Transition Elements (d-Block) (Sc, Ti and V Groups) : Properties, Trends, Oxidation States and Complex Formation Explanation For PGT, TGT, IIT-JAM, GATE, BITSAT, CSIR-NET, JEE Advanced, And BHU Exams

 

Sc, Ti and V Groups: Trends, Oxidation States and Complex Chemistry of Transition Elements

Transition Elements (d-Block Elements): Properties, Trends, Oxidation States and Complex Formation
Complete Guide for JEE Advanced, NEET, IIT-JAM, GATE, CSIR-NET & BITSAT

Imagine a world without iron bridges, without cobalt-blue pigments, without the platinum catalyst that cleans your car's exhaust, without haemoglobin carrying oxygen in your blood — impossible. The transition elements are the workhorses of chemistry and of life itself. They sit in the middle of the periodic table, bridging the reactive s-block metals and the mostly covalent p-block elements, and they bring along an extraordinary bag of tricks: vivid colours, strong magnetism, variable oxidation states, catalytic genius, and an almost obsessive love of forming complex ions.

This article is your complete companion to mastering the d-block (transition elements) — built directly from the celebrated text Concise Inorganic Chemistry (J.D. Lee), with every concept reshaped for competitive exam success.


1. What Are Transition Elements? (Definition of d-Block Elements) 🔬

2. General Properties of Transition Elements

3. Periodic Trends in d-Block Elements

4. Oxidation States and Variable Valency

5. Complex Formation and Coordination Compounds

6. Chemical Properties of Transition Metals

7. Sc, Ti and V Groups: Important Trends

Three series of elements are formed by progressively filling the 3d, 4d, and 5d shells of electrons. Together these constitute the d-block elements. Their periodic table position is between the s-block (Groups 1–2) and p-block (Groups 13–18), hence the term transitional.

  • First row (3d series): Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn (Groups 3–12)
  • Second row (4d series): Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd
  • Third row (5d series): La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg
  • Incomplete fourth row: Ac and actinides (discussed with f-block)
📌 Strict vs. Broad Definition: Strictly, a transition metal is one that has an incompletely filled d orbital in its elemental state OR in its commonly used ionic state. By this definition, Zn, Cd, and Hg are not true transition metals because Zn²⁺ has a d¹⁰ configuration. However, for exam purposes the entire d-block (Groups 3–12) is usually called "transition elements."

Why Group 12 (Zn, Cd, Hg) is Different

These elements have a completely filled d-shell (d¹⁰) even in their ionic forms (Zn²⁺, Cd²⁺, Hg²⁺ are all d¹⁰). So they do not show the typical transition-metal behaviour: no variable oxidation states (beyond +II), no colour from d-d transitions, no ferromagnetism. They are the odd ones out.


2. Electronic Configuration — The Root of All Properties

The general electronic configuration of transition elements is: [Noble gas] (n-1)d1–10 ns1–2

Calcium (the s-block element just before the first row) has the configuration: 1s²2s²2p⁶3s²3p⁶4s². From Sc onward, electrons fill the 3d orbital. In theory we expect a perfectly regular filling: 3d¹ → 3d² → 3d³... up to 3d¹⁰. Reality has two famous exceptions:

ElementExpected Config.Actual Config.Reason
Chromium (Cr)[Ar] 3d⁴ 4s²[Ar] 3d⁵ 4s¹Half-filled d (d⁵) is extra stable
Copper (Cu)[Ar] 3d⁹ 4s²[Ar] 3d¹⁰ 4s¹Fully filled d (d¹⁰) is extra stable
🎯 JEE/NEET Favourite: The configurations of Cr and Cu appear in almost every competitive exam. Remember: one electron from 4s shifts to 3d to achieve either half-filled (d⁵) or fully-filled (d¹⁰) stability.
Mnemonic: "CrCu Cheat the Rule" — Cr and Cu both steal an electron from 4s to give 3d a half/full fill.

