The d- and f-Block Elements
The transition and inner-transition metals — where partly filled d and f shells bring variable valencies, vivid colours, magnetism, and the catalytic power that drives industry
- The precise definition of a transition element and why \(\ce{Zn},\ \ce{Cd},\ \ce{Hg}\) are excluded.
- The general configuration and the anomalies of chromium and copper.
- Why these metals show variable oxidation states, colour, and magnetism.
- The spin-only formula for magnetic moment, and the basis of their catalytic power.
- The chemistry of \(\ce{KMnO4}\) and \(\ce{K2Cr2O7}\) — the two great oxidants.
- The lanthanoid contraction, its consequences, and the contrast with the actinoids.
What Counts as a Transition Element
The d-block fills the columns between the s- and p-blocks (Groups 3–12), as the \((n{-}1)d\) subshell is progressively filled. But not every d-block element is a true transition element. The strict definition requires a partially filled d-subshell in the atom or in one of its common ions.
By the strict definition, \(\ce{Zn},\ \ce{Cd}\) and \(\ce{Hg}\) (\(d^{10}\) full in both atom and \(+2\) ion) are not typical transition metals — they merely sit in the d-block.
General Characteristics
The transition metals are dense, hard, high-melting metals with good conductivity. Most of their distinctive behaviour traces to one feature: partly filled \(d\)-orbitals with unpaired electrons.
| Property | Behaviour | Reason |
|---|---|---|
| Melting / boiling point | very high | strong metallic bonding (s + d electrons) |
| Density | high | small atomic radii, high mass |
| Oxidation states | variable | \(ns\) and \((n{-}1)d\) close in energy |
| Ion colour | usually coloured | d–d electronic transitions |
| Magnetism | often paramagnetic | unpaired d electrons |
| Catalysis | excellent | variable states + surface adsorption |
Atomic & Ionic Radii
Across a transition series, atomic radius first decreases, then stays nearly constant: the rising nuclear charge is largely offset by the poor shielding of the added \(d\)-electrons. Down a group, radius rises from the \(3d\) to the \(4d\) series — but the \(5d\) series is almost the same size as the \(4d\), thanks to the lanthanoid contraction that precedes it.
Variable Oxidation States
Because the \(ns\) and \((n{-}1)d\) electrons are close in energy, a transition metal can lose a variable number of them, giving a range of oxidation states that often differ by one unit. The \(+2\) state is common early in a series (from losing the two \(ns\) electrons); higher states appear in the middle, peaking at manganese.
Mn (\(3d^5 4s^2\)) can in principle lose up to seven electrons. Higher states are stabilised by oxygen or fluorine and become more stable for the heavier \(4d\) and \(5d\) metals.
Colour & d–d Transitions
Most transition-metal ions are coloured. In a complex, the five \(d\)-orbitals split into two energy levels; an electron can absorb a photon of visible light and jump from the lower set to the higher — a d–d transition. The colour we see is the complement of the light absorbed.
Magnetic Properties
An ion with unpaired electrons is paramagnetic — drawn into a magnetic field. For most first-row transition ions the magnetic moment comes almost entirely from electron spin, so it can be estimated from the number of unpaired electrons alone.
\(n\) is the number of unpaired electrons. For \(\ce{Fe^3+}\ (3d^5,\ n=5)\): \(\mu=\sqrt{5\times7}=\sqrt{35}\approx5.92\ \text{BM}\) — the maximum for the first series.
| Ion | d-config | \(n\) | \(\mu\) (BM) |
|---|---|---|---|
| \(\ce{Ti^3+}\) | \(d^1\) | 1 | 1.73 |
| \(\ce{V^3+}\) | \(d^2\) | 2 | 2.83 |
| \(\ce{Cr^3+}\) | \(d^3\) | 3 | 3.87 |
| \(\ce{Mn^2+}/\ce{Fe^3+}\) | \(d^5\) | 5 | 5.92 |
Catalysis, Complexes & Alloys
Three further hallmarks round out the d-block. Catalysis exploits variable oxidation states (offering reaction intermediates) and surface adsorption. Complex formation comes from small, highly charged ions with vacant \(d\)-orbitals to accept lone pairs. And similar atomic sizes let these metals form alloys and interstitial compounds.
| Behaviour | Example | Origin |
|---|---|---|
| Catalysis | \(\ce{Fe}\) (Haber), \(\ce{V2O5}\) (Contact) | variable states, adsorption |
| Complexes | \(\ce{[Fe(CN)6]^4-}\) | vacant d-orbitals accept lone pairs |
| Interstitial | \(\ce{TiC},\ \ce{steel}\) | small atoms (H, C, N) in lattice holes |
| Alloys | brass, bronze | similar radii allow substitution |
Two Great Oxidants: KMnO₄ & K₂Cr₂O₇
Two transition-metal salts dominate the chemistry lab as powerful, well-behaved oxidising agents. Both are made from a cheap ore, and both have a known number of electrons transferred — making them ideal for volumetric titration.
