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‘STRONG’ AND ‘WEAK’ ACIDS AND BASES 259

Multiplying the expressions for K a and K b yields
−
+
−
[A ][H 3 O ] [HA][OH ]
K a × K b = ×
[HA] [A ]
−
−
+
−
TheHAandA terms clearly cancel to yield [H 3 O ][OH ], which is K w .
Why doescarbonicacid behaveasamono-proticacid?

Variations in the value of K a
Carbonic acid, H 2 CO 3 , is naturally occurring, and forms when carbon dioxide from
the air dissolves in water. From its formula, we expect it to be a di-protic acid, but
it is generally classed as mono-protic. Why?
In water at 298 K, the ionization reaction follows the equation
+
H 2 CO 3(aq) + H 2 O −−→ HCO − + H 3 O (aq) (6.37)
3(aq)
−7
The value of K a for the reaction in Equation (6.37) is 4.3 × 10 , so carbonic acid is
−
certainly a very weak acid. The hydrogen carbonate anion HCO 3 could dissociate
further, according to
−
+
HCO 3(aq) + H 2 O −−→ CO 2− + H 3 O (aq) (6.38)
3(aq)
but its value of K a is low at 5.6 × 10 −11 , so we conclude that the HCO ion is too
−
3
weak an acid to shed its proton under normal conditions. Thus, carbonic acid has two
protons: the loss of the first one is relatively easy, but the proportion of molecules
losing both protons is truly minute. Only one of the protons is labile.
This situation is relatively common. If we look, for example, at the values of
K a in Table 6.5, we see that phosphoric acid is a strong acid insofar as the loss of
−3
the first proton occurs with K a = 7.5 × 10 , but the loss of the second proton, to
−8
2−
form HPO , is difficult, as characterized by K a = 6.2 × 10 . In other words, the
4
−
dihydrogen phosphate anion H 2 PO is a very weak acid. And the hydrogen phosphate
4
di-anion HPO 2− has a low a value of K a = 2.2 × 10 −11 , causing us to say that the
4
PO 3− anion does not normally exist. Even the loss of the second proton of sulphuric
4
−2
acid is characterized by a modest value of K a = 10 .
This formal definition of K a can be extended to multi-protic Multi-protic acids have
acids. We consider the dissociation to occur in a step-wise manner, a different value of K a
the acid losing one proton at a time. Consider, for example, the for each proton dona-
two-proton donation reactions of sulphuric acid: tion step, with the
values of K a decreas-
+
(1) H 2 SO 4 −−→ H + HSO −
4 ing with each proton
donation step.
+
−
(2) HSO 4 −−→ H + SO 2−
4