Electronic Configurations of All First-Row Transition Elements

ElementSymbolConfigurationd-electrons
ScandiumSc[Ar] 3d¹ 4s²1
TitaniumTi[Ar] 3d² 4s²2
VanadiumV[Ar] 3d³ 4s²3
ChromiumCr[Ar] 3d⁵ 4s¹5 (exception)
ManganeseMn[Ar] 3d⁵ 4s²5
IronFe[Ar] 3d⁶ 4s²6
CobaltCo[Ar] 3d⁷ 4s²7
NickelNi[Ar] 3d⁸ 4s²8
CopperCu[Ar] 3d¹⁰ 4s¹10 (exception)
ZincZn[Ar] 3d¹⁰ 4s²10

3. Variable Oxidation States — The Hallmark Feature

One of the most striking and exam-relevant features of transition metals is their ability to exist in multiple oxidation states. Unlike s-block elements (Na always +1, Ca always +2), transition metals can show anywhere from +1 to +8 or even negative oxidation states!

Why Variable Oxidation States?

The energy difference between (n-1)d and ns subshells is very small. So both the ns and (n-1)d electrons can participate in bonding and be lost to form ions. More d electrons = more possible oxidation states.

Oxidation State Pyramid — First Row Transition Elements Sc Ti V Cr Mn Fe Co Ni Cu Zn +VII VII +VI VI VI VI +V V V V V V +IV IV IV IV IV IV IV IV +III III III III III III III III III +II II II II II II II II II II Max oxidation Common (+III) Common (+II) Oxidation states form a characteristic pyramid shape across first-row transition elements

Fig. 1 — Oxidation state distribution across first-row transition elements (most stable states in bold font in text)

Key Trends in Oxidation States

  • First five elements (Sc→Mn): Maximum oxidation state equals group number. Example: Mn (Group 7) shows max +VII in KMnO₄.
  • Last five elements (Fe→Zn): After d⁵, tendency of all d electrons to participate in bonding decreases. Fe shows maximum +VI (not +VIII), while Ru and Os show +VIII.
  • Higher oxidation states: Found in fluorides and oxides (F⁻ and O²⁻ are small, highly electronegative — they stabilise high oxidation states).
  • Lower oxidation states: Stabilised by π-bonding ligands like CO and dipyridyl.
  • Isostructural pairs: In highest oxidation state, properties resemble main group. Example: SO₄²⁻ (Group 16) and CrO₄²⁻ (Group 6) are isostructural; SiCl₄ and TiCl₄ are isostructural.
🎯 Exam Trick — Mn oxidation states: Mn shows +II, +III, +IV, +V, +VI, +VII. The +VII state in KMnO₄ is the highest. In neutral/acidic medium KMnO₄ is reduced to Mn²⁺ (colourless); in alkaline medium to MnO₄²⁻ (manganate, green); in neutral/weakly alkaline medium to MnO₂ (brown precipitate).

4. Metallic Character — Why They're All Metals

In the d-block, the penultimate (second-to-last) shell of electrons is expanding. This means the d electrons are being added to an inner shell, not the outermost one. The result? All transition elements are metals with:

  • High electrical and thermal conductivity (delocalised electrons)
  • Metallic lustre
  • Hard, strong and ductile nature
  • High melting and boiling points (due to strong metallic bonding involving d electrons)
  • They form alloys with each other and with other metals
⚠️ Exception Alert: Zn, Cd, and Hg are soft and have low melting points (Hg is liquid at room temperature, m.p. = −38°C) because their d shells are completely filled and do NOT participate in metallic bonding!

Melting Points — A Dramatic Story

Transition metals typically melt above 1000°C. Ten elements melt above 2000°C, and three melt above 3000°C: Ta (3000°C), W (3410°C) and Re (3180°C). Tungsten holds the record for highest melting point of any element. This contrasts sharply with s-block metals like Li (181°C) and Cs (29°C).

Density — Surprisingly Heavy!

