16.3 Ionization of Water

Learning Objectives

By the end of this section, you will be able to:

  • Describe the autoionization of water
  • Use the ion-product constant for water to calculate hydronium and hydroxide ion concentrations

To begin this chapter, Watch How Polarity makes Water Behave Strangely (3min 51s).

Video Source: TED-Ed. (2013, February 4). How polarity makes water behave strangely – Christina Kleinberg [Video]. YouTube.

Earlier in this chapter, the concept of amphoteric species, such as water, was introduced. Because of its highly polar structures, water can function as either an acid or a base, depending on the nature of the solute dissolved in it. In fact, in pure water or in any aqueous solution, water acts both as an acid and a base. A very small fraction of water molecules donate protons to other water molecules to form hydronium ions and hydroxide ions (Figure 16.3a).

This figure has two rows. In both rows, a chemical reaction is shown. In the first, structural formulas are provided. In this model, the O atom has H atoms singly bonded above and to the right. The O atom has pairs of electron dots on its left and lower sides. This is followed by a plus sign, which is followed by an O atom which has H atoms singly bonded above and to the right. The O atom has pairs of electron dots on its left and lower sides. A double arrow follows. To the right, in brackets is a structure with a central O atom with H atoms singly bonded above and to the right. A pair of electron dots is on the lower side of the O atom. To the left of the O atom, a H atom is singly bonded. Outside the brackets to the right is a superscript plus. This is followed by a plus sign and an O atom with pairs of electron dots above, left, and below. An H atom is singly bonded to the right. This atom has a superscript negative sign. The reaction is written in symbolic form below. H subscript 2 O is labeled as “Acid”. This is followed by plus H subscript 2 O, which is labeled as “Base.” A double sided arrow follows. To the right is H subscript 3 O superscript plus, which is labeled as “Acid”. This is followed by O H superscript -, and is labeled "Base".
Figure 16.3a Autoionization of Water: Water acts both as an acid and a base. A very small fraction of water molecules donate protons to other water molecules to form hydronium ions and hydroxide ions (credit: Chemistry (OpenStax), CC BY 4.0).

This type of reaction, in which a substance ionizes when one molecule of the substance reacts with another molecule of the same substance, is referred to as .

To visualize this process in a video simulation, watch Autoionization in Liquid Water (3 min 23s).

Video Source: Akumich (2012, February 22). Autoionization of liquid water. [Video]. YouTube.

Pure water undergoes autoionization to a very slight extent. Only about two out of every 109 molecules in a sample of pure water are ionized at 25 °C. The relationship between products and reactants of any reaction at equilibrium can be expressed by its equilibrium constant, K. The equilibrium constant for the ionization of water is called the :

[latex]\text{H}_2\text{O}(l)\;+\;\text{H}_2\text{O}(l)\;{\leftrightharpoons}\;\text{H}_3\text{O}^{+}(aq)\;+\;\text{OH}^{-}(aq)\\[0.7em] K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}][/latex]

The slight ionization of pure water is reflected in the small value of the equilibrium constant; at 25 °C, Kw has a value of 1.0 × 10−14. The process is endothermic, and so the extent of ionization and the resulting concentrations of hydronium ion and hydroxide ion increase with temperature. For example, at 100 °C, the value for Kw is about 5.6 × 10−13, roughly 50 times larger than the value at 25 °C.

Example 16.3a

Ion Concentrations in Pure Water

What are the hydronium ion concentration and the hydroxide ion concentration in pure water at 25 °C?

Solution

The autoionization of water yields the same number of hydronium and hydroxide ions. Therefore, in pure water, [H3O+] = [OH]. At 25 °C:

[latex]K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = [\text{H}_3\text{O}^{+}]^2 = [\text{OH}^{-}]^2 = 1.0\;\times\;10^{-14}[/latex]

So:

[latex][\text{H}_3\text{O}^{+}] = [\text{OH}^{-}] = \sqrt{1.0\;\times\;10^{-14}} = 1.0\;\times\;10^{-7}\;M[/latex]

The hydronium ion concentration and the hydroxide ion concentration are the same, and we find that both equal 1.0 × 10−7M.

Therefore, at 25 °C, Kw has a value of 1.0 × 10−14.

[latex]K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = 1.0\;\times\;10^{-14}[/latex]

The degree of autoionization of water and hence the value of Kw changes with temperature, so the equation

[latex]K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = 1.0\;\times\;10^{-14}[/latex]

is accurate only at room temperature. If a temperature is not given in a question, assume room temperature.

Exercise 16.3a

The ion product of water at 80 °C is 2.4 × 10−13. What are the concentrations of hydronium and hydroxide ions in pure water at 80 °C?

Check Your Answer[1]

Calculating Hydronium and Hydroxide Concentrations in Solutions using Kw

It is important to realize that the autoionization equilibrium for water is established in all aqueous solutions. Pure water is considered a . Adding an acid or base to water will not change the position of the equilibrium.

