**Chemistry is principally of Ln**^{3+}
##### Why the prevalence of oxidation state III (Ln^{3+})?#### Examine Thermodynamic Parameters:**I**_{1/2/3/4 }**D**_{atm}**H**_{ }**D**_{hyd}**H(Ln**^{3+}**)**_{ }** ****D**_{L}**H(LnX**_{3}**)**
these values are available in a Table(import DHatm from larger table for web!) **Ionization**
For any given Lanthanide - As successive electrons are removed from neutral Ln the
**stabilizing effect** on the orbitals is related to their **principal quantum number**, **4f > 5d > 6s**. - For
**Ln**^{2+} {*except for La & Gd*} the configuration is** [Xe]4f**^{n} - For
**Ln**^{3+} the configuration is always ** [Xe]4f**^{n}the 4f binding energy is so great that remaining 4f electrons are regarded as "*core-like*" (i.e. incapable of modification by *chemical means*) (except Ce) - Note that as a rule of thumb:
**I**_{4}** ~ 2 I**_{3}** ~ 4 I**_{2}** ~ 8 I**_{1}Þ **I**_{4}** > (I**_{1}** + I**_{2}** + I**_{3 }**)** Therefore in almost all cases **Ln**^{3+}** provides the best energetics**
Observing trends across the Lanthanide Series - The general trend is for increasing ionization energies with increasing Z (
*i.e.* with increase in Z_{eff}) - Marked
**Half-Shell Effects** - **magnitude ****‚**** as n in I**_{n}** ****‚** - Also
**Quarter**/**Three-Quarter** **Shell Effects** (compare with transition metals - these are not seen clearly with d^{n} configurations) *Explanation?*: interelectronic repulsion is related not just to electron *pairing* but also to *angular momentum* of the electrons
*e.g.* in Pr^{2+} (4f^{3}) **Æ** Pr^{3+} (4f^{2}) ionization removes repulsion between e^{-} of *like* rotation, whereas Pm^{2+} (4f^{4}) **Æ** Pm^{3+} (4f^{3}) removes the stronger repulsion between e^{-} of *unlike* rotation (Þ latter Ionization Energy is correspondingly lower - hence the local minimum in the I_{3} graph at Pm)
The *three-quarter effect is the bigger*: interelectronic repulsion is bigger in smaller Ln^{n+}
**Atomization**
**D**_{atm}**H** follows the **inverse trend to** **I**_{3} {and therefore also to (I_{1} + I_{2} + I_{3 }) }
Þ *metallic bonding is correlated with ease of ionization to Ln*^{3+} statethis trend is modified slightly due to the different structures of the Ln metals
#### Some Thermodynamic Observations (*Ionic Model style*)### The **trends** in the formation of Ln^{III}**Formation of Compounds** {**D**_{f}**H(LnX**_{3}(s)**)**} *or*** Ln**^{3+}**(aq)** {**E°(Ln**^{3+}**(aq)****/Ln****(s)****)**}
depend on the balance between: Energy Supplied to effect Ln(s) **Æ** Ln(g) **Æ** Ln^{3+}(g) + 3e^{-}_{}^{ }**[****D**_{atm}**H + I**_{1}** + I**_{2}** + I**_{3}**]** versus Energy gained from Ln^{3+}(g) + 3X^{-}(g) **Æ** LnX_{3}(s) **[****D**_{L}**H(LnX**_{3}(s)**)]** or Ln^{3+}(g) **Æ** Ln^{3+}(aq) **[****D**_{hyd}**H(Ln**^{3+})] The energies determining trends in **E°(Ln**^{3+}**(aq)****/Ln****(s)****)** are graphed below: Production of Ln^{3+}(g) shows Hydration Energy of Ln^{3+} (also Lattice Energies of LnX_{3}(s)) shows - only a smooth ionic-
**size-based trend** (the trend based on Z_{eff}) and no shell structure effects
Balance of trends in Ionization + Atomization Energies with Hydration (Lattice) Energy **removes size effects****leaves only the Shell effects** - see values of D_{f}H(Ln^{3+}(aq))
** **
**Overall: ****The most important energy correlations are with I**_{3}
##### "exceptions to +3 rule" can also be rationalized### Occurrence of +4 oxidation statepredicted from ^{ }**[****D**_{atm}**H + I**_{1}** + I**_{2}** + I**_{3}** + I**_{4}**]** which follows trends in **I**_{4} **Ce, Pr ****Æ**** Ce**^{4+} [4f^{0}], Pr^{4+} [4f^{1}] ~ early in series 4f orbitals still comparatively high in energy**Tb ****Æ**** Tb**^{4+} [4f^{7} valence shell] ~ half shell effect
### Occurrence of +2 oxidation statepredicted from ^{ }**[****D**_{atm}**H + I**_{1}** + I**_{2}**]** which follows trends in **D**_{atm}**H**, which is reverse of trend in** I**_{3} *Bibliography* [textbook & online resources] |