Transition metals have small atomic volumes (nuclear charge is poorly screened by d electrons → all electrons pulled inward → compact atom → high density). Almost all have density > 5 g/cm³. The champions are osmium (22.57 g/cm³) and iridium (22.61 g/cm³) — the densest elements known. A football made of osmium measuring 30 cm in diameter would weigh 320 kg!


5. Size of Atoms and Ions — Lanthanide Contraction Explained

Atomic size follows an interesting pattern across the transition series:

Covalent Radius (Å) Element (First Row: Sc → Zn) 1.10 1.20 1.30 1.40 1.50 Sc Ti V Cr Mn Fe Co Ni Cu Zn Covalent Radii of First-Row Transition Elements

Fig. 2 — Covalent radii decrease from Sc to Ni, then slightly increase at Cu and Zn

Key Size Trends

  • Left to right across a row: Radii generally decrease because extra protons are added but d electrons shield the nucleus poorly (d electrons shield less effectively than p or s electrons).
  • Near the end of the row: Slight increase at Cu and Zn due to d–d electron repulsion.
  • Down a group (Sc→Y→La): Radii increase as expected. But from Group 4 onward, the increase from 2nd row to 3rd row is almost zero because of the Lanthanide Contraction.

Lanthanide Contraction — A Critical Concept

Between the second row (4d) and third row (5d) elements, 14 lanthanide elements (filling 4f orbitals) intervene. The 4f electrons are very poor shielders of nuclear charge. So across the 14 lanthanides, the nuclear charge increases by 14 units while shielding barely increases → each atom shrinks progressively. By the time we reach Hf (next to La), the size has contracted back to nearly the same as Zr (previous row)!

📌 Consequences of Lanthanide Contraction:
  • Zr and Hf are almost identical in size → extremely difficult to separate (most difficult pair in periodic table)
  • Nb and Ta have same ionic radii → also very difficult to separate
  • 2nd and 3rd row transition elements are more similar to each other than either is to the 1st row
  • 3rd row elements are denser, have higher melting points, and show stronger covalent bonding

6. Ionization Energies and Electrode Potentials

Ionization energies of transition metals are intermediate between s-block and p-block. First ionization energies vary from 541 kJ mol⁻¹ (La) to 1007 kJ mol⁻¹ (Hg) — comparable to Li and C respectively. This explains why transition metals are less electropositive than Group 1/2 and can form either ionic or covalent bonds depending on conditions.

Standard Electrode Potentials

Noble character (low reactivity with acids) is promoted by:

  • High enthalpy of sublimation (strong metallic bonding)
  • High ionization energies
  • Low solvation enthalpy (large ionic radius → weak hydration)

The platinum group metals (Ru, Rh, Pd, Os, Ir, Pt) and gold are the most noble. Many transition metals dissolve in mineral acids, liberating H₂, but the platinum metals and gold require aqua regia (mixture of concentrated HCl and HNO₃).


7. Colour in Transition Metal Compounds

This is one of the most visually striking and theoretically rich topics in inorganic chemistry — and a favourite in all competitive exams!

Why Are Transition Metal Compounds Coloured?

When light passes through a material, certain wavelengths are absorbed. If absorption occurs in the visible region, the transmitted light has the complementary colour. Transition metal ions with incompletely filled d orbitals can absorb visible light by promoting an electron from a lower d level to a higher d level (d–d transition). This energy jump is small enough to fall in the visible spectrum.

Colour Absorbed vs. Colour Observed Colour Absorbed Colour Observed Violet (400–430 nm) Yellow-green Blue (430–480 nm) Orange Green (490–560 nm) Red Yellow (560–590 nm) Violet Orange (590–625 nm) Blue Red (625–750 nm) Green Absorbed and observed colours are complementary to each other

Fig. 3 — Complementary colour chart for transition metal compounds

Factors That Change the Colour of a Complex

  1. Nature of the ligand: [Ni(NH₃)₆]²⁺ is blue, [Ni(H₂O)₆]²⁺ is green, [Ni(NO₂)₆]⁴⁻ is brown-red.
  2. Number of ligands
  3. Shape of the complex
  4. Oxidation state of the metal

