Understanding pH Calculation in a 10^-8 M KOH Solution at 25°C

When analyzing a 10^-8 M KOH (potassium hydroxide) solution at 25°C, it is crucial to comprehend the contributions of hydroxide ions (OH-) from both the base and the auto-dissociation of water. This article provides a detailed explanation of how to calculate the pH of such a solution, including the steps involved in determining the pOH and pH.

1. Dissociation of KOH

KOH is a strong base and dissociates completely in water according to the following equation:

text{KOH} rightarrow text{K}^ text{OH}^-

This means that in a 10^-8 M KOH solution, the concentration of text{OH}^- ions is equal to the concentration of KOH, which is 10^-8 M. Thus, the text{OH}^- concentration from KOH is 10^-8 M.

2. Auto-dissociation of Water

Water also auto-dissociates to produce text{H}^ and text{OH}^- ions. At 25°C, the auto-dissociation constant (K_w) is given by:

K_w [H^ ][OH^-] 1.0 times 10^{-14}

At neutrality, the concentrations of text{H}^ and text{OH}^- are both 10^-7 M. Thus, the contribution of text{OH}^- ions from water is 10^-7 M.

3. Total text{OH}^- Concentration

The total concentration of text{OH}^- in the solution is the sum of the text{OH}^- from KOH and the water:

[text{OH}^-] 10^{-8} , text{M} 10^{-7} , text{M} 1.1 times 10^{-7} , text{M}

4. Calculating pOH

Using the total concentration of text{OH}^-, we can calculate the pOH:

text{pOH} -log[text{OH}^-] -log(1.1 times 10^{-7}) approx 7.0

5. Calculating pH

The relationship between pH and pOH is given by:

text{pH} text{pOH} 14

Thus, the pH of the solution is:

text{pH} 14 - text{pOH} 14 - 7.0 7.0

6. Revisiting with a Different Molarity

For a 4.9 times 10^{-2} M solution of KOH, the text{OH}^- concentration is equal to 4.9 times 10^{-2} M. The pOH for this solution is calculated as:

text{pOH} -log[text{OH}^-] -log(4.9 times 10^{-2}) 1.31

Using the relationship text{pH} text{pOH} 14, the pH is:

text{pH} 14 - 1.31 12.69

7. Summary and Relevance

This article demonstrates how to calculate the pH of a 10^-8 M KOH solution at 25°C, providing a detailed breakdown of the dissociation of KOH and the auto-dissociation of water. The understanding of these processes is essential for accurately measuring the acidity or basicity of solutions, an important aspect of chemical analysis and environmental science.

Keywords: pH calculation, KOH solution, 25°C, strong base