Page 168 - Modern Analytical Chemistry

1400-CH06 9/9/99 7:40 AM Page 151

Chapter 6 Equilibrium Chemistry 151

Finally, replacing the negative log terms with p-functions and rearranging leaves us
with
F [ – ]
pH = p a +log 6.31
K
[ HF]
F –
Examining equation 6.31 tells us a great deal about the relationship between
–
pH and the relative amounts of F and HF at equilibrium. If the concentrations of
–
F and HF are equal, then equation 6.31 reduces to
–4
pH=pK a,HF = –log(K a,HF ) = –log(6.8 ´10 ) = 3.17 pH pH = pK a,HF = 3.17
–
For concentrations of F greater than that of HF, the log term in equation 6.31 is
positive and
HF
or pH > 3.17
pH>pK a,HF
This is a reasonable result since we expect the concentration of hydrofluoric acid’s
–
conjugate base, F , to increase as the pH increases. Similar reasoning shows that the
–
concentration of HF exceeds that of F when
or pH < 3.17
pH < pK a,HF Figure 6.4
Ladder diagram for HF, showing areas of
Now we are ready to construct the ladder diagram for HF (Figure 6.4).
–
predominance for HF and F .
The ladder diagram consists of a vertical scale of pH values oriented so that
smaller (more acidic) pH levels are at the bottom and larger (more basic) pH
levels are at the top. A horizontal line is drawn at a pH equal to pK a,HF . This line,
or step, separates the solution into regions where each of the two conjugate forms
of HF predominate. By referring to the ladder diagram, we see that at a pH
of 2.5 hydrofluoric acid will exist predominately as HF. If we add sufficient base
to the solution such that the pH increases to 4.5, the predominate form be-
–
comes F .
NH
Figure 6.5 shows a second ladder diagram containing information about 3
+
–
HF/F and NH 4 /NH 3 . From this ladder diagram we see that if the pH is less
+
than 3.17, the predominate species are HF and NH 4 . For pH’s between 3.17
+
–
and 9.24 the predominate species are F and NH 4 , whereas above a pH of pH = pK a,NH 3 = 9.24
–
9.24 the predominate species are F and NH 3 .
Ladder diagrams are particularly useful for evaluating the reactivity of
acids and bases. An acid and a base cannot coexist if their respective areas of
F –
predominance do not overlap. If we mix together solutions of NH 3 and HF, NH 4 +
the reaction
+
–
HF(aq)+NH 3 (aq) t NH 4 (aq)+F (aq) 6.32
pH
pH = pK a,HF = 3.17
occurs because the predominance areas for HF and NH 3 do not overlap. Be-
fore continuing, let us show that this conclusion is reasonable by calculating
the equilibrium constant for reaction 6.32. To do so we need the following
three reactions and their equilibrium constants. HF
+
–
aq
.
HF() + H O( ) l t H O () + F () K a = 68 ´ 10 –4 Figure 6.5
aq
aq
3
2
Ladder diagram for HF and NH 3 .
–

+
NH () + H O( ) l t OH () + NH () K b = 175 ´ 10 –5
.
aq
aq
aq
3
2
4
–
+
aq
l
aq
HO () + OH () t 2 H O( ) K = 1 = 1
3
2
K w . 100 ´10 –14