# D24.4 pH and pOH

The concentrations of H3O+ and OH in a solution are important for the solution’s acid-base properties and often affect the chemical behaviors of other solutes. A solution is neutral if its [H3O+] = [OH]; acidic if its [H3O+] > [OH]; and basic if its [H3O+] < [OH].

A common means of expressing values that span many orders of magnitude is to use a logarithmic scale. One such scale is based on the p-function:

pX = -logX

where “X” is the quantity of interest and “log” is the base-10 logarithm. The pH of a solution is therefore defined as: The reason for dividing by the units “mol/L” (M) is that [H3O+] has units of mol/L and taking the logarithm of a unit makes no sense. From here on we will assume that you are aware that only the numeric value of a concentration (or other quantity) needs to be used as the argument of a logarithm and we will not explicitly divide by the units.

If a pH value is known, the concentration of hydronium ions can be calculated:

[H3O+] = 10-pH

Here we assume that you know that units are required for the concentration obtained from this equation and the units are mol/L.

The hydroxide ion concentration may be similarly expressed as pOH:

pOH = -log[OH]          and          [OH] = 10−pOH

Finally, the relation between pH and pOH can be derived from the Kw expression:

 Kw = [H3O+][OH–] -log(Kw) = -log([H3O+][OH–]) pKw = -log([H3O+]) + (-log([OH–])) pKw = pH + pOH

At 25 °C:

pKw = 14.00 = pH + pOH

Therefore, at this temperature:

Classification Relative Ion Concentrations pH at 25 °C
acidic [H3O+] > [OH] < 7
neutral [H3O+] = [OH] 7
basic [H3O+] < [OH] > 7

Because Kw is temperature dependent, the correlations between pH values and the acidic/neutral/basic adjectives varies at different temperatures. For example, [H3O+] in pure water at 80 °C is 4.9 × 10−7 M, which corresponds to pH and pOH values of:

pH = -log[H3O+] = -log(4.9 × 10−7) = 6.31
pOH = -log[OH] = -log(4.9 × 10−7) = 6.31

At this temperature, neutral solutions have pH = pOH = 6.31, acidic solutions have pH < 6.31 and pOH > 6.31, and basic solutions have pH > 6.31 and pOH < 6.31. This distinction can be important when studying certain processes that occur at temperatures other than 25 °C, such as acid-base reactions in the human body where temperatures are typically 37 °C.

Unless otherwise noted, references to pH values are presumed to be those at 25 °C. The table below shows the relationships among [H3O+], [OH], pH, and pOH, and gives these values for some common substances. Activity: pH and Relative Strengths of Acids

Exercise: pH of Aqueous Solutions

The acidity of a solution is typically determined by measuring its pH. The pOH of a solution is not usually measured, but it is easily calculated from an experimentally determined pH value. The pH of a solution can be directly measured using a pH meter or visually estimated using colored indicators. Figure: pH Meter. (a) A research-grade pH meter used in a laboratory can have a resolution of 0.001 pH units, an accuracy of ± 0.002 pH units, and may cost in excess of 1000 dollars. (b) A portable pH meter has lower resolution (0.01 pH units), lower accuracy (± 0.2 pH units), and a far lower price tag. (credit b: modification of work by Jacopo Werther) Figure: pH Indicators. A universal indicator is a mixture of indicators that assumes a different color at different pH values. (a) A universal indicator has been added to solutions in ten test tubes, each with the pH shown at the top of each tube. (b) pH paper contains a different universal indicator that gives different colors when moistened with solutions of differing pH values. The scale at the top shows colors for even-numbered pH values from 2 to 10.

Activity: Determining Ka

Activity: Using Ka to Calculate Concentrations

The percent ionization of a weak acid is another measure of the strength of an acid, HA: A stronger acid, with a larger Ka, has higher percent ionization than a weaker acid (for the same concentration). The percent ionization for a solution of a weak acid is concentration dependent: it increases with decreasing acid concentration.

Exercise 4: Percent Ionization 