Part 2 · Chapter 18

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

Fundamentals of Chemistry Prof. Mithun Mondal Reading time ≈ 55 min
i What you'll learn
  • 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.
Section 18-1

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.

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General configuration
\((n{-}1)d^{1\text{–}10}\,ns^{1\text{–}2}\)

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.

The two anomalous configurations. Chromium is \([\ce{Ar}]3d^5 4s^1\) and copper is \([\ce{Ar}]3d^{10} 4s^1\), not the "expected" \(d^4 s^2\) and \(d^9 s^2\). The reason is the extra stability of the exactly half-filled (\(d^5\)) and fully filled (\(d^{10}\)) subshells, which the atom reaches by promoting one \(4s\) electron.
Section 18-2

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.

PropertyBehaviourReason
Melting / boiling pointvery highstrong metallic bonding (s + d electrons)
Densityhighsmall atomic radii, high mass
Oxidation statesvariable\(ns\) and \((n{-}1)d\) close in energy
Ion colourusually colouredd–d electronic transitions
Magnetismoften paramagneticunpaired d electrons
Catalysisexcellentvariable states + surface adsorption
Section 18-3

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.

radius Sc → Zn decreases levels off
Atomic radius across a 3d series — falls, then nearly flat
Section 18-4

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.

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Manganese — the widest range
\(+2,\ +3,\ +4,\ +6,\ +7\) (e.g. \(\ce{Mn^2+},\ \ce{MnO2},\ \ce{MnO4^2-},\ \ce{MnO4-}\))

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.

Section 18-5

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.

lower higher absorbs visible light (Δ)
d–d transition — an electron absorbs visible light across the split
The colourless exceptions. Ions with an empty (\(d^0\)) or full (\(d^{10}\)) d-subshell have no possible d–d jump and are colourless: \(\ce{Sc^3+}\ (d^0)\), \(\ce{Ti^4+}\ (d^0)\), \(\ce{Zn^2+}\ (d^{10})\) and \(\ce{Cu+}\ (d^{10})\) are all white or colourless.
Section 18-6

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.

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Spin-only magnetic moment
\(\mu = \sqrt{n(n+2)}\ \text{BM}\)

\(n\) 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.

Iond-config\(n\)\(\mu\) (BM)
\(\ce{Ti^3+}\)\(d^1\)11.73
\(\ce{V^3+}\)\(d^2\)22.83
\(\ce{Cr^3+}\)\(d^3\)33.87
\(\ce{Mn^2+}/\ce{Fe^3+}\)\(d^5\)55.92
Section 18-7

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.

BehaviourExampleOrigin
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
Alloysbrass, bronzesimilar radii allow substitution
Section 18-8

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.

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Potassium permanganate (acidic medium)
\(\ce{MnO4- + 8H+ + 5e- -> Mn^2+ + 4H2O}\) (\(n=5\))

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.

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Potassium dichromate (acidic medium)
\(\ce{Cr2O7^2- + 14H+ + 6e- -> 2Cr^3+ + 7H2O}\) (\(n=6\))

Made from chromite ore via sodium chromate. The chromate–dichromate equilibrium is pH-controlled: \(\ce{2CrO4^2- + 2H+ <=> Cr2O7^2- + H2O}\) (yellow \(\leftrightarrow\) orange).

Section 18-9

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.

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The lanthanoid contraction
a steady decrease in size from \(\ce{La}\) to \(\ce{Lu}\), as poorly shielding \(4f\) electrons are added

Each added \(4f\) electron shields the nucleus imperfectly, so \(Z_{\text{eff}}\) creeps up and the ions contract across the series.

Far-reaching consequences. The contraction makes the second- and third-row transition metals nearly identical in size — \(\ce{Zr}\) and \(\ce{Hf}\), \(\ce{Nb}\) and \(\ce{Ta}\), are notoriously hard to separate. It also makes the later lanthanoid hydroxides less basic, and underlies the difficulty of separating the lanthanoids from one another.
Section 18-10

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.

