Problem 103 - General Chemistry: Principles and Modern Applications

Question

The highest \(\left[\mathrm{H}^{+}\right]\) will be found in an aqueous solution that is (a) \(0.10 \mathrm{M} \mathrm{HCl} ;\) (b) \(0.10 \mathrm{M} \mathrm{NH}_{3} ;\) (c) \(0.15 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COOH} ;(\mathrm{d}) 0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\).

Step-by-Step Solution

Answer

The solution with the highest \(\left[\mathrm{H}^{+}\right]\) concentration is (d) 0.10 M H\( _{2}\)SO\( _{4}\).

Step 1: Understanding the substances

First, familiarize yourself with each substance and their ability to contribute hydrogen ions to the solution. (a) HCl is a strong acid and dissociates completely in solution to give H\(^{+}\) and Cl\(^{-}\). (b) NH\( _{3}\) is a weak base and it does not donate H\(^{+}\) ions, but instead accepts H\(^{+}\) to form NH\( _{4}^{+}\), decreasing the H\(^{+}\) concentration. (c) CH\( _{3}\)COOH is a weak acid and partially dissociates to give H\(^{+}\) and CH\( _{3}\)COO\(^{-}\). (d) H\( _{2}\)SO\( _{4}\) is a strong acid that can donate two H\(^{+}\) ions, one from each hydrogen atom.

Step 2: Evaluating the \(\left[\mathrm{H}^{+}\right]\) concentration provided by each solution

Understand that the strong acids HCl and H\( _{2}\)SO\( _{4}\) will contribute to higher \(\left[\mathrm{H}^{+}\right]\) concentrations than the weak acid and the weak base. Since H\( _{2}\)SO\( _{4}\) is a strong acid and can donate two H\(^{+}\) ions, it will yield a higher concentration than HCl which only donates one H\(^{+}\) ion. NH\( _{3}\) and CH\( _{3}\)COOH will produce less \(\left[\mathrm{H}^{+}\right]\) than the strong acids.

Step 3: Comparing the concentrations and picking the highest

After understanding that strong acids contribute more to \(\left[\mathrm{H}^{+}\right]\) than weak acids and bases, and that H\( _{2}\)SO\( _{4}\) contributes more H\(^{+}\) than HCl, it is safe to say that the highest concentration of \(\left[\mathrm{H}^{+}\right]\) will be found in a 0.10 M H\( _{2}\)SO\( _{4}\) solution.

Key Concepts

Strong Acids and Bases

Strong acids and bases play a significant role in determining the hydrogen ion concentration (\( [\text{H}^{+}] \)) in a solution.

**Strong Acids**

• Completely dissociate in water, releasing all available hydrogen ions (\(\text{H}^{+}\)).
• Examples include hydrochloric acid (\(\text{HCl}\)) and sulfuric acid (\(\text{H}_2\text{SO}_4\)).
• In the context of the exercise, \(\text{HCl}\) and \(\text{H}_2\text{SO}_4\) fully dissociate, contributing significantly to the hydrogen ion concentration.

The result is a high \( [\text{H}^{+}] \), making the solution more acidic. \(\text{H}_2\text{SO}_4\), being able to donate two \(\text{H}^{+}\), further increases this concentration compared to \(\text{HCl}\).

**Strong Bases**

• Completely dissociate, providing hydroxide ions (\(\text{OH}^{-}\)) which neutralize \(\text{H}^{+}\) ions.
• Not directly involved in this problem but important for understanding pH dynamics.

Weak Acids and Bases

Weak acids and bases dissociate only partially in water. This limited dissociation results in a relatively low concentration of hydrogen ions.

**Weak Acids**

• Examples include acetic acid (\(\text{CH}_3\text{COOH}\)).
• They partially dissociate, releasing fewer \(\text{H}^{+}\) ions.
• In the exercise, \(\text{CH}_3\text{COOH}\) has a lower \( [\text{H}^{+}] \) than strong acids because it only partially dissociates.

Weak acid solutions have higher pH compared to strong acids at the same concentration because less \(\text{H}^{+}\) is produced.

**Weak Bases**

• Example: Ammonia (\(\text{NH}_3\)).
• They do not donate hydrogen ions but instead accept them to form \(\text{NH}_4^{+}\), reducing the \( [\text{H}^{+}] \) in the solution.
• This makes them less likely to increase the solution's acidity compared to acids.

Hydrogen Ion Concentration

The hydrogen ion concentration (\( [\text{H}^{+}] \)) is a critical factor in determining the acidity of a solution.

**Key Points**

• The greater the \( [\text{H}^{+}] \), the more acidic the solution.
• Measured using the pH scale, where lower pH indicates higher acidity.
• Strong acids tend to have high \( [\text{H}^{+}] \) due to complete dissociation, making them very acidic.
• Weak acids and bases have lower \( [\text{H}^{+}] \), resulting in higher pH (less acidity).

In the exercise, \(\text{H}_2\text{SO}_4\) produced the highest \( [\text{H}^{+}] \), leading to the most acidic solution of the options given. Understanding these differences in ion concentration helps in predicting a solution's behavior and its interactions.