A metal ion in solution does not exist in isolation, but in combination with ligands (such as solvent molecules or simple ions) or chelating groups, giving rise to complex ions or coordination compounds.
These complexes contain a central atom or ion, often a transition metal, and a cluster of ions or neutral molecules surrounding it. Many complexes are relatively unreactive species remaining unchanged throughout a sequence of chemical or physical operations and can often be isolated as stable solids or liquid compounds.
Other complexes have a much more transient existence and may exist only in solution or be highly reactive and easily converted to other species.
All metals form complexes, although the extent of formation and nature of these depend very largely on the electronic structure of the metal.
The concept of a metal complex originated in the work of Alfred Werner, who in 1913 was awarded the first Nobel Prize in Inorganic chemistry. A description of his life and the influence his work played in the development of coordination chemistry is given by G.B. Kauffman in "Inorganic Coordination Compounds", Heyden & Son Ltd, 1981.
Complexes may be non-ionic (neutral) or cationic or anionic, depending on the charges carried by the central metal ion and the coordinated groups. The total number of points of attachment to the central element is termed the coordination number and this can vary from 2 to greater than 12, but is usually 6.
The term ligand (ligare [Latin], to bind) was first used by Alfred Stock in 1916 in relation to silicon chemistry. The first use of the term in a British journal was by H. Irving and R.J.P. Williams in Nature, 1948, 162, 746.
For a fascinating review of the origin and dissemination of the term 'ligand' in chemistry see: W.H. Brock, K.A Jensen, C.K. Jorgensen and G.B. Kauffman, Polyhedron, 2, 1983, 1-7.
Ligands can be further characterised as monodentate, bidentate, tridentate etc. where the concept of teeth (dent) is introduced, hence the idea of bite angle etc.
The term chelate was first applied in 1920 by
Sir Gilbert T. Morgan and H.D.K. Drew [J. Chem. Soc.,
1920, 117, 1456], who stated:
"The adjective chelate, derived from the great claw or
chela (chely- Greek) of the lobster or other
crustaceans, is suggested for the caliperlike groups which
function as two associating units and fasten to the central atom
so as to produce heterocyclic rings."
M + 4L → ML4then the larger the stability constant, the higher the proportion of ML4 that exists in the solution. Free metal ions rarely exist in solution so that M, will usually be surrounded by solvent molecules which will compete with the ligand molecules, L, and be successively replaced by them. For simplicity, we generally ignore these solvent molecules and write four stability constants as follows:
l. M + L → ML K1 = [ML] / [M] [L]where K1, K2 etc. are referred to as "stepwise stability constants".
2. ML + L → ML2 K2 = [ML2] / [ML] [L]
3. ML2 + L → ML3 K3 = [ML3] / [ML2] [L]
4. ML3 + L → ML4 K4 = [ML4] / [ML3] [L]
M + 4L → ML4 β4 = [ML4]/ [M] [L]4The stepwise and overall stability constants are therefore related as follows:
β4 =K1.K2.K3.K4 or more generally,If we take as an example, the steps involved in the formation of the cuprammonium ion, we have the following:
βn =K1.K2.K3.K4--------------K n
Cu2+ + NH3 ↔ Cu(NH3)2+ K1 = [Cu(NH3)2+]/[Cu2+] [NH3] CuNH32+ + NH3 ↔ Cu(NH3)22+ K2 = [Cu(NH3)22+]/[Cu(NH3)2+] [NH3]etc. where K1, K2 are the stepwise stability constants.
β4 = [Cu(NH3)42+]/[Cu2+] [NH3]4
The addition of the four ammine groups to copper shows a pattern
found for most formation constants, in that the successive
stability constants decrease. In this case, the four constants
are:
logK1 =4.0, logK2 =3.2, logK3 =2.7, logK4 =2.0 or logβ4 =11.9
A number of texts refer to the instability constant or
the dissociation constant of coordination complexes.
This value corresponds to the reciprocal of the
formation constant, since the reactions referred to are those
where fully formed complexes break down to the aqua ion and free
ligands.
It is usual to represent the metal-binding process by a
series of stepwise equilibria which lead to stability constants
that may vary numerically from hundreds to enormous values such
as 1035 and more.
That is 100,000,000,000,000,000,000,000,000,000,000,000.0
For this reason, they are commonly reported as logarithms.
so log10 (β) = log10 (1035) = 35.