When There Is No Colour

Some transition metal compounds are white/colourless:

  • ZnSO₄, TiO₂: Zn²⁺ is d¹⁰ (full d), Ti⁴⁺ is d⁰ (empty d) → no d–d transitions possible.
  • Sc³⁺, Ti⁴⁺, V⁵⁺, Cr⁶⁺, Mn⁷⁺: All have empty d orbitals → colourless in principle, but high oxidation states often form oxo-anions (e.g., CrO₄²⁻ yellow, MnO₄⁻ purple) that are intensely coloured due to charge transfer (not d–d).
🎯 Charge Transfer Colour: MnO₄⁻ (permanganate) is deep purple not because of d–d transition (Mn is +VII, d⁰) but because an electron is momentarily transferred from O²⁻ to Mn(VII), changing O²⁻ to O⁻ and Mn(VII) to Mn(VI). This charge-transfer absorption is very intense and falls in visible region. Charge transfer always gives intense colours because spin and Laporte selection rules don't apply.

8. Magnetic Properties — Paired vs. Unpaired Electrons

Magnetism in transition metal compounds is a direct window into their electronic structure — and one of the most numerical-heavy topics in exams.

Types of Magnetism

  • Paramagnetism: Substance is attracted into a magnetic field. Caused by unpaired electrons. More unpaired electrons → stronger paramagnetism.
  • Diamagnetism: Substance is weakly repelled from a magnetic field. All electron spins are paired. Diamagnetism is much weaker than paramagnetism.
  • Ferromagnetism: Very strong magnetism where unpaired electrons on adjacent atoms align parallel. Fe, Co, and Ni are ferromagnetic. They can form permanent magnets.
  • Antiferromagnetism: Moments on adjacent atoms align antiparallel → nearly zero net moment. Found in salts of Fe³⁺, Mn²⁺, Gd³⁺.

Calculating Magnetic Moment

For first-row transition elements, orbital contribution is quenched by the crystal field. So we use the spin-only formula:

μs = √[n(n + 2)] · μB

where n = number of unpaired electrons and μB = Bohr magneton (9.273 × 10⁻²⁴ J T⁻¹).

n (unpaired e⁻)μs (B.M.)Example IonExperimental μ (B.M.)
11.73Ti³⁺, Cu²⁺1.7–2.1
22.83V³⁺, Ni²⁺2.8–3.5
33.87Cr³⁺, Co²⁺3.7–5.2
44.90Cr²⁺, Mn³⁺, Fe²⁺4.8–5.6
55.92Mn²⁺, Fe³⁺5.7–6.0
🎯 Worked Example (JEE-style): Magnetic measurements on CuSO₄·5H₂O at 293 K gave χM (after diamagnetic correction) = 2.004 × 10⁻⁸ mol⁻¹ m³. Calculate magnetic moment:
μ/μB = 797.5 × √(χM × T) = 797.5 × √(2.004 × 10⁻⁸ × 293) = 1.93 BM
Using spin-only: if n=1, μ = √(1×3) = 1.73 BM ≈ experimental. ∴ Cu²⁺ has 1 unpaired electron.

High Spin vs. Low Spin Complexes

In an octahedral crystal field, the five d-orbitals split into two sets:

  • t₂g (lower energy): dxy, dxz, dyz
  • eg (higher energy): dx²-y², d
Crystal Field Splitting in Octahedral Complex Barycenter t₂g eᵍ Δ₀ Free ion Octahedral field Strong field (large Δ₀) → Low spin | Weak field (small Δ₀) → High spin

Fig. 4 — Crystal field splitting of d-orbitals in an octahedral field into t₂g and eg sets

  • Strong field ligands (large Δ₀): CN⁻, CO, NO⁺ → electrons pair in t₂g → low spin → fewer unpaired electrons
  • Weak field ligands (small Δ₀): F⁻, H₂O, OH⁻ → electrons fill all orbitals first → high spin → more unpaired electrons
Spectrochemical Series Mnemonic:
I⁻ < Br⁻ < S²⁻ < Cl⁻ < NO₃⁻ < F⁻ < OH⁻ < H₂O < NCS⁻ < NH₃ < en < bpy < NO₂⁻ < CN⁻ < CO
"I Brought Some Carrots, Not For Our Home, Never Asked. Enough! No Nicely, Bye Noisy Colleagues!"

