Bioinorganic Chemistry
645
An advantage of such a comparison is that
it greatly reduces the overlooked effect of a
reduction in coordination number from
the aqueous ion for several soft metal
ions in augmenting stability constants by
powers of ten. Similarly, we may compare
the hardness of a ligand by considering the
substitution on the ligand of one metal ion
for another
MX
+
N
−−−→
←−−−
M
+
NX
f
o
rw
h
i
c
ht
h
ef
r
e
ee
n
e
r
g
yc
h
a
n
g
ei
s
proportional
to
log
K
NX
log
K
MX
.B
y
considering such substitution reactions,
one gains consistency in application of
the principle of hard and soft acids and
bases. The scales presented are practical
scales dependent only upon experimental
stability constants determined in aqueous
solutions, and they do not involve any
other quantities such as electron afFnities
and other parameters from gas-phase
reactions, heats of hydration, or heats
of reaction. Nor do the scales presented
assume
a
model
or
rely
on
derived
parameters with arbitrary scaling. The
practical scales probably represent what
most investigators imply when they make
comparisons using the terms
hardness
and
softness
.
8.3
Metal-ion Scales
Of two scales involving oxygen and ni-
trogen donors hydroxide–ammonia and
acetate–ammonia, only the latter is de-
scribed here. As an oxygen donor ligand,
hydroxide may not be typical (see be-
low), and for applications acetate may
offer a more representative oxygen donor
ligand than hydroxide. Acetate–ammonia
stability-constant log differences for 22
metal
ions
and
the
proton
are
or-
dered in the following acetate–ammonia
(O–N) scale, with the differences in paren-
theses. The scale spans 8.0 log units
and each of the 8 greater than signs
indicates
a
factor
of
near
10.
Pear-
son’s hard metal ions appear in nor-
mal type, borderline in bold, and soft
in italics.
Sc(2.8
)>
La(1.6), Ce(1.5), Y(1.3),
Lu(1.2
)>
Tl
(
I
)
(0.8), Ca(0.7), Li(0.6),
Pb
(0.6), Mg(0.3
)>
±e(III)(
0.4),
Mn(
0.4), In(
0.5
)>
Co
(
1.0),
Cd
(
1.1),
Zn
(
1.2
)>
Ni
(
2.0),
Cu
(
2.3
)>
Ag
(
2.9),
Tl(III)
(
2.9)
>
CH
3
Hg
+
(
4.1), H
+
(
4.5)
>
Hg
(
5.2).
O–N scale
Metal ions favoring acetate appear at the
beginning of the O–N scale and those
favoring ammonia at the end. Of the Frst
13 metal ions, 11 are hard, but in this group
there is 1 soft (Tl
+
) and 1 borderline (Pb
2
+
)
metal ion. Next, a group of 4 borderline
metal ions also contains 1 soft metal ion
(Cd
2
+
). The scale ends with four soft metal
ions but also with the hard proton.
Unfortunately, it is impossible to de-
velop a comparable hardness scale with
unidentate sulfur donor ligands as very few
reliable experimentally determined stabil-
ity constants are available. Polymerization
has gone unrecognized in many of the
determinations. Many of the constants
involve chelate rings that introduce the
additional variable of chelate ring bite size
with metal ions of varying radii. Ag
+
and
Hg
2
+
prefer linear coordination making
formation of Fve- and even six-membered
chelate rings highly strained. ±or this rea-
son, unidentate ligands are the focus of
this article.
By
relaxing
the
requirement
for
unidentate ligands, we may compare the
tendency of some metal ions to bind
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