# 7.2.1: Trends in M-L stability (Thermodynamics)


In the context of inorganic chemistry, the sub-field of thermodynamics focuses on how stable or unstable a metal-ligand complex is. This is directly related to the equilibrium constant associated with forming the metal-ligand complex.

## What factors give rise to stability?

We have discussed the trend in stability associated with the chelate effect in a earlier section. The chelate effect is an important and significant factor in determining complex stability. This page will summarize trends in metal-ligand complex stability in the absence of the chelate effect.

### Electrostatics (charge density):

When comparing metal complexes with identical ligand sets, the stability correlates with charge density of the metal ion. The more highly-charged the metal ion is, and the higher its charge density, the more attracted it will be to the ligands, and the more stable the resulting complex becomes.

##### Exercise $$\PageIndex{1}$$

Arrange the following sets of ions according to charge density and expected stability of their hexaaquo complexes.

a) $$Ba^{2+}, Ca^{2+}, Sr^{2+}$$

b) $$Al^{3+}, Li^+, Mg^{2+}$$

This is a series of ions with the same charge and in the same column of the periodic table.

This is a series of ions that are spread across the periodic table. They have similar size but different charges.

### Hard-Soft Acid-Base Character

The hard-soft character of the ligand donor atoms and the metal ion contributes to stability.

### Ligand Field Stabilization Energy

The Irving-Williams series is an observed trend in the stabilities of the divalent (+2) transition metal ions; the trend holds for any set of ligands. For the reaction of the metal hexaaquo complex with any ligand:

$[M(OH_2)_6]^{2+} + L \rightleftharpoons [M(OH_2)_5L]^{2+} + H_2O$

The observed trend in the equilibrium constant for formation of the M-L complex, $$K_{f}$$, (the Irving-Williams series) is:

$Mg^{2+} < Mn^{2+} < Fe^{2+} < Co^{2+} < Ni^{2+} < Cu^{2+} > Zn^{2+}$

This trend can be expanded to include divalent alkali metals:

$Ba^{2+} < Sr^{2+} < Ca^{2+} < Mg^{2+} < Mn^{2+} < Fe^{2+} < Co^{2+} < Ni^{2+} < Cu^{2+} > Zn^{2+}$

This trend also holds for substitution by additional ligands as well as for chelating ligands.

Notice that the metal ions listed above are all $$M^{2+}$$ alkali metals or 3d-transition metals. As written above, from left to right in this series, size decreases while charge remains the same. This means that there should be an increase in charge density across this series, and thus a steady increase in affinity. However, electrostatics alone cannot explain the observed relative stabilities within the Irving-Williams series; the metals $$Fe^{2+}, Co^{2+}, Ni^{2+}$$, and $$Cu^{2+}$$ have significant increases in their $$K_f$$ values compared to the values that would be expected based on electrostatics alone. This increase in $$K_f$$ is proportional to the LFSE value for each ion's d-electron count. The $$K_f$$ values for $$Cu^{2+}$$ are an anomaly, and are unusually high due to additional stability by LFSE due to Jhan-Teller distortion.

The Irving-Williams series can only be explained using a combination of electrostatics and LFSE.