15.4:
pH Scale
The concentration of hydronium ions in an aqueous solution is usually written with negative exponents and can be as small as 1 × 10−14 M. The pH scale was developed by chemist Soren Sorenson in 1909 as a more convenient way to quickly compare the acidity of different solutions.
The pH of a solution is the negative logarithm of its hydronium ion concentration. For example, a solution with 1 × 10−5 M hydronium concentration has a pH of 5. The greater the hydronium ion concentration of a solution, the lower its pH.
As pH is expressed on a logarithmic scale, a single-unit change corresponds to a 10-fold increase or decrease of the hydronium ion concentration. A solution with a pH of 3 will have ten times more hydronium ions than a solution with a pH 4 and one hundred times more than a solution with a pH of 5.
An acidic solution has a higher concentration of hydronium ions than hydroxide ions and a pH less than 7, whereas a basic solution has a lower concentration of hydronium ions than hydroxide ions and a pH greater than 7.
A neutral solution with an equal concentration of hydronium and hydroxide ions has a pH of 7.
The concentration of hydroxide ions can also be expressed as pOH. pOH is the negative logarithm of the hydroxide ion concentration. The higher the hydroxide ion concentration, the lower its pOH value.
A pH or pOH value of an aqueous solution ranges from 0 – 14. This is because KW, the equilibrium constant for the autoionization of water, is equal to 1 × 10−14.
Taking the negative log of both sides of the equation results in an equation where pKW is equal to the sum of pH and pOH. Since the negative log of 1 × 10−14 is 14, the sum of the pH and pOH of an aqueous solution will always be 14. This can be used to determine the pH value when the pOH value is known and vice versa.
For example, a solution with a pOH of 10 has a pH of 4.
15.4:
pH Scale
Hydronium and hydroxide ions are present both in pure water and in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion product of water (Kw). The concentrations of these ions in a solution are often critical determinants of the solution’s properties and the chemical behaviors of its other solutes. Two different solutions can differ in their hydronium or hydroxide ion concentrations by a million, billion, or even trillion times. A common means of expressing quantities that may span many orders of magnitude is to use a logarithmic scale. The pH of a solution is therefore defined as shown here, where [H3O+] is the molar concentration of hydronium ion in the solution:
Rearranging this equation to isolate the hydronium ion molarity yields the equivalent expression:
Likewise, the hydroxide ion molarity may be expressed as a p-function or pOH:
or
Finally, the relation between these two ion concentration expressed as p-functions is easily derived from the KW expression:
At 25 °C, the value of KW is 1.0 × 10−14, and so:
The hydronium ion molarity in pure water (or any neutral solution) is 1.0 × 10−7 M at 25 °C. The pH and pOH of a neutral solution at this temperature are therefore:
And so, at this temperature, acidic solutions are those with hydronium ion molarities greater than 1.0 × 10−7 M and hydroxide ion molarities less than 1.0 × 10−7 M (corresponding to pH values less than 7.00 and pOH values greater than 7.00). Basic solutions are those with hydronium ion molarities less than 1.0 × 10−7 M and hydroxide ion molarities greater than 1.0 × 10−7 M (corresponding to pH values greater than 7.00 and pOH values less than 7.00).
Since the autoionization constant KW is temperature dependent, these correlations between pH values and the acidic/neutral/basic adjectives will be different at temperatures other than 25 °C. For example, the hydronium molarity of pure water at 80°C is 4.9 × 10−7 M, which corresponds to pH and pOH values of:
At this temperature, neutral solutions exhibit pH = pOH = 6.31, acidic solutions exhibit pH less than 6.31 and pOH greater than 6.31, whereas basic solutions exhibit pH greater than 6.31 and pOH less than 6.31. This distinction can be important when studying certain processes that occur at other temperatures, such as enzyme reactions in warm-blooded organisms at a temperature around 36 – 40 °C. Unless otherwise noted, references to pH values are presumed to be those at 25 °C.
This text is adapted from Openstax, Chemistry 2e, Section 14.2: pH and pOH.
Suggested Reading
- van Lubeck, Henk. "Why not replace pH and pOH by just one real acidity grade, AG?." Journal of Chemical Education 76, no. 7 (1999): 892. https://pubs.acs.org/doi/pdf/10.1021/ed076p892