Ion Concentrations in Water

At 25°C,

  • In a neutral solution, the [H3O+] = [OH] = 1.0 x 10-7 M
  • In an acidic solution, the concentration of H3O+(aq) is greater than 1.0 x 10-7 M, and thus, its [OH] will be less than 1.0 x 10-7 M
    • In an acidic solution, the [H3O+] > [OH]
  • For basic solutions, the concentration of OH(aq) is greater than 1.0 x 10-7 M, and thus, its [H3O+] will be less than 1.0 x 10-7 M
    • In a basic solution, the [OH] > [H3O+]

However, remember the product of the two concentrations [H3O+][OH] is always equal to 1.0 x 10-14 M, no matter whether the aqueous solution is an acid, a base, or neutral:

Kw = [H3O+][OH] = 1.0 x 10-14 M

Consequently, if you know [H3O+] for a solution, you can use the Kw formula to calculate the [OH]. Alternatively, if you know [OH], you can calculate [H3O+]. This means in any given acid/base solution the two concentrations are inversely related: As one concentration increases, the other must decrease, so their product always equals the value of Kw.

Source: “Ion Concentrations in Water” by Jackie MacDonald, CC BY-NC-SA 4.0

Example 16.3b demonstrates the quantitative aspects of this relation between hydronium and hydroxide ion concentrations. At 25°C, [latex]K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = 1.0\;\times\;10^{-14}[/latex].

Example 16.3b

The Inverse Proportionality of [H3O+] and [OH]

A solution of carbon dioxide in water has a hydronium ion concentration of 2.0 × 10−6M. What is the concentration of hydroxide ion at 25 °C?

Solution

We know the value of the ion-product constant for water at 25 °C:

[latex]2\text{H}_2\text{O}(l)\;{\leftrightharpoons}\;\text{H}_3\text{O}^{+}(aq)\;+\;\text{OH}^{-}(aq)\\[0.7em] K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = 1.0\;\times\;10^{-14}[/latex]

Thus, we can calculate the missing equilibrium concentration.

Rearrangement of the Kw expression yields that [OH] is directly proportional to the inverse of [H3O+]:

[latex][\text{OH}^{-}] = \frac{K_{\text{w}}}{[\text{H}_3\text{O}^{+}]} = \frac{1.0\;\times\;10^{-14}}{2.0\;\times\;10^{-6}} = 5.0\;\times\;10^{-9}[/latex]

The hydroxide ion concentration in water is reduced to 5.0 × 10−9M as the hydrogen ion concentration increases to 2.0 × 10−6M. This is expected from Le Châtelier’s principle; the autoionization reaction shifts to the left to reduce the stress of the increased hydronium ion concentration and the [OH] is reduced relative to that in pure water.

A check of these concentrations confirms that our arithmetic is correct:

[latex]K_{\text{w}} = [\text{H}_3\text{O}^{+}][\text{OH}^{-}] = (2.0\;\times\;10^{-6})(5.0\;\times\;10^{-9}) = 1.0\;\times\;10^{-14}[/latex]

Exercise 16.3b

What is the hydronium ion concentration in an aqueous solution with a hydroxide ion concentration of 0.001 M at 25 °C?

Check Your Answer[2]

Exercise 16.3c

Practice using the following PhET simulation: pH Scale

Activity source: Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC-BY-4.0

Example 16.3c

For the following solutions, determine whether the solution is acidic, basic or neutral.

  1. A solution that has a [H3O+] = 3.5 x 10-3 M
  2. A solution that has a [OH] = 1.0 x 10-7 M
  3. A solution that has a [H3O+] = 3.5 x 10-12 M

Solution

  1. Since the solution’s [H3O+] of 3.5 x 10-3 M is greater than 1.0 x 10-7M, the solution is acidic.
  2. Since the solution’s [OH] of 1.0 x 10-7M is equal to 1.0 x 10-7M, the solution is neutral.
  3. Since the solution’s [H3O+] of 3.5 x 10-12 M is less than 1.0 x 10-7M, its [OH] will be greater 1.0 x 10-7M, which indicates the solution is basic.

Activity Source: “Example 16.3c” created by Jackie MacDonald is licensed under CC BY-NC-SA 4.0.

Exercise 16.3d

Check Your Learning Exercise (Text Version)

For the following solutions, determine whether the solution is acidic, basic or neutral.

  1. A solution that has a [H3O+] = 2.5 x 10-12 M
  2. A solution that has a [H3O+] = 9.0 x 10-4 M
  3. A solution that has a [H3O+] = 1.0 x 10-7 M
  4. A solution that has a [OH] = 1.0 x 10-9 M
  5. A solution that has a [OH] = 1.0 x 10-7 M
  6. A solution that has a [OH] = 4.8 x 10-2 M

Check Your Answer[3]

Source: “Exercise 16.3d” by Jackie MacDonald, licensed under CC BY NC SA 4.0.

Key Equations

  • Kw = [H3O+][OH] = 1.0 × 10−14 (at 25 °C)

Attribution & References

Except where otherwise noted, this page is adapted from “14.1 Brønsted-Lowry Acids and Bases” In General Chemistry 1 & 2 by Rice University, a derivative of Chemistry (Open Stax) by Paul Flowers, Klaus Theopold, Richard Langley & William R. Robinson and is licensed under CC BY 4.0. ​Access for free at Chemistry (OpenStax)

  1. [H3O+] = [OH] = 4.9 × 10−7M
  2. [H3O+] = 1 × 10−11M
  3. (1) Basic; (2) Acidic; (3) Neutral; (4) Acidic; (5) Neutral; (6) Basic

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Enhanced Introductory College Chemistry Copyright © 2023 by Gregory Anderson; Caryn Fahey; Jackie MacDonald; Adrienne Richards; Samantha Sullivan Sauer; J.R. van Haarlem; and David Wegman is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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