d- and f-Block Elements · Lesson 10 of 12
Lanthanoids: Configurations, Contraction and Chemistry
“Explain the 4f series, its closely related trivalent ions and the consequences of their gradual contraction.”
• Write representative neutral and ionic 4f configurations and explain common +3 chemistry. • Explain lanthanoid contraction and its chemical consequences. • Relate exceptional +2/+4 states to configurations and the complete chemical environment. • Describe magnetic, optical and chemical behaviour and selected uses.
A series with changes hidden inside the atom
The fourteen elements after lanthanum, Ce through Lu, make the conventional lanthanoid series considered here; lanthanum is discussed alongside them because its chemistry is similar. The principal differentiating occupation is 4f, deep inside the outer 6s region. Because these 4f electrons are comparatively shielded from direct ligand contact, the members resemble one another more closely than ordinary transition metals across a row. This is why separating neighbouring rare-earth elements is chemically demanding.
The general neutral-atom pattern is [Xe]4f⁰–¹⁴5d⁰–¹6s², with important individual occupations rather than a rigid filling ladder. La has 5d¹6s², Ce has 4f¹5d¹6s², Gd has 4f⁷5d¹6s² and Lu has 4f¹⁴5d¹6s². The especially widespread +3 ions form a simpler sequence, La³⁺=4f⁰ through Lu³⁺=4f¹⁴ beyond [Xe]. Filling 4f does not mean all neutral atoms lack 5d electrons.
| Z and element | Neutral configuration beyond [Xe] | Ln³⁺ beyond [Xe] |
|---|---|---|
| 57 | 5d¹6s² | 4f⁰ |
| 58 | 4f¹5d¹6s² | 4f¹ |
| 59 | 4f³6s² | 4f² |
| 60 | 4f⁴6s² | 4f³ |
| 61 | 4f⁵6s² | 4f⁴ |
| 62 | 4f⁶6s² | 4f⁵ |
| 63 | 4f⁷6s² | 4f⁶ |
| 64 | 4f⁷5d¹6s² | 4f⁷ |
| 65 | 4f⁹6s² | 4f⁸ |
| 66 | 4f¹⁰6s² | 4f⁹ |
| 67 | 4f¹¹6s² | 4f¹⁰ |
| 68 | 4f¹²6s² | 4f¹¹ |
| 69 | 4f¹³6s² | 4f¹² |
| 70 | 4f¹⁴6s² | 4f¹³ |
| 71 | 4f¹⁴5d¹6s² | 4f¹⁴ |
The atomic numbers in the table correspond to La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu in that order. First and second ionisation enthalpies are broadly around 600 and 1200 kJ mol⁻¹, while the third depends strongly on which occupation is lost or formed. Formation of empty, half-filled or filled f arrangements contributes to irregularities, but the final compound or solution stability also includes bonding and solvation.
Problem
Find Pm³⁺, Ce⁴⁺, Lu³⁺ and Lu²⁺ configurations.
- 1.Pm has Z=61 and neutral [Xe]4f⁵6s². Losing three electrons gives Pm³⁺=[Xe]4f⁴. Ce⁴⁺ has 58−4=54 electrons and is [Xe], or 4f⁰.
- 2.Lu³⁺ has 71−3=68 electrons and retains [Xe]4f¹⁴. Its common trivalent state is a closed f shell.
- 3.For an isolated Lu²⁺ ion, the supported ground configuration is [Xe]4f¹⁴6s¹. A simple “remove 6s first” construction from neutral Lu would leave 4f¹⁴5d¹, but ionic levels can reorder and that is not the isolated-ion ground assignment.
- 4.This exception does not invalidate the reliable 4s-first method for the common first-row cations. It shows why extrapolating that mnemonic unchanged to every f-block ion is unsafe.
Why radii shrink across 4f
The overall decrease in comparable atomic and especially trivalent ionic radii across the lanthanoid sequence as nuclear charge rises while added 4f electrons incompletely screen one another.
