Problem 31 - Chemistry The Science in Context

Question

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of solutions with the following \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) or \(\left[\mathrm{OH}^{-}\right]\) values. Indicate which solutions are acidic, basic, or neutral. a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=5.3 \times 10^{-3} \mathrm{M}\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.8 \times 10^{-9} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.2 \times 10^{-6} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14} \mathrm{M}\)

Step-by-Step Solution

Answer

Question: Classify each of the following solutions as acidic, basic, or neutral based on their concentration: a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=5.3 \times 10^{-3} \mathrm{M}\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.8 \times 10^{-9} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.2 \times 10^{-6} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14} \mathrm{M}\) Answer: a. Acidic b. Basic c. Acidic d. Strongly acidic

Step 1: Calculate pH for the given concentration

\(\mathrm{pH} = -\log_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = -\log_{10}(5.3 \times 10^{-3}) \approx 2.28\)

Step 2: Calculate pOH from pH

\(\mathrm{pOH} = 14 - \mathrm{pH} = 14 - 2.28 \approx 11.72\)

Step 3: Classify the solution

The solution is acidic, as the pH value is less than 7. b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.8 \times 10^{-9} \mathrm{M}\)

Step 4: Calculate pH for the given concentration

\(\mathrm{pH} = -\log_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = -\log_{10}(3.8 \times 10^{-9}) \approx 8.42\)

Step 5: Calculate pOH from pH

\(\mathrm{pOH} = 14 - \mathrm{pH} = 14 - 8.42 \approx 5.58\)

Step 6: Classify the solution

The solution is basic, as the pH value is greater than 7. c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.2 \times 10^{-6} \mathrm{M}\)

Step 7: Calculate pH for the given concentration

\(\mathrm{pH} = -\log_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] = -\log_{10}(7.2 \times 10^{-6}) \approx 5.14\)

Step 8: Calculate pOH from pH

\(\mathrm{pOH} = 14 - \mathrm{pH} = 14 - 5.14 \approx 8.86\)

Step 9: Classify the solution

The solution is acidic, as the pH value is less than 7. d. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14} \mathrm{M}\)

Step 10: Calculate pOH for the given concentration

\(\mathrm{pOH} = -\log_{10}\left[\mathrm{OH}^{-}\right] = -\log_{10}(1 \times 10^{-14}) = 14\)

Step 11: Calculate pH from pOH

\(\mathrm{pH} = 14 - \mathrm{pOH} = 14 - 14 = 0\)

Step 12: Classify the solution

The solution is strongly acidic, as the pH value is 0.

Key Concepts

Acidic Solutions

Understanding acidic solutions starts with recognizing that they have a high concentration of \(\text{H}_3\text{O}^+\) ions. When the pH of a solution is less than 7, it is considered acidic. The pH scale is logarithmic, so a small change in pH represents a significant change in \(\text{H}_3\text{O}^+\) ion concentration. For instance, in this exercise, the solution with \(\left[\text{H}_3\text{O}^+\right]=5.3 \times 10^{-3} \, \text{M}\) has a pH of approximately 2.28, indicating it is acidic.

• An acidic solution means more \(\text{H}_3\text{O}^+\) ions are present than \(\text{OH}^-\) ions.
• The more acidic the solution, the lower the pH value.
• Solutions with a pH close to 0 are considered strongly acidic, like the solution with \(\left[\text{OH}^-\right]=1.0 \times 10^{-14} \, \text{M}\).

This characteristic is important in various chemical processes, biological systems, and industrial applications where acidity or alkalinity affects outcomes.

Basic Solutions

Basic solutions are characterized by a higher concentration of \(\text{OH}^-\) ions compared to \(\text{H}_3\text{O}^+\) ions. When the pH of a solution is greater than 7, it’s considered basic or alkaline. For example, the solution with \(\left[\text{H}_3\text{O}^+\right]=3.8 \times 10^{-9} \, \text{M}\) in our exercise has a pH of approximately 8.42, indicating a basic nature.

• Alkalinity increases and acidity decreases as pH values rise above 7.
• A solution with higher \(\text{OH}^-\) concentration relative to \(\text{H}_3\text{O}^+\) results in a basic environment.
• Household substances like baking soda or soap create basic solutions, contributing to their cleaning properties.

Basic solutions play essential roles in neutralizing acids and enabling various reactions in both nature and industry, such as titrations or wastewater treatment.

Neutral Solutions

A neutral solution is characterized by an equal concentration of \(\text{H}_3\text{O}^+\) and \(\text{OH}^-\) ions, making the pH exactly 7. Water is a classic example of a neutral solution where neither acidic nor basic properties dominate. However, sometimes determining neutrality isn't as straightforward as considering the pH alone, especially in solutions with other substances affecting ion balance.

• Solutions with a pH of 7 are regarded as neutral under standard conditions.
• In pure water, the concentrations of \(\text{H}_3\text{O}^+\) and \(\text{OH}^-\) are both \(1 \times 10^{-7} \, \text{M}\).
• Real-world neutral solutions can be affected by temperature, atmospheric gases, or dissolved substances.

Neutral solutions are key in various biological systems for maintaining stable environments, and in many industrial processes, balancing between acidic and basic states is necessary for optimal performance.