9. Complex Formation — Transition Metals as Superb Lewis Acids

Transition metals have an unparalleled tendency to form coordination compounds with Lewis bases (ligands). A ligand is any neutral molecule (like NH₃) or anion (like Cl⁻ or CN⁻) that can donate a lone pair of electrons to the metal.

Co³⁺ + 6NH₃ → [Co(NH₃)₆]³⁺
Fe²⁺ + 6CN⁻ → [Fe(CN)₆]⁴⁻

Why Do Transition Metals Form So Many Complexes?

  • They have small, highly charged ions → strong electrostatic attraction for ligands
  • They have vacant low-energy d orbitals to accept lone pairs from ligands
  • The +III oxidation state is more stable in complexes than the +II state
  • Cobalt forms more complexes than any other element except carbon!

Class-a vs. Class-b Acceptors (Hard-Soft Acid-Base Theory)

ClassMetal ExamplesPreferred Ligand Donor AtomsHSAB Term
Class-a (hard)Sc, Ti, V, Cr, Mn, Fe, Co (early/first row)N, O, F (small, electronegative)Hard acid
Class-b (soft)Rh, Ir, Pd, Pt, Ag, Au, HgP, S, I (large, polarizable)Soft acid
BorderlineFe, Co, Ni, Cu, Ru, OsBoth typesIntermediate

Coordination Numbers and Shapes

  • CN = 6, Octahedral — by far the most common
  • CN = 4, Tetrahedral — common for d¹⁰ metals (Zn²⁺) and large ligands
  • CN = 4, Square Planar — characteristic of d⁸ metals (Ni²⁺, Pd²⁺, Pt²⁺, Au³⁺)
  • CN = 7 or 8 — rare in first row, but much more common in second and third row (e.g., [ZrF₇]³⁻, [ZrF₈]⁴⁻)
Octahedral Complex [M(L)₆] M L L L L L L CN = 6, all L–M–L angles = 90° (ideal octahedron)

Fig. 5 — Schematic of an octahedral [ML₆] transition metal complex


10. Catalytic Properties — Transition Metals as Nature's Catalysts

Transition metals and their compounds are among the most important catalysts in both industry and biological systems. They catalyse reactions by:

  • Using their variable valency to form unstable intermediate compounds
  • Providing a suitable reaction surface (heterogeneous catalysis)

Key Industrial Catalysts

CatalystProcessReaction
TiCl₃ (Ziegler-Natta)Polymerisation of ethylenen(CH₂=CH₂) → (–CH₂–CH₂–)ₙ
V₂O₅Contact Process (H₂SO₄ manufacture)SO₂ + ½O₂ → SO₃
Fe (promoted)Haber-Bosch Process (NH₃)N₂ + 3H₂ ⇌ 2NH₃
MnO₂Decomposition of KClO₃2KClO₃ → 2KCl + 3O₂
PdCl₂Wacker ProcessC₂H₄ + H₂O + PdCl₂ → CH₃CHO + 2HCl + Pd
Pt/PtO (Adams)Reductions (hydrogenation)R–C≡C–R + H₂ → R–CH₂–CH₂–R
Pt/RhOstwald Process (HNO₃)4NH₃ + 5O₂ → 4NO + 6H₂O
Ni (Raney)Hydrogenation of alkenes, fats–CH=CH– + H₂ → –CH₂–CH₂–

Metalloenzymes — Nature's Own Transition Metal Catalysts

Many biological enzymes require a transition metal ion as a cofactor. These are called metalloenzymes. Examples from living systems:

  • Fe (Haemoglobin): O₂ transport in blood
  • Fe (Cytochrome): Electron transfer in respiration
  • Fe & Mo (Nitrogenase): Biological fixation of N₂ → NH₃
  • Co (Ribonucleotide reductase): DNA biosynthesis
  • Cu (Tyrosinase): Skin pigmentation
  • Zn (Carbonic anhydrase): CO₂ regulation (pH control in blood)
  • Mn (Arginase): Urea formation
📌 Enzymes can speed up reactions by a factor of 10⁶ to 10¹² compared to uncatalysed reactions, working under mild conditions (body temperature, normal pressure) and giving nearly 100% yield!

