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21.11: The pOH Concept

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    53940
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    The pOH Concept

    As with the hydrogen-ion concentration, the concentration of the hydroxide ion can be expressed logarithmically by the pOH. The pOH of a solution is the negative logarithm of the hydroxide-ion concentration.

    \[\text{pOH} = -\text{log} \left[ \ce{OH^-} \right]\]

    The pH of a solution can be related to the pOH. Consider a solution with a pH \(= 4.0\). The \(\left[ \ce{H^+} \right]\) of the solution would be \(1.0 \times 10^{-4} \: \text{M}\). Dividing \(K_\text{w}\) by this yields a \(\left[ \ce{OH^-} \right]\) of \(1.0 \times 10^{-10} \: \text{M}\). Finally the pOH of the solution equals \(-\text{log} \left( 1.0 \times 10^{-10} \right) = 10\). This example illustrates the following relationship.

    \[\text{pH} + \text{pOH} = 14\]

    The pOH scale is similar to the pH scale in that a pOH of 7 is indicative of a neutral solution. A basic solution has a pOH less than 7, while an acidic solution has a pOH of greater than 7. The pOH is convenient to use when finding the hydroxide ion concentration from a solution with a known pH.

    Example 21.11.1

    Find the hydroxide concentration of a solution with a pH of 4.42.

    Solution:

    Step 1: List the known values and plan the problem.

    Known

    • pH \(= 4.42\)
    • pH \(+\) pOH \(= 14\)

    Unknown

    • \(\left[ \ce{OH^-} \right] = ? \: \text{M}\)

    First, the pOH is calculated, followed by the \(\left[ \ce{OH^-} \right]\).

    Step 2: Solve.

    \[\begin{align} \text{pOH} &= 14 - \text{pH} = 14 - 4.42 = 9.58 \\ \left[ \ce{OH^-} \right] &= 10^{-\text{pOH}} = 10^{-9.58} = 2.6 \times 10^{-10} \: \text{M} \end{align}\]

    Step 3: Think about your result.

    The pH is that of an acidic solution, and the resulting hydroxide-ion concentration is less than \(1 \times 10^{-7} \: \text{M}\). The answer has two significant figures because the given pH has two decimal places.

    The diagram below shows all of the interrelationships between \(\left[ \ce{H^+} \right]\), \(\left[ \ce{OH^-} \right]\), pH, and pOH.

    Figure 21.11.1: Relationships between hydrogen ion concentration, hydroxide ion concentration, pH and pOH.

    Summary

    • pOH is defined.
    • Calculations involving pOH are described.

    Contributors

    • CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon.