Take a breath. If you have already flipped through this chapter once and thought “this is just a wall of facts I have to memorise”, you are not alone — almost everyone reacts that way the first time. But here is the secret that changes everything: the d- and f-block chapter is not a list. It is one idea with many symptoms. A single structural fact about where the d and f electrons sit inside the atom quietly produces every single property in this unit — variable oxidation states, colour, magnetism, catalysis, complex formation, and the famous lanthanoid contraction. Learn the cause once, and the symptoms stop being things you memorise and start being things you can derive in the exam hall.
This page is your complete Unit 4 companion: d and f block elements class 12 notes, the full d and f block class 12 formula and oxidation state list, lanthanoid contraction explained with consequences, and a set of d and f block elements class 12 important questions with worked model answers that show exactly where the marks sit. Unit 4 carries 7 marks in the 70-mark CBSE Class 12 Chemistry theory paper for 2026-27, and it is one of the most reliably scoring units in the whole syllabus — because the questions repeat, and because almost all of them can be answered from one root idea.
We will go slowly. No step is skipped. Every configuration, every oxidation state, every balanced equation on this page has been checked against NCERT Class 12 Chemistry Part I, and every magnetic moment has been calculated rather than copied. Ready? Let us begin.
Meet Your Tutor
The d- and f-Block Elements can look like a catalogue of colours, oxidation states and exceptions. I will help you build the chapter from electronic configuration and recurring trends first, then attach each compound and reaction to that framework. Keep a small comparison table nearby and update it as the patterns become visible.
What You’ll Learn
- One Cause, Many Symptoms: The Root Idea
- Position in the Periodic Table
- Electronic Configuration of the d-Block Elements (Cr and Cu Anomalies)
- Atomic and Ionic Radii Across a Series
- Ionisation Enthalpy and Standard Electrode Potentials
- Variable Oxidation States: The d and f Block Oxidation State List
- Formation of Coloured Ions
- Magnetic Properties and the Spin-Only Formula
- Catalytic Behaviour
- Complex Formation
- Interstitial Compounds and Alloy Formation
- Potassium Dichromate: Preparation, Structure, Oxidising Action
- Potassium Permanganate: Preparation, Structure, Oxidising Action
- The Lanthanoids: Lanthanoid Contraction Explained With Consequences
- The Actinoids
- Some Applications of d- and f-Block Elements
- Memory Devices and the Formula List
- Practice Worksheet
Your Game Plan
- Day 1 — learn the cause. Read the root-idea section and the position/configuration sections. Write the 3d series configurations from memory until you get all ten right, including Cr and Cu.
- Day 2 — derive the symptoms. Radii, ionisation enthalpy, oxidation states, colour, magnetism. Do not memorise these as separate facts; each time, ask “how does the poorly-shielding d electron explain this?”
- Day 3 — the two flagship compounds. K2Cr2O7 and KMnO4. Write out the preparation and the oxidation equations by hand three times. These are guaranteed marks.
- Day 4 — lanthanoids and actinoids. Lanthanoid contraction, its consequences, the comparison table, applications.
- Day 5 — practice. Do the worksheet at the bottom of this page with your book closed, then mark yourself honestly against the model answers.
Study Notes
One Cause, Many Symptoms: The Root Idea Behind This Whole Chapter
Imagine a school where the senior students sit in the outermost row of the hall and a group of newer students keeps getting seated in a row behind them — between the seniors and the stage. Every new student added to that inner row should, in principle, block a bit of the stage light from reaching the seniors. But these particular students are oddly shaped and sit in awkward gaps, so they block the light very badly. The seniors keep feeling the stage lights getting brighter and brighter even though the hall is filling up.
That is exactly what happens in the d- and f-block. As you move across a transition series, each new electron goes into the inner (n−1)d sub-shell, not the outer ns sub-shell. In the f-block, each new electron goes into the even more deeply buried (n−2)f sub-shell. Because d orbitals and especially f orbitals are diffuse and poorly directed, they shield the outer electrons from the nucleus very badly. Meanwhile the nuclear charge goes up by one proton at every step.
Two consequences follow immediately, and they are the whole chapter:
- Consequence A — the effective nuclear charge creeps up. Sizes shrink slowly across a series; this is the seed of the lanthanoid contraction and of the near-identical sizes of the 4d and 5d metals.
- Consequence B — the (n−1)d and ns orbitals end up almost equal in energy. Because they are so close, both sets of electrons are available for bonding. That single fact gives you variable oxidation states, partly-filled d sub-shells in ions, d–d transitions (colour), unpaired electrons (paramagnetism), empty low-lying d orbitals (complex formation) and easy switching between oxidation states (catalysis).
Throughout this page, every time we cash out a symptom of that root cause we will tag it with a navy Key Idea box. Collect those boxes and you have the chapter.
Position in the Periodic Table
The d-block is the wide central slab of the periodic table — groups 3 to 12. It contains four series, each named after the d sub-shell being filled:
- 3d series (first transition series): Sc (Z = 21) to Zn (Z = 30) — period 4. This is the series your board paper cares about.
- 4d series (second): Y (39) to Cd (48) — period 5.
- 5d series (third): La (57), then Hf (72) to Hg (80) — period 6, skipping over the lanthanoids which are pulled out below.
- 6d series (fourth): Ac (89), then Rf (104) onwards — period 7, mostly synthetic and radioactive, and incomplete.
The f-block sits inside the d-block conceptually — that is why its members are called inner transition elements. There are two series: the lanthanoids, Ce (58) to Lu (71), filling 4f; and the actinoids, Th (90) to Lr (103), filling 5f. Lanthanum (57) and actinium (89) are studied along with them because they sit immediately before each series.
Apply the definition to zinc. Zn is [Ar] 3d10 4s2; its only common ion, Zn2+, is [Ar] 3d10. Both the atom and the ion have a completely filled d sub-shell, so strictly Zn, Cd and Hg are not transition elements. We still study them with the d-block because they close each series and their chemistry is discussed alongside. Notice the contrast with Cu: copper’s atom is 3d10 4s1 (full d), but its common Cu2+ ion is 3d9 — incompletely filled — so copper is a genuine transition element.
Where students lose the mark: writing only “because Ag+ is 4d10” — that is the argument against. You must produce Ag2+.
Before you go further, it is worth refreshing the Class 10 picture of how metals behave — reactivity order, alloys, corrosion and electrolytic refining all reappear in this chapter in a more sophisticated form. If any of that feels hazy, ten minutes on our Metals and Non-metals chapter for Class 10 will pay for itself.
Electronic Configuration of the d-Block Elements (Cr and Cu Anomalies)
The general outer configuration of a d-block element is
For the 3d series that reads [Ar] 3d1–10 4s1–2. Here is the complete, verified list. Fill it in from memory every morning for a week and it will never leave you.
| Element | Sc | Ti | V | Cr | Mn | Fe | Co | Ni | Cu | Zn |
|---|---|---|---|---|---|---|---|---|---|---|
| Atomic number Z | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 3d electrons | 1 | 2 | 3 | 5 | 5 | 6 | 7 | 8 | 10 | 10 |
| 4s electrons | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 1 | 2 |
Why do Cr and Cu break the pattern? Because 3d and 4s are almost equal in energy (that is Consequence B of our root idea), an electron can slide from 4s into 3d if doing so buys enough stability. Two arrangements are unusually stable: a half-filled d5 and a completely filled d10. Both maximise the number of parallel-spin electron pairs, which maximises the exchange energy — a quantum-mechanical stabilisation with no everyday analogue, but you can picture it as electrons of the same spin being able to swap places freely, and more swapping options meaning lower energy.
So chromium prefers [Ar] 3d5 4s1 over the “expected” 3d4 4s2, and copper prefers [Ar] 3d10 4s1 over 3d9 4s2.
• Fe = [Ar] 3d6 4s2 → Fe2+ = [Ar] 3d6. Six electrons in five orbitals: one pair plus four singles → 4 unpaired. (1 mark)
• Fe3+ = [Ar] 3d5. Five electrons, one in each orbital → 5 unpaired — the maximum possible, which is why Fe3+ is unusually stable. (1 mark)
• Cu = [Ar] 3d10 4s1 → remove the 4s electron and then one 3d electron → Cu2+ = [Ar] 3d9 → 1 unpaired. (1 mark)
Marker’s note: you get no credit for writing 3d4 4s2 for Fe2+. The 4s-first rule is not optional.
Why do the anomalies not repeat cleanly lower down? In the 4d and 5d series the energy gaps are different, and several elements (Nb, Mo, Ru, Rh, Pd, Ag) show their own irregularities — palladium is the extreme case at 4d10 5s0. For the board paper you only need the 3d series and the two anomalies; just do not write “only Cr and Cu are exceptions in the whole d-block”, because that is not true.
Atomic and Ionic Radii Across a Series
Here is our first symptom of the root cause. Move left to right across the 3d series: nuclear charge rises by one unit each step, but the added electron goes into the inner 3d sub-shell where it shields the 4s electrons poorly. Net effect — the effective nuclear charge felt by the outer electrons creeps upward and the atom shrinks.
But the shrinking is gentle, not dramatic like in the p-block, and it does not continue all the way. The pattern across the 3d series is:
- Sc to Cr: a noticeable decrease, as the added d electrons shield poorly.
- Fe, Co, Ni: the radii become almost constant. By now there are enough d electrons that the extra electron–electron repulsion roughly cancels the extra nuclear pull.
- Cu and Zn: the radii rise again. The d sub-shell is now full (d10), repulsion dominates, and the atom expands slightly.
Down a group the story is stranger, and it is one of the most-asked questions in this unit. Going 3d → 4d, radii increase as you would expect. But going 4d → 5d the radii barely change at all. Zirconium has an atomic radius of about 160 pm and hafnium, one full period below it, about 159 pm. The reason is the lanthanoid contraction, which we unpack in detail later — fourteen 4f electrons are inserted before the 5d series begins, and their catastrophically poor shielding eats up the size increase you would otherwise get from an extra shell.
One more radius fact worth carrying: density increases steadily across the 3d series, from roughly 3.4 g cm−3 for scandium to about 8.9 g cm−3 for copper. Same reason — atomic mass climbs while the metallic radius shrinks or stays flat, so you are packing more mass into the same volume.
Ionisation Enthalpy and Standard Electrode Potentials
Ionisation enthalpy generally increases across the 3d series, but the rise is much gentler than in the s- or p-block, and it is bumpy rather than smooth. The gentleness is our root cause again: the added d electrons partly shield the 4s electrons, so the outer electron does not feel the full weight of the extra protons. The bumps come from exchange-energy stabilisation — whenever removing an electron would destroy a d5 or d10 arrangement, that ionisation costs extra.
Two classic bumps worth knowing:
- The second ionisation enthalpies of Cr and Cu are unusually high, because Cr+ is 3d5 and Cu+ is 3d10 — you are being asked to break an extra-stable shell.
- The third ionisation enthalpy of Mn is unusually high and that of Fe is comparatively low, because Mn2+ (3d5) is stable and resists further ionisation, whereas Fe2+ (3d6) actually gains the half-filled configuration on losing an electron to become Fe3+ (3d5).
Now to standard electrode potentials. Three energy terms decide E°(M2+/M): the enthalpy of atomisation (breaking the metal apart), the first two ionisation enthalpies (stripping two electrons), and the hydration enthalpy (the reward for surrounding M2+ with water). Across the series the E° values generally become less negative, with three famous outliers.
Zn: E° = −0.76 V — more negative than expected, because Zn2+ reaches 3d10.
Cu: E° = +0.34 V — the only positive value in the row. Copper has a very high enthalpy of atomisation and its hydration enthalpy is not large enough to compensate, so copper simply does not want to ionise. That is why copper does not liberate hydrogen from dilute HCl or dilute H2SO4 and needs an oxidising acid such as hot concentrated H2SO4 or nitric acid.
The other couple you must know is E°(M3+/M2+), because it tells you at a glance which ion is an oxidising agent and which is a reducing agent. A very positive value means M3+ badly wants to become M2+, so M3+ is a strong oxidant. A very negative value means M2+ badly wants to become M3+, so M2+ is a strong reductant.
| Couple M3+/M2+ | Ti | V | Cr | Mn | Fe | Co |
|---|---|---|---|---|---|---|
| E° / V | −0.37 | −0.26 | −0.41 | +1.57 | +0.77 | +1.97 |
| What it tells you | Ti2+ reducing | V2+ reducing | Cr2+ strongly reducing | Mn3+ strongly oxidising | Fe3+ moderately oxidising | Co3+ strongly oxidising |
Cr2+: configuration [Ar] 3d4. On losing one more electron it becomes Cr3+, [Ar] 3d3 — a half-filled t2g set, which is a particularly stable arrangement in an octahedral aqueous environment. Cr2+ therefore gives away an electron readily, i.e. it acts as a reducing agent. This matches E°(Cr3+/Cr2+) = −0.41 V. (1½ marks.)
Mn3+: configuration [Ar] 3d4. On gaining an electron it becomes Mn2+, [Ar] 3d5 — the extra-stable half-filled d sub-shell. Mn3+ therefore grabs an electron readily, i.e. it acts as an oxidising agent. This matches E°(Mn3+/Mn2+) = +1.57 V. (1½ marks.)
Notice the elegance: both ions are d4. What differs is the destination. Always argue from the stability of the product, not the reactant.
Variable Oxidation States: The d and f Block Class 12 Oxidation State List
Variable oxidation state is the defining habit of the transition metals, and it is Consequence B of our root idea in its purest form. Because 3d and 4s sit at almost the same energy, both sets of electrons are available for bonding — and the atom can hand over two, three, four or even seven of them depending on what the other reagent offers in return.
Three rules organise everything:
- The states differ by 1, not by 2. Vanadium shows +2, +3, +4 and +5 — a continuous ladder. Contrast the p-block, where the inert pair effect gives jumps of two (Sn is +2 or +4, never +3).
- From Sc to Mn, the maximum oxidation state equals the total number of 4s + 3d electrons. Sc has 3 such electrons and reaches +3; Mn has 5 + 2 = 7 and reaches +7. That is the rising half of the fan chart.
- After Mn the maximum falls away sharply. Once the d sub-shell is more than half full the electrons start pairing, and paired d electrons are far harder to remove. Fe reaches +6 only with difficulty; Cu manages +2; Zn is stuck at +2.
| Element | Sc | Ti | V | Cr | Mn | Fe | Co | Ni | Cu | Zn |
|---|---|---|---|---|---|---|---|---|---|---|
| Maximum | +3 | +4 | +5 | +6 | +7 | +6 | +4 | +4 | +2 | +2 |
| Most common | +3 | +4 | +4 | +3 | +2 | +3 | +2 | +2 | +2 | +2 |
| Number of states shown | one only | +2 to +4 | +2 to +5 | +2 to +6 | +2 to +7 | +2 to +6 | +2 to +4 | +2 to +4 | +1, +2 | +2 only |
Why do the highest states only ever appear with oxygen and fluorine? Look at where +7 actually turns up: Mn2O7 and MnO4−, never MnCl7. Oxygen can form multiple bonds and fluorine is tiny with a very high bond enthalpy; both are able to stabilise a heavily positive metal centre. A big soft halide simply cannot.
A useful contrast with the p-block. Going down a d-block group, the higher oxidation state becomes more stable — Cr(VI) in Cr2O72− is a fierce oxidant, but Mo(VI) and W(VI) in MoO3 and WO3 are mild. That is the exact opposite of the inert pair effect you learned for the p-block.
Formation of Coloured Ions
Pour copper sulfate into water and you get that unmistakable blue. Nickel salts give green, cobalt gives pink, potassium dichromate gives orange. Why does one whole region of the periodic table behave like a paint box while sodium and magnesium salts are stubbornly colourless?
When a transition metal ion sits in water, the surrounding water molecules act as ligands. Their electric field splits the five d orbitals, which were degenerate in the free ion, into two groups with a small energy gap between them. That gap happens to correspond to the energy of visible light. An electron in a lower d orbital absorbs a photon of exactly the right wavelength and jumps to a higher d orbital — a d–d transition. The light that survives is the original white light minus the absorbed colour, and what reaches your eye is the complementary colour.
• d0 — no electron to promote: Sc3+, Ti4+, V5+; or
• d10 — no vacancy to receive: Zn2+, Cu+, Cd2+, Hg2+.
Everything from d1 to d9 is normally coloured. Memory device: “empty or full means colourless”.
Magnetic Properties and the Spin-Only Formula
An unpaired electron is a tiny spinning magnet. Pair it up with another electron of opposite spin and the two magnets cancel. So the magnetic behaviour of a transition metal ion is a direct read-out of how many unpaired d electrons it has.
- Diamagnetic — all electrons paired; the substance is weakly repelled by a magnetic field.
- Paramagnetic — one or more unpaired electrons; weakly attracted.
- Ferromagnetic — an extreme case where spins align across whole domains of the solid; very strongly attracted. Iron, cobalt and nickel metals are the classic examples.
Here are the five values, each computed rather than copied. Learn these and you can answer any magnetic-moment question in seconds.
| Unpaired electrons, n | n(n + 2) | μ = √(n(n+2)) / BM | A 3d ion with this n |
|---|---|---|---|
| 0 | 0 | 0 (diamagnetic) | Sc3+ (3d0), Zn2+ (3d10) |
| 1 | 3 | 1.73 | Ti3+ (3d1), Cu2+ (3d9) |
| 2 | 8 | 2.83 | V3+ (3d2), Ni2+ (3d8) |
| 3 | 15 | 3.87 | Cr3+ (3d3), Co2+ (3d7) |
| 4 | 24 | 4.90 | Mn3+ (3d4), Fe2+ (3d6) |
| 5 | 35 | 5.92 | Mn2+ and Fe3+ (both 3d5) |
Step 2 — count unpaired electrons. Five electrons spread singly across the five d orbitals by Hund’s rule, so n = 5. (½ mark.)
Step 3 — substitute. μ = √(5 × 7) = √35 = 5.92 BM. (1 mark — carry the unit, BM.)
This is the largest spin-only moment available to any 3d ion, which is a useful sanity check: if your answer for a 3d ion exceeds 5.92 BM, you have miscounted.
Step 2 — find a divalent 3d ion with three unpaired electrons. Three unpaired electrons occur in d3 and also in d7. A divalent ion means M2+, which is [Ar] 3dn after losing the two 4s electrons. Co2+ is 3d7, giving one pair plus three singles → n = 3. So the metal is cobalt. (1 mark.)
Careful: V2+ is also 3d3 with n = 3 and the same moment, so if the question gives no extra clue, state both and say the data alone cannot distinguish them. Examiners reward that honesty.
Catalytic Behaviour
A catalyst is a chemical middleman: it takes something from one reactant, hands it to another, and walks away unchanged. To do that job repeatedly, a species has to be able to change its state and then change back. Transition metals are built for exactly this, because switching between oxidation states costs them almost nothing — Consequence B again.
The textbook illustration is iron catalysing the otherwise sluggish reaction between iodide ions and persulfate ions. Both reactants are negatively charged, so they repel each other and rarely meet. Iron solves the problem by splitting the job in two:
2 Fe2+ + S2O82− → 2 Fe3+ + 2 SO42−
Overall: 2 I− + S2O82− → I2 + 2 SO42−, with iron regenerated exactly as it started.
Transition metals also catalyse heterogeneously, by adsorbing reactants onto their surface using partly filled d orbitals. This holds the molecules in place, weakens their bonds and lowers the activation energy. Industrially important examples worth memorising:
- V2O5 — Contact process, 2 SO2 + O2 → 2 SO3.
- Finely divided Fe — Haber process, N2 + 3 H2 → 2 NH3.
- Ni — hydrogenation of unsaturated vegetable oils into vanaspati.
- TiCl4 with Al(C2H5)3 — the Ziegler–Natta catalyst for polythene.
- PdCl2 — Wacker process, converting ethene to ethanal.
- MnO2 — decomposition of potassium chlorate to oxygen.
Reason 1 — variable oxidation states. Because the (n−1)d and ns levels are close in energy, a transition metal can accept electrons from one reactant and pass them to another, cycling between two oxidation states and being regenerated at the end. The Fe3+/Fe2+ catalysis of the iodide–persulfate reaction is the standard example. (1 mark.)
Reason 2 — surface adsorption using partly filled d orbitals. Reactant molecules are adsorbed on the metal surface through the vacant d orbitals; this increases their local concentration, weakens the bonds to be broken and lowers the activation energy. Iron in the Haber process works this way. (1 mark.)
Complex Formation
Transition metal ions are unusually good at gathering ligands around themselves — [Fe(CN)6]3−, [Cu(NH3)4]2+, [Co(NH3)6]3+ and so on. Three features make this possible, and an examiner wants all three:
- Small size — the ion is compact, so its electric field at the surface is intense.
- High charge density — a +2 or +3 charge packed into that small volume strongly attracts electron-pair donors.
- Vacant d orbitals of the right energy — empty, low-lying orbitals that can accept lone pairs from the ligands.
Compare with sodium: Na+ is larger, carries only +1, and has no accessible vacant d orbitals, so it forms hardly any stable complexes. The contrast makes the point sharply.
Interstitial Compounds and Alloy Formation
Picture a crate of oranges. However tightly you pack them, there are gaps — small triangular holes between the fruit. Now imagine dropping peas into those gaps. The crate does not get bigger, but it does get much harder to squash. That is exactly an interstitial compound.
