0.21 Acid ionization equilibrium  (Page 4/7)

We make two final notes about the results in Table 5. First, it is clear the larger the value of K _a , the stronger the acid. That is, when K _a is a larger number, the percent ionization of the acid is larger, and vice versa. Second, the values of K _a vary over many orders of magnitude. As such, it is often convenient to define the quanity pK _a , analogous to pH, for purposes of comparing acid strengths:

pK _a = -log ₁₀ K _a

The value of pK _a for each acid is also listed in Table 5. 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 might seem that this would make no sense, as we would expect [H ₃ O ⁺ ] to equal zero exactly in pure water. Surprisingly, this is incorrect: a measurement on pure water at 25 ºC yields pH = 7, so that [H ₃ O ⁺ ] = 1.0·10 ^-7 M. There can be only one possible source for these ions: water molecules. The process

H ₂ O(l) + H ₂ O(l) → H ₃ O ⁺ (aq) + OH ^- (aq)

is referred to as the "autoionization" of water. Note that, in this reaction, some water molecules behave as acid, donating protons, while other acid 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 Reaction (6), following our previous convention of omitting the pure water from the expression, and we find that, at 25 ºC,

K _w = [H ₃ O ⁺ ][OH ^- ] = 1.0·10 ^-14

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

Reaction (6) occurs in pure water but must also occur when ions are dissolved in aqueous solutions. This includes the presence of acids ionized in solution. For example, we consider a solution of 0.1 M 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 autoionization equilibrium constant remains the same at 1.0·10 ^-14 . From these notes, we can conclude that the autoionization equilibrium of water occurs in acid solution, but the extent of autoionization is suppressed by the presence of the acid in solution.

We consider a final note on the autoionization of water. The pH of pure water is 7 at 25 ºC. Adding any acid to pure water, no matter how weak the acid, must increase [H ₃ O ⁺ ], thus producing a pH below 7. As such, we can conclude that, for all acid solutions at 25 ºC, their pH is less than 7, or in other words, any solution with pH less than 7 is acidic.

Observation 4: base ionization, neutralization and hydrolysis of salts

We have not yet examined the behavior of base molecules in solution, nor have we compared the relative strengths of bases. We have defined a base molecule as one which accepts a positive hydrogen ion from another molecule. One of the most common examples is ammonia, NH ₃ . When ammonia is dissolved in aqueous solution, the following reaction occurs: