pK_a

The pK_a of an acid is the negative logarithm of its acid dissociation constant. Just as pH can be used to describe the hydrogen ion concentration of a solution, pK_a can be used to describe the dissociation constant of a weak acid. The higher the pK_a of an acid, the weaker is the acid.

Table 12.7 repeats the weak acids listed in Table 12.4 and gives the pK_a of each. Notice that the acids with larger ionization constants have smaller pK_a's.

**TABLE 12.7**
The pK_a of some weak acids
Weak acid	K_a	pK_a
acetic acid	1.8 X 10^-5	4.74
formic acid	1.8 X 10^-4	3.74
nitrous acid	4.6 X 10^-4	3.34
hydrocyanic acid	4.9 X 10^-10	9.31
carbonic acid: K_a₁	4.3 X 10^-7	6.37
K_a₂	5.6 X 10^-11	10.25
phosphoric acid:K_a₁	7.5 X 10-3	2.12
K_a₂	6.2 X 10^-8	7.21
K_a₃	2.2 X 10^-13	12.67
ammonium ion	5.5 X 10^-10	9.26

For example, formic acid (K_a = 1.8 X 10^-4) is a stronger acid than acetic acid (K_a = 1.8 X 10^-5). The pK_a of formic acid is 3.74, a smaller number than 4.74, the pK_a of acetic acid. Notice too that, for the polyprotic acids, the pK_a increases with each ionization. For example, the pK_a for the first ionization of phosphroic acid:

H₃PO₄ H⁺ + H₂PO₄^- pK_a = 2.12

is much smaller than that of the second ionization:

H₂PO₄^- H⁺ + HPO₄^2- pK_a = 7.21

Phosphoric acid is a much stronger acid and therefore much more completely ionized in solution than the dihydrogen phosphate ion.

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