11. Nonstoichiometry — An Unusual Feature

Another fascinating property of transition metal compounds is their tendency to form nonstoichiometric compounds — compounds with variable, non-integer ratios of atoms. This arises directly from the variable oxidation states of transition metals.

Iron(II) oxide (FeO) is the textbook example. It should be written as FeO, but the actual formula varies between Fe0.94O and Fe0.84O! The formula is written with a bar: FeO (with overbar) to indicate this variability. The structure contains a mixture of Fe²⁺ and Fe³⁺ ions.

Nonstoichiometric iron oxide: Fe0.84O to Fe0.94O (mixed Fe²⁺/Fe³⁺)

Vanadium and selenium form a series: VSe0.98 → VSe1.0 → VSe1.6 — all related by the variable valency of vanadium.


12. Differences Between First Row and Second/Third Row Transition Elements

This topic is very important for IIT-JAM and CSIR-NET examinations.

Metal–Metal Bonding and Cluster Compounds

Metal-metal (M–M) bonding is quite rare in first-row elements — it occurs mainly in carbonyls like Fe₂(CO)₉ and Co₄(CO)₁₂. In the second and third row, M–M bonds are much more common:

  • Carbonyls: Ru₃(CO)₁₂, Os₃(CO)₁₂, Rh₄(CO)₁₂, Ir₄(CO)₁₂ — also the unique Rh₆(CO)₁₆ (no first-row analogue)
  • Halide cluster ions: [Re₂Cl₈]²⁻ and [Mo₂Cl₈]⁴⁻ have M–M bonds
  • Cluster compounds: Nb and Ta form octahedral 6-metal-atom clusters, e.g. [Nb₆Cl₁₂]²⁺ — 6 Nb atoms at corners of an octahedron with 12 bridging Cl atoms along edges

Stability of Oxidation States

  • First row: +II and +III states are most important. Simple M²⁺ and M³⁺ ions are very common.
  • Second and third row: Higher oxidation states are more stable. Example: CrO₄²⁻ is a strong oxidiser, but MoO₄²⁻ and WO₄²⁻ are stable. MnO₄⁻ is a strong oxidiser, but TcO₄⁻ and ReO₄⁻ are stable.
  • Some second/third row compounds have no first-row counterpart: WCl₆, ReF₇, RuO₄, OsO₄, PtF₆.

Magnetism Differences

Second and third row elements tend to give low-spin complexes regardless of the ligand field strength. The crystal field splitting Δ is larger for heavier elements (diffuse 4d/5d orbitals → better overlap with ligands → larger splitting). So electrons always pair up in the lower energy levels. This makes the spin-only formula less applicable for second and third row elements.


13. Abundance and Occurrence

Three first-row transition metals are very abundant in Earth's crust:

  • Iron (Fe): 60,000 ppm — 4th most abundant element, most abundant transition metal
  • Titanium (Ti): 6,320 ppm — 9th most abundant element
  • Manganese (Mn): 1,060 ppm — 12th most abundant

The first row elements as a group make up 6.79% of Earth's crust. The second and third row elements are mostly rare (Technetium does not occur naturally at all!). Of the last six elements in 2nd and 3rd rows (Tc, Ru, Rh, Pd, Ag, Cd; Re, Os, Ir, Pt, Au, Hg), none exceeds 0.16 ppm in Earth's crust.


