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Encyclopedia of Physical Science and Technology EN003D-147 June 13, 2001 22:58

742 Coordination Compounds

+
pM n+ + qL + rH [M p L q H r ] (7) formation of M(NH 3 ) 6 decrease (electrical charge on ions

is omitted):
is written

MW(NH 3 ) 5 + NH 3 M(NH 3 ) 6 + W (18)
+ r
q
p
β pqr = [M p L q H r ]/[M] [L] [H ] (8) M + L ML (19)

For example, K 110 = [ML]/[M][L] (20)

ML + L ML 2 (21)
Ag 2+ (aq) + 4C 5 H 5 N (aq) [Ag(C 5 H 5 N) ] 2+ (aq) (9)

4
K 120 = [ML 2 ]/[ML][L] (22)
2+
β 140 = [Ag(C 5 H 5 N) 4 ]/[Ag ][C 5 H 5 N] 4 (10)
(23)
ML 2 + L ML 3
log β 140 = 25 (11)
K 130 = [ML 3 ]/[ML 2 ][L] (24)
These overall stability constants describe only the equi-
So K 110 > K 120 > K 130 on these statistical grounds.
librium of a given stochiometric composition of formation
Furthermore, if we consider a similar series [Eqs. (25)–
of a complex and do not, for example, distinguish between
(28)] in which the ligand is an anion, carrying a negative
the forms of [MW 4 A 2 ] above [the trans (7) and the cis (8)].
charge, we can see a similar trend due to the effect of
These are macroconstants and are a weighted sum of the
charge neutralization (here the ionic charges are printed):
individual microconstants. For example, the macrocon-
−

stantβ 120 forEq.(12)ismadeupofthetwomicroconstants M n+ + L (ML) (n−1)+ (25)
β 120(cis) [Eq. (13)] and β 120(trans) [Eq. (14)]:
K 110 = [ML] (n−1)+ /{[M] }[L ] (26)
−
n+

Ni 2+ (aq) + 2NH 3 [Ni(NH 3 ) 2 (H 2 O) 4 ] 2+ (12) (ML) (n−1)+ + L (ML 2 ) (n−2)+ (27)
−

Ni 2+ (aq) + 2NH 3 cis-[Ni(NH 3 ) 2 (H 2 O) 4 ] 2+ (13) K 120 = [ML 2 ] (n−2)+ [ML] (n−1)+ [L ]

−

Ni 2+ (aq) + 2NH 3 trans-[Ni(NH 3 ) 2 (H 2 O) 4 ] 2+ (14) (28)
The first stepwise complexation, in Eq. (25), involves the
The constant describing the equilibrium [Eq. (15)] be-
neutralization, by mutual Coulombic attraction, of the full
tween the forms with the same stoichiometry is simply
+
n charge of the metal ion by the single negative charge
Eq. (16).
of L . However, for the second step, in Eq. (27), the
−
Coulombic interaction is smaller, now being between the
cis-[M(NH 3 ) 2 (H O ) 4 ] 2+ trans-[M(NH 3 ) 2 (H 2 O) 4 ] 2−

same single negative charge on L and the less intensely
−
(15)
charged (ML) species, with only (n − 1) charge. Typi-
n−
3−
−
−
(16) cally, if M were Al , and L were F , the attraction
K isom = [trans]/[cis] = β 120(trans) β 120(cis)
in Eq. (25) would be between a 3+ and a 1− pair, but that
Reverting to the ammine system above, if everything in Eq. (27) would be between the 2− of [AlF] 2− and the
else were unchanged (if A and W had an equal chance 1− of the fluoride ligand.
of being attached to M), then the statistical proportions In the final stages of stepwise coordination, the nega-
shown would apply. Furthermore, if the probability were tively charged anionic ligand is being added to an already
the same of attaching an ammonia to the metal and remov- negatively charged metal species. The Pauling electroneu-
ing it from the metal, then we would expect the probability trality principle reminds us that ligands will add readily
of complexing to be 36 times greater for the first substitu- only until the affinity for electrons of the central metal ion
tion of water by ammonia [Eq. (17)]: is essentially satisfied.
Thus, on the grounds both of statistics and of charge

MW 6 + NH 3 M(NH 3 )W 5 + W (17) interaction, the order K 11 > K 12 > K 13 > ··· K 1n is ex-
pected (and almost always observed). Table I lists some
(six equivalent ways forward, only one back) than for examples.
replacing the final water ligand by a sixth ammonia If there is a departure from this order or a sharp, distinct
[Eq. (18)] (only one possible place where the water can irregularity, something in the system has changed, often
be replaced by ammonia and six ways back where any of the coordination number of the metal ion. For example,
3+
−
the six ammonia ligands can be replaced by water). On with Cl + Fe , K 11 , K 12 , and K 13 decrease steadily but
these grounds, the stepwise equilibrium constants for the K 14 shows a sudden drop. This suggests that the octahedral