Question

Determining Charge and Solubility of Organic Acids Suppose that, for a typical carboxyl-containing compound, the \(\mathrm{p} K_{\mathrm{a}}\) is approximately 3. Suppose \(\mathrm{HOOC}-\left(\mathrm{CH}_{2}\right)_{4}-\mathrm{COOH}, \mathrm{CH}_{3}-\left(\mathrm{CH}_{2}\right)_{4}-\mathrm{COOH}_{2}\) and \(\mathrm{HOOC}-\left(\mathrm{CH}_{2}\right)_{2}-\mathrm{COOH}\) are added to water at pH \(7 .\) a. What is the net charge of each compound in the solution? b. List the compounds in order from most soluble to least soluble.

Short answer

The net charge for each compound is -2. From most to least soluble: Compound 3, Compound 2, Compound 1.

Step-by-step solution

Understanding pH and pKa

To determine the charge of the carboxyl-containing compounds, compare the given pH of the solution (7) with the \( \mathrm{p} K_{\mathrm{a}} \) of the carboxyl groups (3). Since pH > pKa, the carboxyl groups are deprotonated, meaning they lose protons and become negatively charged (COO^-).

Determining Net Charge of Each Compound

- **Compound 1**: \( \mathrm{HOOC}-(\mathrm{CH}_2)_4-\mathrm{COOH} \): Two carboxylic groups can be deprotonated, resulting in a charge of -2.- **Compound 2**: \( \mathrm{CH}_3-(\mathrm{CH}_2)_4-\mathrm{COOH}_2 \): One molecule seems to incorrectly have \( COOH_2 \), assuming this was intended as \( COOH \), otherwise, this compound does not exist as shown, please clarify it. Assuming two carboxyl groups again, result in a charge of -2 if assumed typo.- **Compound 3**: \( \mathrm{HOOC}-(\mathrm{CH}_2)_2-\mathrm{COOH} \): Two carboxylic groups also result in a charge of -2.

Solubility and Charge Relation

Compounds with higher charge remain more soluble in water due to stronger interactions with water molecules. Since all compounds have the same net charge (-2), focus on molecular size as the additional factor.

Ordering Based on Molecular Weight

Compare the carbon chains: - Compound 1: 6-carbon chain. - Compound 2: 5-carbon chain. - Compound 3: 4-carbon chain. Smaller chains are more soluble, thus: Compound 3 is the most soluble, followed by Compound 2, and then Compound 1.

Key concepts

Acid-base chemistry

Acid-base chemistry deals with the concepts of acids, bases, and their reactions. A crucial part of this is understanding the behavior of acids and bases in water. An acid is a substance that can donate a proton \(H^+\), while a base can accept a proton. In water, acids like carboxylic acids can donate a proton to water molecules, forming a negatively charged carboxylate ion (\(COO^-\)).

When discussing organic compounds with acidic groups, such as carboxyl groups, knowing the compound's pKa is essential. The pKa is a measure of acidity, specifically how easily an acid gives up a proton. A lower pKa means a stronger acid.

In the context of our exercise, we deal with carboxylic acids having a pKa of about 3. In a solution of pH 7, which is significantly higher than the pKa, these acids lose their protons, forming deprotonated carboxylate ions (negatively charged anions). This negative charge influences their behavior in solution, affecting properties like solubility.

Solubility

Solubility refers to how well a substance dissolves in a solvent, like water. It's crucial for understanding how and why substances mix or separate in liquids. Solubility is influenced by several factors, including molecular structure, charge, and size.

Charged molecules, like deprotonated carboxylate ions, interact strongly with water molecules. These interactions enhance solubility because water, being a polar solvent, stabilize charges through electrical attractions.

Moreover, when comparing organic compounds with the same charge but different carbon chain lengths, smaller molecules tend to be more soluble. This is because smaller molecules have less surface area that needs to interact with water, making the overall dissolution process easier. In our exercise, all three compounds have the same net charge of -2, focusing attention on their carbon chain lengths. The chain sizes are:

• Compound 1: 6-carbon chain
• Compound 2: 5-carbon chain
• Compound 3: 4-carbon chain

Hence, Compound 3, with the shortest chain, is the most soluble.

pH and pKa relationship

The relationship between pH and pKa is a fundamental concept in acid-base chemistry. It helps determine the state of ionization of an acid in a solution. The pH of a solution measures its acidity, while the pKa indicates the acid strength.

When the pH of a solution is less than the pKa, the acidic form (protonated form) is prevalent. Conversely, when the pH is higher than the pKa, the basic form (deprotonated form) dominates. This tendency is due to the fact that acids donate protons when they are in environments that are less acidic (higher pH) than themselves.

In our scenario, the solution's pH is 7, higher than the given pKa of 3. Thus, the carboxyl groups on the organic compounds are deprotonated, resulting in negatively charged carboxylate ions. This deprotonation not only affects the compound's solubility but also its reactivity and interactions with other molecules.
Understanding this relationship is crucial for predicting how substances will behave in different environments, particularly in biochemical systems where pH can vary significantly.