pH and pOH Calculations - Chemistry

1. Fundamental Concepts

Definition: pH is a measure of the hydrogen ion concentration $$ [H^+] $$ in a solution, and pOH is a measure of the hydroxide ion concentration $$ [OH^-] $$.
pH Scale: The pH scale ranges from 0 to 14, where 7 is neutral, below 7 is acidic, and above 7 is basic (alkaline).
Relationship Between pH and pOH: In aqueous solutions at 25°C, the sum of pH and pOH is always 14: $$ pH + pOH = 14 $$

2. Key Concepts

pH Calculation: $$pH = -\log_{10} [H^+]$$

pOH Calculation: $$pOH = -\log_{10} [OH^-]$$

Application: Used to determine the acidity or basicity of solutions in various fields such as environmental science, medicine, and industrial processes.

3. Examples

Example 1 (Basic)

Problem: Calculate the pH of a solution with a hydrogen ion concentration of $$ 1 \times 10^{-4} M $$.

Step-by-Step Solution:

Use the pH formula: $$ pH = -\log_{10} [H^+] $$
Substitute the given concentration: $$ pH = -\log_{10} (1 \times 10^{-4}) $$
Calculate the logarithm: $$ pH = -(-4) = 4 $$

Validation: The pH of a solution with $$ [H^+] = 1 \times 10^{-4} M $$ is 4, which is consistent with the calculation.

Example 2 (Intermediate)

Problem: Calculate the pOH of a solution with a hydroxide ion concentration of $$ 1 \times 10^{-9} M $$, and then find the pH.

Step-by-Step Solution:

Use the pOH formula: $$ pOH = -\log_{10} [OH^-] $$
Substitute the given concentration: $$ pOH = -\log_{10} (1 \times 10^{-9}) $$
Calculate the logarithm: $$ pOH = -(-9) = 9 $$
Use the relationship between pH and pOH: $$ pH + pOH = 14 $$
Solve for pH: $$ pH = 14 - 9 = 5 $$

Validation: The pOH of a solution with $$ [OH^-] = 1 \times 10^{-9} M $$ is 9, and the corresponding pH is 5, which is consistent with the calculation.

4. Problem-Solving Techniques

Logarithmic Properties: Use the properties of logarithms to simplify calculations, such as $$ \log_{10} (a \times b) = \log_{10} a + \log_{10} b $$.
Significant Figures: Ensure that the number of significant figures in the final answer matches the least precise measurement in the problem.
Concept Reinforcement: Always check the relationship between pH and pOH to ensure consistency in your calculations.