Transition metal lattices have these holes, and small atoms — H, C, N and B — fit into them. The resulting solids have four signature properties:
- Non-stoichiometric — the formulae are odd because the holes need not all be filled: VH0.56, TiH1.7, Fe3H, Mn4N, TiC.
- Very hard — the trapped small atoms block the metal layers from sliding over one another. Steel is harder than pure iron for exactly this reason.
- Very high melting points — often higher than the pure metal.
- Still metallic in conductivity — the delocalised electron sea survives.
Alloys work on the neighbouring principle. Because transition metals across a series have very similar metallic radii — within about fifteen percent of each other — the atoms of one can simply replace the atoms of another in the lattice without wrecking it. These are called substitutional alloys. Familiar examples: stainless steel (Fe with roughly 12–18 percent Cr plus Ni), brass (Cu–Zn), bronze (Cu–Sn). If you want the Class 10 groundwork on why alloying changes hardness and corrosion resistance, it is set out in the Metals and Non-metals notes.
Potassium Dichromate: Preparation, Structure and Oxidising Action
This is one of the two compounds the board asks about almost every year. Take it slowly and write every equation out by hand at least three times — these are the easiest marks in the unit. If balancing redox equations feels shaky, spend fifteen minutes first on the Chemical Reactions and Equations foundation from Class 10; everything below is built on it.
Preparation from chromite ore, FeCr2O4 — three steps.
4 FeCr2O4 + 8 Na2CO3 + 7 O2 → 8 Na2CrO4 + 2 Fe2O3 + 8 CO2
Step 2 — acidify the yellow sodium chromate:
2 Na2CrO4 + 2 H+ → Na2Cr2O7 + 2 Na+ + H2O
Step 3 — swap the cation; the less soluble potassium salt crystallises out:
Na2Cr2O7 + 2 KCl → K2Cr2O7 + 2 NaCl
The chromate–dichromate equilibrium. This is the colour change every practical student remembers: add acid to a yellow chromate solution and it turns orange; add alkali to an orange dichromate solution and it turns yellow.
Cr2O72− (orange) + 2 OH− ⇌ 2 CrO42− (yellow) + H2O
Structure. The chromate ion CrO42− is a simple tetrahedron with chromium at the centre and four equivalent Cr–O bonds. The dichromate ion Cr2O72− is two CrO4 tetrahedra joined at a shared corner oxygen, with a Cr–O–Cr bridge angle of 126°. Think of two tents pegged to the same central peg.
Oxidising action. In acidic solution dichromate accepts six electrons and the solution changes from orange to the green of Cr3+:
Bolt any six-electron supply onto that half-reaction and you have a complete equation. The four you should be able to write cold:
| Reducing agent | Balanced ionic equation in acidic medium |
|---|---|
| Iodide, I− | Cr2O72− + 14 H+ + 6 I− → 2 Cr3+ + 3 I2 + 7 H2O |
| Iron(II), Fe2+ | Cr2O72− + 14 H+ + 6 Fe2+ → 2 Cr3+ + 6 Fe3+ + 7 H2O |
| Hydrogen sulfide, H2S | Cr2O72− + 8 H+ + 3 H2S → 2 Cr3+ + 3 S + 7 H2O |
| Tin(II), Sn2+ | Cr2O72− + 14 H+ + 3 Sn2+ → 2 Cr3+ + 3 Sn4+ + 7 H2O |
Reduction: Cr2O72− + 14 H+ + 6 e− → 2 Cr3+ + 7 H2O
Oxidation: Fe2+ → Fe3+ + e− (1 mark for both halves.)
Step 2 — equalise the electrons. The reduction needs six electrons, so multiply the oxidation half by six.
Step 3 — add.
Cr2O72− + 14 H+ + 6 Fe2+ → 2 Cr3+ + 6 Fe3+ + 7 H2O (1 mark.)
Step 4 — check. Charge on the left = −2 + 14 + 12 = +24; on the right = +6 + 18 = +24. Balanced.
Colour change: orange (Cr2O72−) to green (Cr3+). (1 mark.)
Tip: always show the charge check. It takes ten seconds and it catches the most common slip, forgetting the 14 H+.
Uses of K2Cr2O7: a primary standard in volumetric analysis (it is not deliquescent and can be obtained pure), chrome tanning of leather, preparation of azo dyes, and as a laboratory oxidant. Titrations with it are done at a known concentration, so if molarity and normality feel rusty, revisit the Solutions chapter of Class 12 Chemistry.
Potassium Permanganate: Preparation, Structure and Oxidising Action
The second flagship compound, and the one with the most quotable equations. Permanganate is that deep purple solid you have probably seen used as a disinfectant.
Preparation from pyrolusite, MnO2 — two steps.
2 MnO2 + 4 KOH + O2 → 2 K2MnO4 + 2 H2O
Step 2 — convert manganate(VI) into permanganate(VII), either by electrolytic oxidation in alkaline solution:
MnO42− → MnO4− + e−
or by disproportionation in acidic or neutral solution:
3 MnO42− + 4 H+ → 2 MnO4− + MnO2 + 2 H2O
In the laboratory Mn(II) can also be taken all the way to Mn(VII) in one go using peroxodisulfate:
2 Mn2+ + 5 S2O82− + 8 H2O → 2 MnO4− + 10 SO42− + 16 H+
Structure. Both MnO4− and MnO42− are tetrahedral. The interesting difference is electronic:
| Ion | Oxidation state of Mn | d configuration | Unpaired e− | Magnetism | Colour |
|---|---|---|---|---|---|
| Manganate, MnO42− | +6 | 3d1 | 1 | paramagnetic | green |
| Permanganate, MnO4− | +7 | 3d0 | 0 | diamagnetic | deep purple |
Oxidising action. Unlike dichromate, permanganate has three different behaviours depending on the pH. This is the single most examinable fact about it.