Each step adds a proton and approximately one 4f electron. The added electron does not cancel the extra nuclear attraction completely, so the electron cloud contracts. Compare ions with the same charge and coordination environment to see the trend clearly. Metallic radii are more irregular because crystal bonding and accessible divalent character, especially near Eu and Yb, also matter. A diagram mixing Ln²⁺, Ln³⁺ and Ln⁴⁺ should not be mistaken for one continuous same-charge trend.
| Trivalent ion | Representative radius / pm |
|---|---|
| La³⁺ | 106 |
| Ce³⁺ | 103 |
| Pr³⁺ | 101 |
| Nd³⁺ | 99 |
| Pm³⁺ | 98 |
| Sm³⁺ | 96 |
| Eu³⁺ | 95 |
| Gd³⁺ | 94 |
| Tb³⁺ | 92 |
| Dy³⁺ | 91 |
| Ho³⁺ | 89 |
| Er³⁺ | 88 |
| Tm³⁺ | 87 |
| Yb³⁺ | 86 |
As Ln³⁺ becomes smaller, its charge density increases. Hydroxide basicity generally decreases from earlier to later members as metal–oxygen interactions gain more polarising character. The small size differences also permit separation by carefully chosen complexation or ion-exchange conditions, while their overall similarity makes simple separation difficult. The accumulated contraction accounts for near equality of Zr/Hf and other 4d/5d pairs. It affects chemistry beyond the 4f series itself.
Why +3 dominates but is not the only possibility
Three outer electrons can be removed or involved in bonding while the remaining f electrons are held comparatively strongly. Thus +3 is the dominant lanthanoid state; La(III), not La(II), belongs in this statement. Exceptional states include +4 for Ce, and in suitable solid oxides for Pr, Nd, Tb or Dy, and +2 for Sm, Eu, Tm or Yb in appropriate compounds. Their accessibility and persistence differ, and not every listed ion is a stable simple aqueous species.
| Species | f occupation | Useful interpretation |
|---|---|---|
| Ce⁴⁺ | 4f⁰ | Closed-shell endpoint supports +4; still a strong oxidant in suitable acid |
| Tb⁴⁺ | 4f⁷ | Half-filled f arrangement helps stabilise certain +4 compounds |
| Eu²⁺ | 4f⁷ | Half-filled arrangement favours an accessible divalent state |
| Yb²⁺ | 4f¹⁴ | Filled shell favours divalent compounds |
| Sm²⁺ | 4f⁶ | Accessible even without an exactly half-filled f shell |
| Tm²⁺ | 4f¹³ | Demonstrates that f⁰/f⁷/f¹⁴ is not an exclusive requirement |
Ce(IV) commonly oxidises a suitable reductant while becoming Ce(III); a quoted acidic potential near +1.74 V belongs to a specified medium and can shift with complexation. Eu(II) and Yb(II) can act as reductants as they return to +3. A favourable shell occupation supports the existence of a state but does not guarantee that it dominates against every reaction partner. This is the same complete-energy principle used earlier for copper.
Colour, magnetism and physical properties
Many Ln³⁺ ions have narrow f–f absorption bands because the 4f shell is less perturbed by ligands than an exposed d shell. Some are visibly coloured, but not all partially filled 4f ions are visibly coloured: Gd³⁺ is a useful colourless yet strongly paramagnetic f⁷ example. La³⁺ and Lu³⁺ have f⁰ and f¹⁴ and are diamagnetic. A visible-colour rule must consider transition energies and selection restrictions, not only occupancy.
Most open-shell lanthanoid ions are paramagnetic, with orbital and spin–orbit contributions often important. If asked for the spin-only estimate for Ce³⁺, one unpaired 4f electron gives √3≈1.73 BM. It is a deliberately limited model calculation; the actual free-ion magnetic behaviour is not predicted accurately by discarding its orbital contribution.
