Page 106 - Basic physical chemistry for the atmospheric sciences

92 Basic physical chemistry

C2 H302(aq) + H30 + ( a ) ? H20(1) + HC2 H30z(aq) (5.23)
q
2H20(1) ? H30 + (aq) + OH - (aq) (5.24)

which is Reaction (5. 2 0). [We see from Reaction (5 . 19) that
HC2H302(aq) is the conjugate acid of C2H30 2(aq), because the ion
.
H
can be converted to the acid by attaching an + ( aq) ] Similar y , from
l
Reaction (5. 2 0), the acetate ion, C2H30 2(aq), is the conjugate base of
acetic acid, HC 2 HP2(aq). )
The equilibrium constant for the forward reaction of (5.23) is 1/Ka,
where Ka is the acid-dissociation (or ionization) constant of acetic
acid. Also, the equilibrium constant for the forward reaction of (5.24)
is the ion-product constant for water (Kw). Since the equilibrium
constant for a net reaction is equal to the product of the equilibrium
constants for the individual reactions (see Exercise l . 14c , the equilib­
)
rium constant for Reaction (5.20), namely Kh, is given by

(5.25)

Equation (5. 2 5) is a general relation. It shows that salts associated
with weak acids (low values of K,J and strong bases [e .g. , the acid
associated with sodium acetate is acetic acid, which is weak, and the
base associated with sodium acetate is OH -(aq), which is strong]
s
hydrolyze to produce basic solutions with large Kh value . For such
salts, it is the anion that hydrolyzes [e.g . , C2H30 2(aq) in Reaction
(5.20)] to produce the OH -(aq) ions. 5 Similarly, salts that form the
conjugates of strong acids and weak bases (e.g. , NH4Cl) hydrolyze to
produce acidic solutions with large Kh values ( = Kwl Kb, where Kb is
the base-dissociation constant). For such salts, it is the cation that
hydrolyzes [e.g. , NH ! ( aq) for NH4Cl] to produce the H30 + (aq) ions .
Salts that form the conjugates of strong acids and strong bases (e.g. ,
i
NaCl) do not u n dergo hydrolys s , so they produce solutions with pH
= 7 . If a salt forms the conjugates of a weak acid and a weak base,
the solution will be neutral, acidic, or basic depending on the relative
values of Ka and Kb.
Exercise 5 .3 . What is the pH of a 0. 1 0 M solution of NH4CI if the
base-dissociation constant for NH3 is 1 . 8 x 1 0 - 5 7 What fraction of the
NH4CI is hydrolyzed?
Solution. As noted above, NH4 CI dissolves to form the conjugates