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7.5: Autoionization of Water

  • Page ID
    221511
  • Learning Objectives

    • Describe the autoionization of water.
    • Calculate the concentrations of H+ and OH in solutions, knowing the other concentration.

    We have already seen that H2O can act as an acid or a base:

    NH3 + H2O → NH4+ + OH (H2O acts as an acid)

    HCl + H2O → H3O+ + Cl (H2O acts as a base)

    It may not be surprising to learn, then, that within any given sample of water, some H2O molecules are acting as acids, and other H2O molecules are acting as bases. The chemical equation is as follows:

    H2O + H2O → H3O+ + OH

    This occurs only to a very small degree: only about 6 in 108 H2O molecules are participating in this process, which is called the autoionization of water. At this level, the concentration of both H+(aq) and OH(aq) in a sample of pure H2O is about 1.0 × 10−7 M. If we use square brackets—[ ]—around a dissolved species to imply the molar concentration of that species, we have

    [H+] = [OH] = 1.0 × 10−7 M

    for any sample of pure water because H2O can act as both an acid and a base. The product of these two concentrations is 1.0 × 10−14:

    [H+] × [OH] = (1.0 × 10−7)(1.0 × 10−7) = 1.0 × 10−14

    In acids, the concentration of H+(aq)—[H+]—is greater than 1.0 × 10−7 M, while for bases the concentration of OH(aq)—[OH]—is greater than 1.0 × 10−7 M. However, the product of the two concentrations—[H+][OH]—is always equal to 1.0 × 10−14, no matter whether the aqueous solution is an acid, a base, or neutral:

    [H+][OH] = 1.0 × 10−14

    This value of the product of concentrations is so important for aqueous solutions that it is called the autoionization constant of water and is denoted Kw:

    Kw = [H+][OH] = 1.0 × 10−14

    This means that if you know [H+] for a solution, you can calculate what [OH] has to be for the product to equal 1.0 × 10−14, or if you know [OH], you can calculate [H+]. This also implies that as one concentration goes up, the other must go down to compensate so that their product always equals the value of Kw.

    Example \(\PageIndex{1}\):

    What is [OH] of an aqueous solution if [H+] is 1.0 × 10−4 M?

    Solution

    Using the expression and known value for Kw,

    Kw = [H+][OH] = 1.0 × 10−14 = (1.0 × 10−4)[OH]

    We solve by dividing both sides of the equation by 1.0 × 10−4:

    \[\left [ OH^{-} \right ]=\frac{1.0\times 10^{-14}}{1.0\times 10^{-4}}=1.0\times 10^{-10}M\nonumber \]

    It is assumed that the concentration unit is molarity, so [OH] is 1.0 × 10−10 M.

    Exercise \(\PageIndex{1}\)

    What is [H+] of an aqueous solution if [OH] is 1.0 × 10−9 M?

    Answer

    1.0 × 10−5 M

     

    Summary

    In any aqueous solution, the product of [H+] and [OH−] equals \(1.0 \times 10^{−14}\) (at room temperature).