Determining the pH of a Solution Given [OH-]

Understanding the relationship between the concentration of hydroxide ions [OH-] and the pH of a solution is crucial in many scientific and engineering applications. This article will guide you through the process of calculating the pH of a solution when the hydroxide ion concentration is given. The specific case of [OH-] 4.5 x 10-3 will be used as an example to demonstrate the steps involved.

Step-by-Step Calculation

Calculate the pOH:

First, you need to calculate the pOH of the solution using the given hydroxide ion concentration. The formula to find pOH is:

pOH -log[OH^-]

Substituting the given value:

pOH -log(4.5 times 10^{-3}) approx 2.35

Calculate the pH:

Once pOH has been determined, the next step is to find the pH. The relationship between pH and pOH is given by:

pH pOH 14

Using this relationship:

pH 14 - pOH 14 - 2.35 approx 11.65

Therefore, the approximate pH of the solution is 11.65.

Additional Calculations

For a more comprehensive understanding, let's explore additional calculations to determine the concentration of hydrogen ions [H] and the final pH using the same [OH-] value.

Calculate [H] given [OH-]:

The product of the concentrations of hydrogen ions [H] and hydroxide ions [OH-] in water at a given temperature is constant. At 25°C, this value is 1.0 x 10-14 (Kw, the ion product constant for water).

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

Solving for [H]:

[H] frac{1.0 times 10^{-14}}{4.5 times 10^{-3}} 2.22 times 10^{-12} text{ M}

Calculate the pH:

The pH is defined as the negative logarithm of the hydrogen ion concentration:

pH -log[H]

Substituting the value:

pH -log(2.22 times 10^{-12}) approx 11.65

The calculations confirm that the pH is indeed 11.65 when [OH-] 4.5 x 10-3.

Conclusion

By understanding and applying the logarithmic relationships between pH, pOH, and the concentrations of hydrogen and hydroxide ions, you can accurately determine the pH of a solution given any [OH-] value. This knowledge is vital in various scientific and industrial processes, from environmental chemistry to industrial water treatment systems.

References

Rossotti, H. J. F. and Rossotti, F. D. H. (1961). Acids and Bases: Their Chemistry Explained. London: Constable.