Question

Determine if each solution is acidic, basic, or neutral. (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-5} \mathrm{M}\); \(\left[\mathrm{OH}^{-}\right]=1 \times 10^{-9} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-6} \mathrm{M}\); \(\left[\mathrm{OH}^{-}\right]=1 \times 10^{-8} \mathrm{M}\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-7} \mathrm{M} ;\left[\mathrm{OH}^{-}\right]=1 \times 10^{-7} \mathrm{M}\) (d) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1 \times 10^{-8} \mathrm{M}\); \(\left[\mathrm{OH}^{-}\right]=1 \times 10^{-6} \mathrm{M}\)

Short answer

(a) Acidic, (b) Acidic, (c) Neutral, (d) Basic.

Step-by-step solution

- Understanding the pH, pOH, and the ionic product of water

The nature of a solution, whether it is acidic, basic, or neutral, depends on the concentrations of hydrogen ions (\text{H}_3O^+) and hydroxide ions (\text{OH}^-). The ionic product of water (Kw) is always \(1 \times 10^{-14} \text{M}^2\) at 25°C. For a solution to be acidic, [\text{H}_3O^+] > [\text{OH}^-]. For a solution to be basic, [\text{H}_3O^+] < [\text{OH}^-]. For a neutral solution, [\text{H}_3O^+] = [\text{OH}^-]. pH is a measure of the hydrogen ion concentration and is defined as -\text{log}[\text{H}_3O^+], while pOH is a measure of the hydroxide ion concentration and is defined as -\text{log}[\text{OH}^-].

- Analyzing solution (a)

For solution (a), compare the concentrations of [\text{H}_3O^+] and [\text{OH}^-]. Since [\text{H}_3O^+] = \(1 \times 10^{-5} \text{M}\) is greater than [\text{OH}^-] = \(1 \times 10^{-9} \text{M}\), the solution is acidic.

- Analyzing solution (b)

For solution (b), compare the concentrations of [\text{H}_3O^+] and [\text{OH}^-]. Since [\text{H}_3O^+] = \(1 \times 10^{-6} \text{M}\) is greater than [\text{OH}^-] = \(1 \times 10^{-8} \text{M}\), the solution is acidic.

- Analyzing solution (c)

For solution (c), since [\text{H}_3O^+] = [\text{OH}^-] = \(1 \times 10^{-7} \text{M}\), the solution is neutral.

- Analyzing solution (d)

For solution (d), compare the concentrations of [\text{H}_3O^+] and [\text{OH}^-]. Since [\text{H}_3O^+] = \(1 \times 10^{-8} \text{M}\) is less than [\text{OH}^-] = \(1 \times 10^{-6} \text{M}\), the solution is basic.

Key concepts

pH calculation

Understanding the pH of a solution is crucial for determining its acidity or basicity. pH is a logarithmic scale used to quantify the hydrogen ion concentration (\text{[H}_3\text{O}^+\text{]}) in a solution. The calculation of pH is given by the formula: \( pH = -\log[\text{H}_3O^+] \).

For instance, if a solution has a hydrogen ion concentration of \(1 \times 10^{-5} \text{M}\), the pH is calculated as \( -\log(1 \times 10^{-5}) \) which equals 5. This indicates an acidic solution because a pH less than 7 is characteristic of an acid. In contrast, if the hydrogen ion concentration were \(1 \times 10^{-9} \text{M}\), the pH would be 9, suggesting a basic solution as it is above the neutral pH of 7. Understanding and applying this calculation allows students to easily determine whether a solution is acidic, basic, or neutral based on its pH value.

Hydrogen ion concentration

Hydrogen ion concentration, often represented as \( [\text{H}_3\text{O}^+] \), directly influences the pH of a solution. In solutions where the hydrogen ion concentration is high, the solution is more acidic. Conversely, a low concentration indicates a lesser degree of acidity or a basic solution. The concentration of hydrogen ions can be expressed in molarity (M), which is moles of solute per liter of solution.

To connect this with the real-world example, consider lemon juice and soap. Lemon juice has a higher hydrogen ion concentration, making it acidic, while soap has a lower hydrogen ion concentration, rendering it basic. This concept helps explain the behavior of substances and their interactions based on their acidity or basicity.

Hydroxide ion concentration

Conversely to hydrogen ions, the hydroxide ion concentration, represented as \( [\text{OH}^-] \), defines the basicity of a solution. When hydroxide ion concentration is high, the solution is basic; when it’s low, the solution may be either neutral or acidic depending on the relative concentration of hydrogen ions. The pOH of a solution is the negative logarithm of the hydroxide ion concentration (\( pOH = -\log[\text{OH}^-] \)).

For example, household bleach has a high concentration of hydroxide ions, indicating its basic nature. In the context of the given problems, by calculating the pOH, students can understand the basic properties of a solution. If both pH and pOH are known, the pH scale's full scope—from very acidic to very basic—can be comprehended.

Ionic product of water

The ionic product of water (Kw) is an essential concept and constant in chemistry, defined as the product of the concentrations of hydrogen ions and hydroxide ions in pure water. At 25°C, it is always \(1 \times 10^{-14} \text{M}^2\). The equation \( [\text{H}_3\text{O}^+][\text{OH}^-] = 1 \times 10^{-14} \text{M}^2 \) must hold true for any aqueous solution. Neutral water, for example, will have equal concentrations of hydrogen and hydroxide ions, both at \(1 \times 10^{-7} \text{M}\), whose product equals \(1 \times 10^{-14} \text{M}^2\).

This constant is foundational when evaluating the acidity or basicity of solutions. For example, a shift in the balance by adding more \( [\text{H}_3\text{O}^+] \) or \( [\text{OH}^-] \) will result in an acidic or basic solution, respectively. Educators can emphasize that at constant temperature, the product of these two ion concentrations must remain at Kw, which serves as a critical balance point for understanding the nature of aqueous solutions.