Made from pyrolusite: \(\ce{2MnO2 + 4KOH + O2 -> 2K2MnO4 + 2H2O}\), then the green manganate is oxidised to the purple permanganate. Mn goes from \(+7\) to \(+2\), gaining five electrons.
Made from chromite ore via sodium chromate. The chromate–dichromate equilibrium is pH-controlled: \(\ce{2CrO4^2- + 2H+ <=> Cr2O7^2- + H2O}\) (yellow \(\leftrightarrow\) orange).
The Lanthanoids
The f-block — the inner transition elements — fills the deep \((n{-}2)f\) subshell. The first row, the lanthanoids (\(\ce{Ce}\) to \(\ce{Lu}\), filling \(4f\)), are remarkably alike: nearly all show the \(+3\) state, with a few exceptions (\(\ce{Ce^4+},\ \ce{Eu^2+}\)). Their defining feature is a steady shrinkage across the row.
Each added \(4f\) electron shields the nucleus imperfectly, so \(Z_{\text{eff}}\) creeps up and the ions contract across the series.
The Actinoids
The second f-row, the actinoids (\(\ce{Th}\) to \(\ce{Lr}\), filling \(5f\)), are all radioactive. Their \(5f\) electrons shield even more poorly than \(4f\), giving an actinoid contraction that is greater still — and because the \(5f\), \(6d\) and \(7s\) levels lie close together, they show a far wider range of oxidation states than the lanthanoids.
| Feature | Lanthanoids | Actinoids |
|---|---|---|
| Subshell filled | \(4f\) | \(5f\) |
| Common oxidation state | mostly \(+3\) | \(+3\) to \(+7\) (variable) |
| Radioactivity | only \(\ce{Pm}\) | all radioactive |
| Contraction | lanthanoid contraction | actinoid contraction (greater) |
Putting It to Work
Problem. Write the ground-state configuration of chromium (\(Z=24\)) and explain it.
Solution. A half-filled \(3d^5\) is extra stable, so one \(4s\) electron shifts:
Problem. Calculate the spin-only magnetic moment of \(\ce{Fe^2+}\) (\(3d^6\)).
Solution. \(d^6\) has 4 unpaired electrons; apply \(\mu=\sqrt{n(n+2)}\):
Problem. Which is coloured in solution, \(\ce{Sc^3+}\) or \(\ce{Cu^2+}\)? Explain.
Solution. Colour needs a partly filled d-subshell for a d–d jump:
Problem. Explain why zinc is not regarded as a typical transition element.
Solution. Check the d-subshell in the atom and its common ion:
Problem. How many electrons does one \(\ce{MnO4-}\) ion gain in acidic medium, and what is its \(n\)-factor?
Solution. Mn falls from \(+7\) to \(+2\):
Problem. Why are zirconium and hafnium so difficult to separate?
Solution. The lanthanoid contraction makes their sizes almost equal:
Chapter Summary
Partly filled d-subshell in atom or ion; \(\ce{Zn, Cd, Hg}\) excluded; Cr and Cu anomalous.
High mp, dense, variable states, coloured, paramagnetic, catalytic — all from partly filled d.
d–d transitions give colour; \(\mu=\sqrt{n(n+2)}\) gives the spin-only moment.
\(\ce{KMnO4}\) (\(n=5\)) and \(\ce{K2Cr2O7}\) (\(n=6\)) — the lab's great oxidising agents.
Mostly \(+3\); the lanthanoid contraction makes 4d/5d metals near-identical in size.
All radioactive; more variable oxidation states; greater contraction than lanthanoids.
Problems
For each item, first decide which property it tests — configuration, a periodic trend, colour/magnetism, or the f-block — then apply the relevant rule. Difficulty rises down the list.
- Define a transition element and explain why \(\ce{Zn}\) is not regarded as typical.
- Write the ground-state configurations of \(\ce{Cr}\) and \(\ce{Cu}\), and account for both anomalies.
- Why do transition metals generally have high melting points?
- Explain why atomic radius is nearly constant across the middle of a transition series.
- Why does manganese show the widest range of oxidation states in the first series?
- Explain, with the help of d–d transitions, why \(\ce{Cu^2+}\) is coloured but \(\ce{Zn^2+}\) is not.
- Calculate the spin-only magnetic moment of \(\ce{Mn^2+}\) and \(\ce{Cr^3+}\).
- Give two reasons transition metals make good catalysts.
- Write the half-reaction for \(\ce{MnO4-}\) in acidic medium and state its \(n\)-factor.
- Write the dichromate half-reaction and the chromate–dichromate equilibrium.
- What is the lanthanoid contraction? Give two of its consequences.
- Compare lanthanoids and actinoids in oxidation states and radioactivity.