14. Important Reaction Equations — Exam Ready

Reactions of Transition Metals with Acids

Fe + 2HCl → FeCl₂ + H₂↑
Fe + H₂SO₄(dil.) → FeSO₄ + H₂↑
Fe + 4HNO₃(dil.) → Fe(NO₃)₃ + NH₄NO₃ + 3H₂O
Cr + 6HCl(conc.) → 2CrCl₃ + 3H₂↑ (Cr passivated by HNO₃)

Reactions of KMnO₄ (Acidic Medium)

MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O    E° = +1.51 V
2KMnO₄ + 5H₂C₂O₄ + 3H₂SO₄ → 2MnSO₄ + K₂SO₄ + 10CO₂ + 8H₂O
2KMnO₄ + 5FeSO₄ + 4H₂SO₄ → 2MnSO₄ + K₂SO₄ + 5Fe₂(SO₄)₃ + 4H₂O

Reactions of K₂Cr₂O₇ (Acidic Medium)

Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O    E° = +1.33 V
K₂Cr₂O₇ + 6FeSO₄ + 7H₂SO₄ → K₂SO₄ + Cr₂(SO₄)₃ + 3Fe₂(SO₄)₃ + 7H₂O
K₂Cr₂O₇ + 3SO₂ → K₂SO₄ + Cr₂(SO₄)₃

Interconversion of Cr Species

CrO₄²⁻ (yellow, alkaline) + H⁺ ⇌ Cr₂O₇²⁻ (orange, acidic) + H₂O
Cr₂O₇²⁻ + 2NaOH → 2Na₂CrO₄ + H₂O

Cu²⁺ and Fe³⁺ Reactions

Cu²⁺ + 2I⁻ → CuI↓(white) + ½I₂ (Cu²⁺ oxidises I⁻)
Fe³⁺ + SCN⁻ → [Fe(SCN)]²⁺ (blood red — qualitative test)
Cu²⁺ + 4NH₃ → [Cu(NH₃)₄]²⁺ (deep blue/Schweitzer's reagent)

Disproportionation Reactions

2Cu⁺ → Cu + Cu²⁺    (Cu⁺ disproportionates in aqueous solution)
3MnO₄²⁻ + 4H⁺ → 2MnO₄⁻ + MnO₂ + 2H₂O    (Manganate disproportionation)

15. Molecular Structures by SVG

Structure of Permanganate Ion (MnO₄⁻)

MnO₄⁻ (Tetrahedral) Mn O O O O O–Mn–O angle = 109.5° Mn oxidation state = +VII, d⁰

Fig. 6 — Tetrahedral structure of permanganate ion MnO₄⁻

Structure of Chromate vs. Dichromate Ions

CrO₄²⁻ (Chromate) vs. Cr₂O₇²⁻ (Dichromate) CrO₄²⁻ (Tetrahedral) Cr O O O O Yellow, Cr = +VI, d⁰ Cr₂O₇²⁻ (Two tetrahedra sharing O) Cr Cr O O O O O O O Orange, Cr = +VI, d⁰; bridging O shown in blue Cr–O–Cr angle = ~120°

Fig. 7 — Structures of chromate (CrO₄²⁻) and dichromate (Cr₂O₇²⁻) ions


16. Special Topics for Advanced Exams (IIT-JAM / GATE / CSIR-NET)

The Curie and Curie-Weiss Laws

Pierre Curie showed that the paramagnetic susceptibility χM of most materials varies inversely with absolute temperature:

χM = C / T    (Curie Law)

Many systems deviate and obey the Curie-Weiss Law:

χM = C / (T + θ)

where θ (the Weiss constant) is an empirical correction factor. This deviation often signals ferromagnetic or antiferromagnetic interactions between neighbouring atoms.