The metals are generally silvery, conductive and reactive toward air; hardness tends to increase along the series, with exceptions and crystal effects. Their melting points span a substantial range rather than fitting one narrow universal band. Samarium melts near 1345 K, not 1623 K. Eu and Yb show conspicuous deviations in several physical properties associated with their distinctive bonding and accessible divalent character.
Reactions and uses connect the series to materials
| Reaction context | Representative balanced equation |
|---|---|
| Oxide formation | 4Ln+3O₂→2Ln₂O₃ |
| Halide formation with X₂ | 2Ln+3X₂→2LnX₃ |
| Acid dissolution | 2Ln+6H⁺→2Ln³⁺+3H₂ |
| Water reaction forming hydroxide | 2Ln+6H₂O→2Ln(OH)₃+3H₂ |
| Nitride formation on heating | 2Ln+N₂→2LnN |
| Sulfide formation on heating | 2Ln+3S→Ln₂S₃ |
| Dicarbide formation at high temperature | Ln+2C→LnC₂ |
These are representative series equations, not claims that every member has only one product under all conditions. Hydrides form on heating with hydrogen; several carbide compositions, including Ln₃C, Ln₂C₃ and LnC₂, occur under different conditions. Ln(OH)₃ denotes a hydroxide compound rather than merely an undefined amount of water attached to an oxide. Standard Ln³⁺/Ln reduction potentials are strongly negative, broadly around −2.2 to −2.4 V in the described comparison, with Eu differing; their readiness to oxidise explains their reactivity.
Mischmetal is typically a rare-earth-metal mixture, about 95%, with about 5% iron and small other constituents. It is used in lighter flints and alloy additions. Lanthanoid additions help produce selected steels and magnesium alloys. Mixed oxides serve in catalytic materials such as petroleum-cracking systems, while selected ions and oxides provide phosphor or fluorescent functions. The useful property belongs to the actual alloy or compound formulation, not automatically to every member of the series.
Quick Quiz
Quiz
What is the configuration of Pm³⁺ beyond [Xe]?
Explanation: Pm has seven electrons beyond [Xe] as an atom and four after losing three.
What causes lanthanoid contraction?
Explanation: Same-charge ions contract because effective attraction increases.
Which exceptional ion has 4f⁷?
Explanation: Eu has Z=63; Eu²⁺ has seven electrons beyond [Xe].
Which statement about Gd³⁺ is correct?
Explanation: Its f⁷ shell has unpaired electrons, but its absorption need not produce visible colour.
What is the dominant lanthanoid oxidation state?
Explanation: Trivalent chemistry is widespread, with meaningful +2/+4 exceptions.
Practice Problems
- Explain three consequences of lanthanoid contraction.
- Calculate the spin-only estimate for Ce³⁺ and state its limit.
- Correlate Ce⁴⁺, Tb⁴⁺, Eu²⁺ and Yb²⁺ with f occupations.
- Find the ground configurations of Pm atom, Ce⁴⁺ and isolated Lu²⁺.
- Balance lanthanoid reaction with water to form trihydroxide and hydrogen.
- Why are Ln³⁺ radii smoother than neutral-metal radii?
- What is mischmetal and why is it an alloy rather than a single compound?
Comparable Ln³⁺ ions shrink as nuclear attraction outruns 4f screening. Their small size differences complicate ordinary separation but support selective complexation methods; hydroxide basicity broadly decreases; accumulated contraction makes corresponding 4d and 5d metals such as Zr/Hf unusually similar in radius and chemistry.
Key Takeaways
• The 4f series is discussed with chemically similar lanthanum. • Trivalent ions follow a much simpler f-electron sequence than the neutral atoms. • Incomplete 4f screening causes lanthanoid contraction and affects later d metals. • The dominant +3 state has meaningful medium-dependent +2 and +4 exceptions. • Special f occupations help explain states but do not replace full energy balances. • Visible colour and paramagnetism are different properties. • Orbital contributions limit spin-only magnetic predictions for f-block ions. • Reactive metals and useful alloys, catalysts and phosphors arise from different forms of lanthanoid chemistry.