MnO4− + 8 H+ + 5 e− → Mn2+ + 4 H2O E° = +1.52 V
Neutral or faintly alkaline (gains 3 e−, ends as brown MnO2):
MnO4− + 4 H+ + 3 e− → MnO2 + 2 H2O E° = +1.69 V
Strongly alkaline (gains 1 e−, ends as green manganate):
MnO4− + e− → MnO42− E° = +0.56 V
| Reaction in acidic medium | Balanced ionic equation |
|---|---|
| Iron(II) to iron(III) | MnO4− + 8 H+ + 5 Fe2+ → Mn2+ + 5 Fe3+ + 4 H2O |
| Oxalate to carbon dioxide (warm, about 333 K) | 2 MnO4− + 5 C2O42− + 16 H+ → 2 Mn2+ + 10 CO2 + 8 H2O |
| Iodide to iodine | 2 MnO4− + 16 H+ + 10 I− → 2 Mn2+ + 5 I2 + 8 H2O |
| Hydrogen sulfide to sulfur | 2 MnO4− + 6 H+ + 5 H2S → 2 Mn2+ + 5 S + 8 H2O |
| Sulfite to sulfate | 2 MnO4− + 6 H+ + 5 SO32− → 2 Mn2+ + 5 SO42− + 3 H2O |
| Nitrite to nitrate | 2 MnO4− + 6 H+ + 5 NO2− → 2 Mn2+ + 5 NO3− + 3 H2O |
Two more storage facts worth a mark: KMnO4 decomposes on heating at about 513 K to K2MnO4, MnO2 and O2, and its solutions decompose slowly in light — which is why laboratory bottles are dark brown.
Reduction: MnO4− + 8 H+ + 5 e− → Mn2+ + 4 H2O (× 2)
Oxidation: C2O42− → 2 CO2 + 2 e− (× 5) (1 mark.)
Step 2 — add, ten electrons each side:
2 MnO4− + 5 C2O42− + 16 H+ → 2 Mn2+ + 10 CO2 + 8 H2O (1 mark.)
Step 3 — check. Charge left = −2 − 10 + 16 = +4; right = +4. Oxygen: 8 + 20 = 28 on the left; 20 + 8 = 28 on the right. Balanced.
Why warm it? The oxalate–permanganate reaction is very slow at room temperature; warming to about 333 K supplies the activation energy so the reaction proceeds at a usable rate. Once some Mn2+ has formed it also autocatalyses the reaction, which is why the first drop of permanganate decolourises slowly and later drops vanish instantly. (1 mark.)
MnO4− + 8 H+ + 5 Fe2+ → Mn2+ + 5 Fe3+ + 4 H2O (1½ marks.)
Charge check: −1 + 8 + 10 = +17 on the left; +2 + 15 = +17 on the right.
(ii) In strongly alkaline solution. Permanganate accepts only one electron and is reduced to the green manganate(VI) ion:
MnO4− + e− → MnO42−, so the solution turns from purple to green. (1½ marks.)
Uses of KMnO4: oxidising agent in volumetric analysis and in organic synthesis (for example oxidising the side chain of toluene to benzoic acid), bleaching of wool, cotton, silk and oils, and as a topical disinfectant.
The Lanthanoids: Lanthanoid Contraction Explained With Consequences
The lanthanoids are the fourteen elements from cerium (Z = 58) to lutetium (Z = 71), in which the 4f sub-shell is progressively filled. Lanthanum (57) is always discussed with them. The general configuration is [Xe] 4f1–14 5d0 or 1 6s2, and the common tripositive ion has the tidy form Ln3+ = [Xe] 4fn.
The oxidation state story is refreshingly simple. Almost every lanthanoid shows only +3. The exceptions all come from the same source you have already met — the extra stability of empty, half-filled and completely filled sub-shells:
- Ce4+ is 4f0 (the bare xenon core) — hence cerium’s +4 state, and Ce4+ is a good oxidising agent because it wants to fall back to Ce3+.
- Tb4+ is 4f7 — half filled.
- Eu2+ is 4f7 — half filled, and Eu2+ is a good reducing agent because it wants to rise to Eu3+.
- Yb2+ is 4f14 — completely filled.
Now the headline act: the lanthanoid contraction. As you cross the series from La to Lu, the atomic and (much more regularly) the ionic radii steadily decrease. The ionic radius of Ln3+ falls from 106 pm for La3+ to 85 pm for Lu3+ — a total contraction of 21 pm, roughly 1.5 pm at each step.
The three consequences you must be able to state.
- The second and third transition series become almost the same size. Fourteen f-electron insertions cancel out the size increase you would expect from adding a shell. Zr (about 160 pm) and Hf (about 159 pm) are the standard pair; Nb/Ta and Mo/W behave the same way. Because their radii and configurations are so alike, their chemistry is nearly identical and they are extremely difficult to separate — hafnium was not identified as a distinct element until 1923, well over a century after zirconium.
- The lanthanoids themselves are hard to separate. Their chemistry is dominated by the +3 state and their sizes differ by only about 1.5 pm per step, so classical chemical separation fails. Modern separation uses ion-exchange chromatography, exploiting the fact that complex stability rises smoothly as the ion gets smaller.
