0.9 Bis2a 02.appendix ii detailed look at acid-base equilibrium  (Page 4/8)

We note that the function K in [link] is approximately, though only approximately, the same for all conditions analyzed in [link] . Variation of the concentration by a factor of 1000 produces a change in K of only 10%to 15%. Hence, we can regard the function K as a constant which approximately describes the acid ionizationequilibrium for nitrous acid. By convention, chemists omit the constant concentration of water from the equilibrium expression,resulting in the acid ionization equilibrium constant , K _a , defined as:

From an average of the data in [link] , we can calculate that, at 25°C for nitrous acid,K _a = 5 × 10 ^–4 . Acid ionization constants for the other weak acids in [link] are listed in [link] .

We make two final notes about the results in [link] . First, it is clear the larger the value ofK _a , the stronger the acid. That is, whenK _a is a larger number, the percent ionization of the acid is larger, and vice versa. Second, the values ofK _a very over many orders of magnitude. As such, it is often convenient to define the quanitypK _a , analogous to pH, for purposes of comparing acid strengths:

The value of pK _a for each acid is also listed in [link] . Note that a small value of pK _a implies a large value of K _a and thus a stronger acid. Weaker acids have larger values of pK _a . K _a and pK _a thus give a simple quantitative comparison of the strength of weak acids.

Observation 3: autoionization of water

Since we have the ability to measure pH for acid solutions, we can measure pH for pure water as well. It mightseem that this would make no sense, as we would expect [H ₃ O ⁺ ] to equal zero exactly in pure water. Surprisingly, this isincorrect: a measurement on pure water at 25°C yields pH,so that [H ₃ O ⁺ ] = 1.0 × 10 ^–7 M. There can be only one possible source for these ions: watermolecules. The process

is referred to as the autoionization of water. Note that, in this reaction, some water molecules behave as acid, donating protons, while otherwater molecules behave as base, accepting protons.

Since at equilibrium [H ₃ O ⁺ ] = 1.0 × 10 ^–7 M, it must also be true that[OH ^– ] = 1.0 × 10 ^–7 M . We can write the equilibrium constant for [link] , following our previous convention of omitting the pure water from the expression, and we find that,at 25°C,

(In this case, the subscript "w" refers to "water".)

[link] occurs in pure water but must also occur when ions are dissolved inaqueous solutions. This includes the presence of acids ionized in solution. For example, we consider a solution of 0.1M acetic acid.Measurements show that, in this solution [H ₃ O ⁺ ] = 1.3 × 10 ^–3 M and[OH ^– ] = 7.7 × 10 ^–12 M. We note two things from this observation: first, the value of[OH ^– ] is considerably less than in pure water; second, the autoionizationequilibrium constant remains the same at 1.0 × 10 ^–14 . From these notes, we can conclude that the autoionizationequilibrium of water occurs in acid solution, but the extent of autoionization is suppressed by the presence of the acid insolution.