It is additionally useful to use logarithms, since log(K) is directly
proportional to the free energy of the reaction.
It has been known for many years that a comparison of this
type always shows that the complex resulting from coordination
with the chelating ligand is much more thermodynamically
stable. This can be seen by looking at the values for
adding two monodentates compared with adding one bidentate, or
adding four monodentates compared to two bidentates, or adding
six monodentates compared to three bidentates.
| # of ligands | ΔG° (kJmol-1) | ΔH° (kJmol-1) | ΔS° (JK-1mol-1) | log β |
| 2 NH3(1 en) | -28.24 (-33.30) | -29.79 (-29.41) | -5.19 (+13.05) | 4.95 (5.84) |
| 4 NH3(2 en) | -42.51 (-60.67) | -53.14 (-56.48) | -35.50 (+13.75) | 7.44 (10.62) |
| # of ligands | log β | ΔG° (kJmol-1) |
| 2 py (1 bipy) | 3.5 (6.9) | -20 (-39) |
| 4 py (2 bipy) | 5.6 (13.6) | -32 (-78) |
| 6 py (3 bipy) | 9.8 (19.3) | -56 (-110) |
| # of ligands | log β | ΔG° (kJmol-1) |
| 1 NH3 | 2.8 | -16 |
| 2 NH3 (1 en) | 5.0 (7.51) | -28.5 (-42.8) |
| 3 NH3 | 6.6 | -37.7 |
| 4 NH3 (2 en) | 7.87 (13.86) | -44.9 (-79.1) |
| 5 NH3 | 8.6 | -49.1 |
| 6 NH3 (3 en) | 8.61 (18.28) | -49.2 (-104.4) |
In the case of complex formation of Ni2+ with ammonia or 1,2-diaminoethane, by rewriting the equilibria, the following equations are produced.
ΔG° = -2.303 RT log10 (K)Based on measurements made over a range of temperatures, it is possible to break down the ΔG° term into the enthalpy and entropy components. ΔG° = ΔH° - TΔS°
= -2.303 R T (18.28 - 8.61)
= -54 kJ mol-1
ΔH° = -29 kJ mol-1
- TΔS° = -25 kJ mol-1
and at 25C (298K)
ΔS° = +88 J K-1 mol-1
ΔG° = -67 kJ mol-1The conclusion they drew from these incorrect numbers was that the chelate effect was essentially an entropy effect, since the TΔS° contribution was nearly 5 times bigger than ΔH°.
ΔH° = -12 kJ mol-1
- TΔS° = -55 kJ mol-1
In fact, the breakdown of the ΔG° into ΔH° and
TΔS° shows that the two terms are nearly equal (-29 cf. -25 kJ mol-1)
with the ΔH° term a little bigger! The entropy term
found is still much larger than for reactions involving a
non-chelating ligand substitution at a metal ion.
How can we explain this enhanced contribution from entropy? One
explanation is to count the number of species on the left and
right hand side of the equation above.
It will be seen that on the left-hand-side there are 4 species,
whereas on the right-hand-side there are 7 species, that is a net
gain of 3 species occurs as the reaction proceeds. This can
account for the increase in entropy since it represents an
increase in the disorder of the system.
An alternative view comes from trying to understand how the
reactions might proceed. To form a complex with 6 monodentates
requires 6 separate favourable collisions between the metal ion
and the ligand molecules. To form the tris-bidentate metal
complex requires an initial collision for the first ligand to
attach by one arm but remember that the other arm is always going
to be nearby and only requires a rotation of the other end to
enable the ligand to form the chelate ring.
If you consider dissociation steps, then when a monodentate
group is displaced, it is lost into the bulk of the solution. On
the other hand, if one end of a bidentate group is displaced the
other arm is still attached and it is only a matter of the arm
rotating around and it can be reattached again.
Both sets of conditions favour the formation of the complex with
bidentate groups rather than monodentate groups.
For a problem relating to metal complex formation and calculations of thermodynamic values, try your hand at CALCULATION # TWO. Once again, further problems can be found in the Tutorial papers for this course.
To get a simplistic view of the replacement of ammonia groups
by 1,2-diaminoethane try downloading a movie clip (1.7 MB, .avi
format).
Note, for those linking in from off-campus this may not
be possible due to bandwidth and timeout problems!
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