How to Determine a pH From a Kw

Kw represents the equilibrium between water's forward and reverse chemical reactions.

Kw, or the equilibrium constant of water, describes the balance between the forward reaction that occurs when water molecules form hydroxide (OH-) and hydronium (H3O+) ions and the reverse reaction of those elements back into water. At 25 degrees Celsius and one atmosphere of pressure, the Kw is 1.008 * 10^-14. As the temperature and pressure change, the value of Kw also changes, which simultaneously affects the pH of the water. If you know the new value of the Kw, you can calculate the new pH by using algebra to manipulate the equilibrium equation Kw = [H3O+][OH-].

Things You'll Need

• Scientific calculator

Instructions

1. Substitute the value of Kw into the equilibrium equation Kw = [H3O+][OH-].

   For example, if Kw = 51.3 * 10^-14, the equation would look like this: 51.3 * 10^-14 = [H3O+][OH-].

2. Change [H3O+][OH-] to [H3O+][H3O+] or [H3O+]^2, since the hydronium and hydroxide concentrations are identical in pure water.

   The equation now states that 51.3 * 10^-14 = [H3O+]^2.

3. Take the square root of both sides. This leaves you with the concentration of the hydronium ions.

   √(51.3 * 10^-14) = √[H3O+]^2, which approximately equals 7.16 * 10^-7 = [H3O+].

4. Find the negative log of the concentration. The answer is the pH of the water.

   -log(7.16 * 10^-7) = 6.15. Therefore, the pH of the water is about 6.15.

Tips & Warnings

• [H3O+] is often shortened to [H+].

• The equilibrium equation of water only applies to pure water. If another substance is dissolved in the liquid, a different equilibrium constant applies and you must know the concentration of the hydroxide ions as well as the Kw to determine the pH.

References

• Chemguide: The Ionic Product for Water, Kw