group does not interact well with water molecules and decreases the solubility of benzoic acid. In benzene, the non-polar -C6H5 group strongly interacts with benzene molecules, making the solubility of benzoic acid much higher in benzene than in water. The dimer formation (molecules forming pairs) in benzene also contributes to the higher solubility, as it is a non-polar interaction.

To determine if benzoic acid will be more or less soluble in a 0.1-M NaOH solution than it is in water, we need to consider the chemical reaction that occurs when benzoic acid reacts with NaOH. When benzoic acid is added to a NaOH solution, it reacts with NaOH to form sodium benzoate (C6H5COONa) and water: \[ HC_7H_5O_2 + NaOH \rightarrow C_6H_5COONa + H_2O \] Sodium benzoate is the salt of benzoic acid and is more soluble in water than benzoic acid itself due to the ionic nature of the sodium benzoate. The presence of NaOH in solution promotes the formation of sodium benzoate, which increases the solubility of benzoic acid in the NaOH solution compared to water alone.

Benzoic acid is more soluble in benzene than in water due to the non-polar character of benzene, which favors the solubility of benzoic acid's non-polar -C6H5 group. The formation of dimers also contributes to its high solubility in benzene. Additionally, benzoic acid is more soluble in a 0.1-M NaOH solution than in water because it reacts with NaOH, increasing the solubility by forming the more soluble sodium benzoate salts.