- The basicity of the hydroxides decreases from La(OH)3 to Lu(OH)3. As the cation shrinks, its polarising power rises, the Ln–OH bond becomes more covalent, and the hydroxide becomes progressively less basic.
Other general characteristics worth a line each: lanthanoids are silvery-white, soft, highly electropositive metals that tarnish rapidly in air; most Ln3+ ions are coloured because of f–f transitions, with La3+ (4f0) and Lu3+ (4f14) colourless; most Ln3+ ions are paramagnetic, although for the f-block the spin-only formula does not work well because orbital angular momentum is not quenched.
Consequence 1 (1 mark). The elements of the second and third transition series have almost identical radii — for example Zr about 160 pm and Hf about 159 pm — so their chemical properties are extremely similar and they are very difficult to separate.
Consequence 2 (1 mark). The basicity of the lanthanoid hydroxides decreases from La(OH)3 to Lu(OH)3, because the polarising power of the cation increases as its size falls.
Eu2+ is [Xe] 4f7; it readily loses one electron to become Eu3+ ([Xe] 4f6), the ordinary and much more stable oxidation state for a lanthanoid. Because it gives electrons away easily, it acts as a reducing agent. (1 mark.)
Ce4+ is [Xe] 4f0; it readily gains one electron to become Ce3+ ([Xe] 4f1), again reaching the normal +3 state. Because it takes electrons readily, it acts as an oxidising agent. (1 mark.)
The Actinoids
The actinoids are the fourteen elements from thorium (Z = 90) to lawrencium (Z = 103), in which the 5f sub-shell fills. Actinium (89) is discussed alongside them. Their general configuration is [Rn] 5f1–14 6d0–1 7s2.
The single structural difference that drives everything: 5f orbitals are not buried as deeply as 4f orbitals. They extend further out, so 5f electrons are more available for bonding and are more easily ionised. Two things follow at once — actinoid chemistry is richer than lanthanoid chemistry, and the actinoid contraction is sharper per step because 5f shielding is even poorer than 4f shielding.
The other headline fact is that all actinoids are radioactive. Thorium and uranium have very long half-lives and occur naturally in reasonable quantity; the later members are synthetic, short-lived and available only in vanishingly small amounts, which is why their chemistry is patchily known.
| Point of comparison | Lanthanoids (4f) | Actinoids (5f) |
|---|---|---|
| Sub-shell being filled | 4f, deeply buried | 5f, less buried and more exposed |
| Oxidation states | Almost always +3; +2 and +4 only in a few cases | +3 is common to all, but +4, +5, +6 and even +7 are well known |
| Radioactivity | Non-radioactive apart from promethium | All members are radioactive |
| Contraction | Lanthanoid contraction — regular and gradual | Actinoid contraction — greater per step and less regular |
| Ionisation enthalpy | Higher | Lower, because 5f electrons are less tightly held |
| Bonding character | Compounds largely ionic; weak complex formation | More covalent character; much stronger tendency to form complexes |
| Magnetic behaviour | Follows f–f behaviour fairly predictably | More complex; harder to interpret |
Some Applications of d- and f-Block Elements
This sub-topic is usually worth one or two marks and it is pure recall, so build a short list you can reproduce quickly.
| Element or compound | Application |
|---|---|
| Iron and its alloys | The dominant construction material. Stainless steel is Fe with roughly 12–18 percent Cr plus Ni. |
| TiO2 | White pigment in paint, paper, plastics and sunscreen. |
| MnO2 | Cathode material in dry cells; starting material for KMnO4. |
| V2O5 | Catalyst in the Contact process for sulfuric acid. |
| Finely divided Fe | Catalyst in the Haber process for ammonia. |
| Ni | Catalyst for hydrogenating vegetable oils. |
| AgBr | Light-sensitive emulsion in photographic film. |
| Zn, Ni–Cd | Galvanising; rechargeable battery electrodes. |
| Mischmetall | About 95 percent lanthanoid metals with about 5 percent iron plus traces of S, C, Ca and Al. Used in magnesium-based alloys and famously in lighter flints. |
| Mixed lanthanoid oxides | Catalysts in petroleum cracking. |
| Lanthanoid phosphors | Colour emitters in television screens, fluorescent lamps and X-ray imaging plates. |
| Uranium and thorium oxides | Nuclear reactor fuel; thorium is central to India’s three-stage nuclear programme. |
Memory Devices and the d and f Block Class 12 Formula List
Everything you might need to reproduce under time pressure, on one screen.
Lanthanoid configuration: [Xe] 4f1–14 5d0–1 6s2
Actinoid configuration: [Rn] 5f1–14 6d0–1 7s2
Spin-only magnetic moment: μ = √(n(n + 2)) BM
Dichromate reduction: Cr2O72− + 14 H+ + 6 e− → 2 Cr3+ + 7 H2O, E° = +1.33 V
Permanganate, acidic: MnO4− + 8 H+ + 5 e− → Mn2+ + 4 H2O, E° = +1.52 V
Permanganate, neutral: MnO4− + 4 H+ + 3 e− → MnO2 + 2 H2O, E° = +1.69 V
Permanganate, strongly alkaline: MnO4− + e− → MnO42−, E° = +0.56 V
Chromate–dichromate: 2 CrO42− + 2 H+ ⇌ Cr2O72− + H2O
2. Ionisation: “s leaves before d” — always strip the ns electrons first.
3. Maximum oxidation state: “3, 4, 5, 6, 7 — then fall” for Sc, Ti, V, Cr, Mn onwards. Up to Mn it equals the total number of 4s + 3d electrons.
