How To Calculate The pH Of Water Using pKa

Water has many useful and interesting properties, and some of these are evident at a glance. It is clear that the world is made up of a lot of water, but almost no water that you ever see is "just" water. Some water, like tap water, looks crystal-clear and contains only a small amount if impurities, while most pond and ocean water has visible matter dissolved or suspended in it.

Another interesting property of water is that in terms of pH, a term popular in shampoo ads as well as on chemistry tests, it sits right in the middle of the scale: It is neither an acid nor a base and perfectly neutral. Keep reading to discover what this means in terms of the math of the pH formula and the definitions of acids and bases in chemistry.

The term pH is associated with acidity. Acids are compounds capable of donating a proton, or hydrogen ion (H+), in aqueous solution, leaving behind an anion (negatively charged ion) called a conjugate base and generating a hydronium (H₃O+) ion in water. Strong acids such as HCl donate their protons even when a solution is already relatively high in protons. Weak acids donate theirs in solutions closer to being pH-neutral, a value of 7.0.

Bases are compounds that can accept protons, or equivalently in aqueous solutions, donate a hydroxyl group (–OH). A strong base such as NaOH can do this even in the presence of a high concentration of hydroxyl ions (or a low concentration of H+ ions). Weak bases, like weak acids, tend to not ionize until the pH is close to neutral.

While pH refers to a measure of acidity (or alkalinity, also called basicity) it actually stands for pouvoir hydrogenem, or "power of hydrogen" in French. In areas of chemistry, the small "p" is an operator that means "take the negative logarithm of."

Math aside, it is a scale that compresses the very wide range of hydronium and hydroxide concentrations seen in water into a scale that runs from 0 to 14 for practical purposes.

A solution with a pH of 1.0 is strongly acidic and has a [H⁺] concentration 10 times higher than a solution with a pH of 2.0, 100 times higher than a solution with a pH of 3.0 and 1,000 times higher than a solution with a pH of 4.0. This is because of the qualities of logarithms, as you'll see in a couple of examples.

The pH formula most often assumes the form pH = –log[H⁺], where [H+] is the concentration in moles per liter (mol/L, or M). An equivalent formula exists for the concentration of hydroxide ions:

pOH = –[OH^–]

Example: What is the pH of a solution with an [H⁺] of 2.8 × 10^–3 M?

pH = –log[2.8 × 10^–3] = 2.55

Water has a pH of 7.0; for every H+ ion that "breaks free," one OH^– ion exists to balance it off. Water is thus amphoteric, or capable of acting as both an acid and a base (while not being especially "good" at either).

The self-ionization of water is represented by the expression K_w= [H₃O+][OH⁻] = 1.0 × 10⁻¹⁴, where K_w is the constant of water. Because pK_w= –log[K_w] and K_w is the constant 1.0 × 10⁻¹⁴ , pK_w = 14, which determines the strangely numbered pH scale.

More generally, K_w is represented by the dissociation constant for acids **K_a**, which varies from species to species.

You don't have to do pH problems or pK_a problems involving water in your head; you can use a standard calculator's log function, or visit a page like the one in the Resources that allows you to input different values of pH for a variety of different acids in different concentrations in solution.