ABSE_Auto-Ionization of Water Lesson

Auto-Ionization of Water

You just learned that water is amphoteric. You saw examples of this as water reacted with other substances. The reality is that water will actually react with another water molecule where one of the water molecules behaves as an acid and the other behaves as a base. This is known as auto-ionization. The reaction is:  

H₂O   +   H₂O   → H₃O⁺   + OH^-

H₂O   +   H₂O ⇌ H₃O⁺   + OH^-

This is an equilibrium equation, therefore we can write an equilibrium expression for this reaction.

$k_{eq}=\frac{[H_3O^+][OH^-]}{[H_2O][H_2O]}$

The molarity of water is a constant value and can be combined with the equilibrium constant to form a new constant, k_w.

Such a small value of k_w means that water does produce some ions, but to a very small degree. You need to memorize this k_w and also know that this is the value for this constant at 25°C. If the temperature were different, k_w would also be different.

Because the auto-ionization of water takes place in any aqueous solution, the equation for k_w can be used on solutions as well as pure water. In a neutral solution [H₃O⁺] and [OH^-] are equal. We can solve for these concentrations.

1.0 x 10^-14 = [H₃O⁺][OH^-]

1.0 x 10^-14 = (x)(x)

1.0 x 10^-14 = (x)²

1.0 x 10^-7 =(x)

The values of [H₃O⁺] and [OH^-] are always equal in pure water. In an acidic or basic solution, [H₃O⁺] is not equal to [OH^-]. According to Le Chatelier's principle, addition of an acid to pure water will increase [H₃O⁺], shift the auto-ionization equilibrium to the left, and decrease [OH^-]. Addition of a base to pure water will have the opposite effect, increasing [OH^-] and decreasing [H₃O⁺].  Nevertheless, their product, Kw, is the same. 

When [H₃O⁺] is greater than [OH^-], the solution is acidic.

When [H₃O⁺] is less than [OH^-], the solution is basic (sometimes called alkaline).

The pH Concept

Many solutions of acids and bases have small concentrations of H₃O⁺ and OH^-. To allow for easy comparison between these concentrations and to make identification of a solution as acid, base, or neutral easier, a log system was developed called pH. When calculating pH, the numbers usually fall between 1 and 14. This is referred to as the pH scale and is interpreted as given below.

Check out the list below of some common substances and their pH.

Many other quantities can use the same basic equation as the one used to solve for pH. Below, X represents these other quantities.

pX = -log[X]

Using this basic equation, we can get the following equations:

The pH equation and scale is more common than the pOH scale, but pOH can be very useful in calculations. Note that the interpretation of the pOH scale is opposite that of the pH scale. On the pOH scale, a value less than 7 means basic and a value greater than 7 means acidic.

A useful relationship among pH, pOH, and pK_w can be derived from the equation for k_w.

Using a combination of these formulas, you can perform many calculations.

Remember to work on the module practice problems as you complete each section of content.  

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