7.4 pH and pOH

The pH of an aqueous solution is a measure of the hydronium ion concentration.

\[\mathrm{pH} = -\log [\mathrm{H_3O^+}]\] and

\[[\mathrm{H_3O}^+] = 10^{-\mathrm{pH}}\]

The pOH is a measure of the hydroxide ion concentration

\[\mathrm{pOH} = -\log [\mathrm{OH^-}]\] and

\[[\mathrm{OH}^-] = 10^{-\mathrm{pOH}}\]

The pH and pOH of solution is related through pKw such that

\[\mathrm{p}K_{\mathrm{w}} = \mathrm{pH} + \mathrm{pOH}\]

Acidic, basic, and neutral solutions are defined by the relative amounts of H3O+ and OH in the solution.


Solution   at 25 °C
Acidic [H3O+] > [OH] pH < 7, pOH > 7
Basic [H3O+] < [OH] pH > 7, pOH < 7
Neutral [H3O+] = [OH] pH = 7, pOH = 7


The image below illustrates a wide variety of substances across the pH scale of 0 to 14.


Given that pH is a log scale of hydronium ion concentration, it is important to understand that a small change in pH results in a large change in acidity.


Practice


The pH of an aqueous acidic solution is 3.45 at 25 °C. What is the pOH?

Solution

The pKw of water is 14 at 25 °C. Therefore,

\[\begin{align*} \mathrm{p}K_{\mathrm{w}} &= \mathrm{pH} + \mathrm{pOH} \\[1.5ex] \mathrm{pOH} &= \mathrm{p}K_{\mathrm{w}} - \mathrm{pH} \\[1.5ex] &= 14.00 - 3.45 \\[1.5ex] &= 10.55 \end{align*}\]


Practice


The pH of an aqueous acidic solution is 3.45 at 50 °C. What is the pOH?

Solution

The pKw of water is 13.26 at 50 °C. Therefore,

\[\begin{align*} \mathrm{p}K_{\mathrm{w}} &= \mathrm{pH} + \mathrm{pOH} \\[1.5ex] \mathrm{pOH} &= \mathrm{p}K_{\mathrm{w}} - \mathrm{pH} \\[1.5ex] &= 13.26 - 3.45 \\[1.5ex] &= 9.81 \end{align*}\]


Practice


The pH of pure water at 50 °C is 6.63. Is the water acidic, basic, or neutral?

Solution

Neutral. pH is equal to pOH.