Page 112 - Basic physical chemistry for the atmospheric sciences

98 Basic physical chemistry

[HA]initial = [HA(aq)] + [ A - (aq)] (5.35)
where [HA] initial is the amount of acid in the water before any dissocia­
tion occurs, and [HA(aq)] and [A - (aq)] are the equilibrium concentra­
tions of HA(aq) and A - ( aq) in Reaction (5. 3 1 ) . Note that Eq. (5 . 3 5) is
written as an approximate relation because it assumes that the mass of
-
hydrogen atoms that have dissociated from the A ( aq) is small com­
pared to the masses of the species in Eq. (5.35). Equation (5.35) is
called the mass balance relation.
The fourth relationship between the concentrations of the species in
Reactions (5 . 3 I ) and (5.32) expresses the fact that the solution is
electrically neutral ; therefore, the total concentration of positive ions
must equal the total concentration of negative ions

[Hp + (aq)] = [ A - (aq)] + [OH - ( aq)] (5 .36)

This is called the charge balance relation. In practice, the solution of
s
Eq . (5 . 3 3) through (5 .36) may involve some laborious algebra, but
judicious approximations can often simplify the solution, as illustrated
in the next section.

5 . 1 2 The pH of rainwater
5
Exercise . 2 suggested that the absorption of C02 in rainwater to form
a weak solution of carbonic acid would give natural rainwater a pH of
about . 6 . We can now consider this exercise quantitatively by using
5
i
some of the concepts just n troduced.
As we have seen, carbonic acid is polyprotic
H2C0 (aq) + H20(l ) µ H C0 3 ( aq) + H 3 0 + ( aq) (5 .37)
3
HC0 3 (aq) + H20(l) µ C05 - ( aq) + H3Q + (aq) (5.38)

with successive acid-dissociation constants at 25°C of Kai = 4 . 2 x 1 0 - 7
and Ka = 2 5 .0 x 1 0 - 1 1 • Therefore,

[H 3 0 + (aq)][HC03 (aq)]
[H 2COiaq) ] = K ai = 4 . 2 x 1 0 - 1 (5 . 3 9)

and,

(5 .40)