Problem 29 - General Chemistry: Principles and Modern Applications

Question

What are \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],\left[\mathrm{OH}^{-}\right], \mathrm{pH},\) and \(\mathrm{pOH}\) of \(0.55 \mathrm{M}\) \(\mathrm{M} \mathrm{HClO}_{2} ?\)

Step-by-Step Solution

Answer

The concentration of hydronium ions is 0.55 M, the concentration of hydroxide ions is \(1.82 \times 10^{-14} M\), the pH is approximately 0.26 and the pOH is approximately 13.74.

Step 1: Calculation of Hydronium Ion Concentration

Since HClO2 is a strong acid, it dissociates completely in water to form hydronium ions (H3O+) and chlorite ions (ClO2-). Therefore, the concentration of hydronium ions will be equal to the molarity of the HClO2, i.e. \( [\mathrm{H}_{3}\mathrm{O}^{+}]= 0.55 M\)

Step 2: Calculation of Hydroxide Ion Concentration

The product of the concentrations of hydronium and hydroxide ions in water at 25°C is always \(1 \times 10^{-14}\). Therefore, use this relation to find the concentration of hydroxide ions: \(\left[\mathrm{OH}^{-}\right]=\frac{1 \times 10^{-14}}{\left[\mathrm{H}_{3}\mathrm{O}^{+}\right]}\). Substitute values to get \(\left[\mathrm{OH}^{-}\right]\), which turns out to be \(1.82 \times 10^{-14} M\)

Step 3: Calculation of pH and pOH

The pH is the negative logarithm (base 10) of the concentration of hydronium ions. Therefore, calculate it as: pH = -log(\( [\mathrm{H}_{3}\mathrm{O}^{+}] \)), which equals -log(0.55) or approximately 0.26. Similarly, the pOH is the negative logarithm (base 10) of the concentration of hydroxide ions: pOH = -log(\(\left[\mathrm{OH}^{-}\right]\)), which equals -log(\(1.82 \times 10^{-14}\)) or approximately 13.74

Key Concepts

Hydronium Ion Concentration

When discussing solutions like a 0.55 M HClO2, understanding hydronium ion concentration is crucial. When a strong acid like HClO2 is dissolved in water, it fully dissociates into its ions. This means it separates into hydronium ions (\( \text{H}_3\text{O}^+ \)) and other ions completely.
For HClO2, full dissociation implies that the concentration of \( \text{H}_3\text{O}^+ \) ions will be equal to the original concentration of the acid.
Thus, in a 0.55 M solution of HClO2, the \( \text{H}_3\text{O}^+ \) concentration is also 0.55 M.

• Hydronium ions are responsible for the acidic properties of the solution.
• The concentration of hydronium ions can directly affect the pH of the solution.

pH and pOH Calculation

Calculating pH and pOH is an essential part of understanding an acid's or base's strength in a solution. The pH is a measure of the acidity, while the pOH gives insight into the basicity. They both provide a sense of the balance of hydronium and hydroxide ions in the solution.
Let's break this down:
- **pH Calculation**: The pH is calculated as the negative logarithm of the hydronium ion concentration (\( \text{H}_3\text{O}^+ \)). For example, in a 0.55 M HClO2 solution, pH = -log(0.55), which results in a pH of approximately 0.26. This low pH indicates a highly acidic environment.
- **pOH Calculation**: Similarly, pOH is determined by the concentration of hydroxide ions (\( \text{OH}^- \)). Using the relationship \( \left[\text{H}_3\text{O}^+\right] [\text{OH}^-] = 1 \times 10^{-14} \) at 25°C, we find that for a hydronium ion concentration of 0.55 M, \( \left[\text{OH}^-\right] \approx 1.82 \times 10^{-14} \). Thus, pOH = -log(\(1.82 \times 10^{-14}\)), which is approximately 13.74.
These calculations highlight the inverse relationship between pH and pOH in any given solution.

Strong Acid Dissociation

To understand why strong acids like HClO2 affect hydronium concentration so effectively, you must grasp the concept of strong acid dissociation.
Here's what happens:

• **Total dissociation**: Strong acids fully ionize in solution, meaning every molecule of HClO2 separates into hydronium ions (\( \text{H}_3\text{O}^+ \)) and other ions.
• **Impact**: This complete separation maximizes the acid's ability to increase the hydronium ion concentration.
• **Effect on pH**: As the concentration of hydronium ions increases, the pH decreases, indicating a stronger acidic solution.

Strong acid dissociation explains why the concentration of hydronium ions (\( \text{H}_3\text{O}^+ \)) in the solution mirrors the starting concentration of the strong acid. This property is what characterizes strong acids and distinguishes them from weak acids, which do not dissociate completely in water.