4. Colour: “Empty or full means colourless” — d0 and d10 only.
5. Lanthanoid exceptions: “Ce and Tb go up, Eu and Yb go down” — because f0, f7, f7 and f14 are extra stable.
Practice Worksheet
Ten original questions in board style. Close the book, write full answers on paper, and only then open the accordions. Marks are indicated so you can practise pacing.
Q1. Write the ground-state electronic configurations of chromium (Z = 24) and copper (Z = 29), and explain why neither follows the expected pattern. (3 marks)
Show Answer
Q2. Calculate the spin-only magnetic moments of Ni2+ and Cr3+. (3 marks)
Show Answer
Cr3+: Cr is [Ar] 3d5 4s1; removing three electrons gives Cr3+ = [Ar] 3d3. Three electrons occupy three separate orbitals, so n = 3. μ = √(3 × 5) = √15 = 3.87 BM (1½ marks).
Note: √8 = 2.828, so 2.83 and 2.84 are both accepted.
Q3. Zinc, cadmium and mercury are placed in the d-block but are not regarded as transition elements. Justify. (2 marks)
Show Answer
Q4. Write the balanced ionic equation for the reaction of acidified potassium dichromate with potassium iodide, and state what is oxidised and what is reduced. (3 marks)
Show Answer
Charge check: left = −2 + 14 − 6 = +6; right = +6. Balanced.
Iodide is oxidised from −1 to 0 in I2; chromium is reduced from +6 in the dichromate to +3 in Cr3+ (1 mark). The solution changes from orange to green.
Q5. An orange solution of potassium dichromate is treated with sodium hydroxide and then re-acidified with dilute sulfuric acid. Describe the colour changes and state the oxidation state of chromium at each stage. (3 marks)
Show Answer
Cr2O72− + 2 OH− → 2 CrO42− + H2O — the solution turns orange to yellow (1 mark).
Re-acidifying reverses it:
2 CrO42− + 2 H+ → Cr2O72− + H2O — the solution turns yellow back to orange (1 mark).
Chromium remains in the +6 oxidation state throughout; this is an acid–base shift of an equilibrium, not a redox reaction (1 mark). This last point is where most students lose the mark.
Q6. E°(Mn3+/Mn2+) = +1.57 V while E°(Cr3+/Cr2+) = −0.41 V. Interpret both values. (3 marks)
Show Answer
A negative E° means the M2+ ion is readily oxidised, so Cr2+ is a strong reducing agent. Cr2+ is 3d4 and on losing one electron becomes Cr3+, 3d3 — a stable half-filled t2g arrangement (1½ marks).
Both ions are d4; what differs is the stability of the product.
Q7. The atomic radii of zirconium (about 160 pm) and hafnium (about 159 pm) are nearly identical even though hafnium lies one full period lower. Name and explain the effect responsible, and give one further consequence of it. (3 marks)
Show Answer
Further consequence (any one, 1 mark): Zr and Hf, Nb and Ta, Mo and W have nearly identical chemistry and are very hard to separate; or the second and third transition series have similar ionisation enthalpies and reactivity; or the basicity of the lanthanoid hydroxides decreases from La(OH)3 to Lu(OH)3.
Q8. Describe the preparation of potassium permanganate from pyrolusite. Give balanced equations for both steps. (3 marks)
Show Answer
2 MnO2 + 4 KOH + O2 → 2 K2MnO4 + 2 H2O (1½ marks).
Step 2 — oxidation of manganate(VI) to permanganate(VII). Industrially this is done by electrolytic oxidation in alkaline solution:
MnO42− → MnO4− + e−
In the laboratory the manganate is disproportionated in acidic or neutral solution:
3 MnO42− + 4 H+ → 2 MnO4− + MnO2 + 2 H2O (1½ marks).
Q9. A first-row transition metal forms only one oxidation state, +3. Its aqueous ion is colourless and diamagnetic. Identify the metal and justify all three observations. (3 marks)
Show Answer
Only +3: losing all three valence electrons (two 4s and one 3d) gives Sc3+ with the stable argon core, so no other state is accessible (½ mark).
Colourless: Sc3+ is 3d0. With no d electron there is nothing to promote, so no d–d transition is possible and no visible light is absorbed (¾ mark).
Diamagnetic: 3d0 means zero unpaired electrons, so μ = √(0 × 2) = 0 BM and the ion is repelled rather than attracted by a magnetic field (¾ mark).
Q10. (a) Why must dilute sulfuric acid, and not hydrochloric acid, be used to acidify potassium permanganate in a titration? (b) Manganese in MnO4− is d0, yet the ion is intensely purple. Explain. (3 marks)
Show Answer
(b) Since Mn(VII) has no d electrons, a d–d transition is impossible. The colour arises instead from a charge-transfer transition, in which an electron is momentarily transferred from an oxygen lone-pair orbital into an empty d orbital of manganese. Charge-transfer bands are far more intense than d–d bands, which is why even a very dilute solution appears deeply coloured (1½ marks).
Score yourself honestly. Anything below 24 out of 30 means you should re-read the two sections that cost you marks rather than re-reading the whole chapter — targeted repair beats broad revision every time.
Kaizen: you do not need to master this chapter today. You need to be one percent clearer about it than you were yesterday. Ten focused minutes tonight — one table rewritten from memory, one equation balanced by hand — compounds into a score you will be proud of in March.