FeatureLanthanoidsActinoids
Subshell filled\(4f\)\(5f\)
Common oxidation statemostly \(+3\)\(+3\) to \(+7\) (variable)
Radioactivityonly \(\ce{Pm}\)all radioactive
Contractionlanthanoid contractionactinoid contraction (greater)
Worked Examples

Putting It to Work

1 The anomalous configuration

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:

Working
\[ \ce{Cr}:[\ce{Ar}]\,3d^5 4s^1\ \text{(not }3d^4 4s^2) \]
2 Magnetic moment

Problem. Calculate the spin-only magnetic moment of \(\ce{Fe^2+}\) (\(3d^6\)).

Solution. \(d^6\) has 4 unpaired electrons; apply \(\mu=\sqrt{n(n+2)}\):

Working
\[ \mu=\sqrt{4\times6}=\sqrt{24}\approx 4.90\ \text{BM} \]
3 Coloured or colourless?

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:

Working
\[ \ce{Sc^3+}(d^0)\ \text{colourless};\quad \ce{Cu^2+}(d^9)\ \text{blue} \]
4 Why Zn is not "transition"

Problem. Explain why zinc is not regarded as a typical transition element.

Solution. Check the d-subshell in the atom and its common ion:

Working
\[ \ce{Zn}:3d^{10}4s^2,\ \ce{Zn^2+}:3d^{10}\ \Rightarrow\ \text{d-subshell always full} \]
5 Electrons gained by permanganate

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 \(+2\):

Working
\[ 7-2 = 5\ \text{electrons};\quad n\text{-factor}=5 \]
6 A consequence of the contraction

Problem. Why are zirconium and hafnium so difficult to separate?

Solution. The lanthanoid contraction makes their sizes almost equal:

Working
\[ r(\ce{Zr})\approx r(\ce{Hf})\ \Rightarrow\ \text{near-identical chemistry} \]
Review

Chapter Summary

Definition

Partly filled d-subshell in atom or ion; \(\ce{Zn, Cd, Hg}\) excluded; Cr and Cu anomalous.

Properties

High mp, dense, variable states, coloured, paramagnetic, catalytic — all from partly filled d.

Colour & magnetism

d–d transitions give colour; \(\mu=\sqrt{n(n+2)}\) gives the spin-only moment.

Oxidants

\(\ce{KMnO4}\) (\(n=5\)) and \(\ce{K2Cr2O7}\) (\(n=6\)) — the lab's great oxidising agents.

Lanthanoids

Mostly \(+3\); the lanthanoid contraction makes 4d/5d metals near-identical in size.

Actinoids

All radioactive; more variable oxidation states; greater contraction than lanthanoids.

Practice

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.

  1. Define a transition element and explain why \(\ce{Zn}\) is not regarded as typical.
  2. Write the ground-state configurations of \(\ce{Cr}\) and \(\ce{Cu}\), and account for both anomalies.
  3. Why do transition metals generally have high melting points?
  4. Explain why atomic radius is nearly constant across the middle of a transition series.
  5. Why does manganese show the widest range of oxidation states in the first series?
  6. Explain, with the help of d–d transitions, why \(\ce{Cu^2+}\) is coloured but \(\ce{Zn^2+}\) is not.
  7. Calculate the spin-only magnetic moment of \(\ce{Mn^2+}\) and \(\ce{Cr^3+}\).
  8. Give two reasons transition metals make good catalysts.
  9. Write the half-reaction for \(\ce{MnO4-}\) in acidic medium and state its \(n\)-factor.
  10. Write the dichromate half-reaction and the chromate–dichromate equilibrium.
  11. What is the lanthanoid contraction? Give two of its consequences.
  12. Compare lanthanoids and actinoids in oxidation states and radioactivity.
Tip: nearly every property in this chapter is one idea wearing different clothes — the partly filled d (or f) subshell. Unpaired d-electrons give colour and magnetism; closely spaced \(d\)/\(s\) levels give variable states and catalysis; poorly shielding f-electrons give the contraction. Count the d (or f) electrons first and the behaviour follows.