Problem 14 - General Chemistry: Principles and Modern Applications

Question

Which aqueous solution has the greatest \(\left[\mathrm{H}^{+}\right]:\) (a) \(0.011 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH} ;\) (b) \(0.010 \mathrm{M} \mathrm{HCl} ;\) (c) \(0.010 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4} ;\) (d) \(1.00 \mathrm{M} \mathrm{NH}_{3} ?\) Explain your choice.

Step-by-Step Solution

Answer

The solution with the highest concentration of \( [\mathrm{H}^+] \) ions is the 0.010 M H2SO4 solution.

Step 1: Analyze the aqueous compounds

Analyze each compound to understand the degree to which they dissociate in solution: (a) CH3COOH is a weak acid and only partially ionizes, (b) HCl is a strong acid and fully ionizes, (c) H2SO4 is a strong acid that fully ionizes and can release two Hydrogen ions per molecule, (d) NH3 is a weak base that produces OH- ions in solution, therefore reducing the concentration of H+ ions.

Step 2: Determine the concentration of H+ ions

Using the information from step 1, we can determine the concentration of H+ ions for each solution: (a) For CH3COOH, the concentration of \( [\mathrm{H}^+] \) ions will be less than the molarity of the solution, (b) For HCl, the concentration of \( [\mathrm{H}^+] \) ions will be equal to the molarity of the solution, 0.01 M, (c) For H2SO4, every molecule can produce two \( [\mathrm{H}^+] \) ions, so the concentration will be twice the molarity of the solution, 2*0.01 M = 0.02 M, (d) For NH3, since it is a base, the concentration of \( [\mathrm{H}^+] \) ions will be lower than the molarity of the solution.

Step 3: Compare the concentrations.

Comparing the results from step 2, it can be concluded that the solution with H2SO4, having the highest concentration of \( [\mathrm{H}^+] \) ions (0.02 M), has the greatest \( [\mathrm{H}^+] \).

Key Concepts

Acid Dissociation

Acid dissociation refers to the process where an acid breaks apart in water to form ions. This is crucial for understanding how acids behave in solutions. When an acid dissolves, it releases hydrogen ions (\(\mathrm{H}^+\)) which is the key to its acidic nature.
Different acids dissociate to varying degrees. This affects their strength and how they react in chemical processes.

• Full Dissociation: Strong acids, like hydrochloric acid (HCl), break down completely in water, releasing a high concentration of hydrogen ions.
• Partial Dissociation: Weak acids, such as acetic acid (CH3COOH), only partially break down, resulting in a lower concentration of hydrogen ions in solution.

Understanding dissociation helps predict the acidity and behavior of various solutions.

Strong and Weak Acids

Acids are classified as either strong or weak based on their ionization in water. This classification is key to anticipating how acids will perform in reactions and their relative strengths.

Strong Acids

These acids completely dissociate in water, which means all their molecules release hydrogen ions (\(\mathrm{H}^+\)). Common examples include:

• Hydrochloric acid (HCl)
• Sulfuric acid (H2SO4)

For H2SO4, note that each molecule can release two \(\mathrm{H}^+\) ions, affecting the overall concentration.

Weak Acids

These acids only partially dissociate in water, meaning they produce fewer hydrogen ions. Acetic acid is a prime example. Understanding the distinction is essential for predicting reaction outcomes and pH levels.

Concentration of Hydrogen Ions

The concentration of hydrogen ions (\(\left[\mathrm{H}^+\right]\)) is a measure of how acidic a solution is. This concentration determines the pH level, which affects chemical reactions and biological processes.

Calculating \(\left[\mathrm{H}^+\right]\)

For solutions, the concentration is directly related to how much the acid dissociates:

• Strong Acids: The \(\left[\mathrm{H}^+\right]\) is equal to their molarity, because they fully dissociate.
• Weak Acids: The \(\left[\mathrm{H}^+\right]\) is less than the molarity due to partial dissociation.

For example, HCl at 0.010 M will have \(\left[\mathrm{H}^+\right] = 0.010\ \mathrm{M}\), while CH3COOH at 0.011 M will have a lower \(\left[\mathrm{H}^+\right]\).

Influence on pH

The hydrogen ion concentration directly influences the solution's pH. More hydrogen ions mean a lower pH and a more acidic solution. Sulfuric acid (H2SO4) can even double the hydrogen ion concentration because each molecule releases two ions, emphasizing its strong acidic nature.