Russell-Saunders Coupling (for Lanthanides)

For lanthanide elements (and in some heavy transition metals), the spin contribution S and orbital contribution L couple together to give a total angular momentum quantum number J. The magnetic moment must be calculated using:

μ = g√[J(J + 1)] · μB

where g = Landé g-factor = 1 + [S(S+1) − L(L+1) + J(J+1)] / 2J(J+1)

Orbital Contribution in Magnetism

The orbital contribution to magnetism exists when a t₂g orbital can be transformed into an equivalent orbital by rotation (i.e., the orbital is not quenched). In octahedral complexes, orbital contribution is significant for:

(t₂g)¹(eg)⁰   (t₂g)²(eg)⁰   (t₂g)⁴(eg)²   (t₂g)⁵(eg)²

For these configurations, the measured μ is higher than the spin-only value. Co²⁺ (d⁷) is a classic example — it has the (t₂g)⁵(eg)² configuration, giving an orbital contribution and an experimental μ of 4.3–5.2 BM, significantly above the spin-only value of 3.87 BM.


17. High-Yield Exam Tips and Tricks

🎯 Top 15 Exam Points You Must Know:
  1. Cr and Cu exceptions: [Ar]3d⁵4s¹ and [Ar]3d¹⁰4s¹ — non-negotiable for JEE/NEET
  2. Highest melting point: Tungsten (W), 3410°C
  3. Densest elements: Os and Ir (~22.6 g/cm³)
  4. Only liquid transition metal: Mercury (Hg), m.p. = −38°C
  5. Mn oxidation states: +II to +VII (+VII in KMnO₄)
  6. Maximum oxidation state > group number: Ru and Os can show +VIII (RuO₄, OsO₄) — Fe (same group) only shows +VI
  7. MnO₄⁻ in acidic medium: → Mn²⁺ (colourless); alkaline: → MnO₄²⁻ (green); neutral: → MnO₂ (brown)
  8. CrO₄²⁻ ⇌ Cr₂O₇²⁻: Add acid → dichromate (orange); add base → chromate (yellow)
  9. Spin-only formula: μ = √[n(n+2)] BM — valid for first-row only
  10. KMnO₄ is d⁰ yet purple: Colour due to charge transfer, not d-d transition
  11. Ziegler-Natta catalyst: TiCl₃ + AlEt₃ → stereoregular polythene (Nobel Prize 1963)
  12. Haber-Bosch: Fe catalyst, K₂O promoter, Al₂O₃ support, 450°C, 200 atm
  13. Lanthanide contraction causes: Zr ≈ Hf in size; Nb ≈ Ta in size
  14. Class-b (soft) metals: Rh, Ir, Pd, Pt, Ag, Au, Hg — prefer P, S, I ligands
  15. Square planar geometry: Characteristic of d⁸ metal ions (Ni²⁺, Pd²⁺, Pt²⁺, Au³⁺)
⚠️ Common Mistakes to Avoid:
  • Don't assume all transition metals show variable oxidation states — Sc³⁺ is the only stable state for Sc
  • Don't confuse "spin-only" formula with Russell-Saunders formula — spin-only works for first row only
  • Don't say KMnO₄ is purple due to d-d transition — Mn is +VII (d⁰) in KMnO₄; it's charge transfer
  • Zn, Cd, Hg are d-block but NOT transition metals by the strict definition
  • Cu⁺ (d¹⁰) is colourless in solution but Cu²⁺ (d⁹) is blue — don't mix them up

18. Quick Revision Summary

PropertyTrend / Key Fact
Electronic configuration[Noble gas] (n-1)d¹⁻¹⁰ ns¹⁻²
Exceptions (config.)Cr: 3d⁵4s¹; Cu: 3d¹⁰4s¹
Oxidation statesMultiple; max = group no. for Sc→Mn; decreases after Mn
Melting/boiling pointsVery high (d electrons in metallic bond); exceptions: Zn, Cd, Hg
Density>5 g/cm³ for most; Os and Ir densest (22.6 g/cm³)
Atomic size (across row)Decreases Sc→Ni, slightly increases Cu, Zn
Lanthanide contraction2nd and 3rd row have almost same size → Zr≈Hf, Nb≈Ta
Colourd-d transitions; absent for d⁰ and d¹⁰ ions (unless charge transfer)
Magnetismμ = √[n(n+2)] BM for first row; orbital contribution for some
Complex formationSmall, charged ions + vacant d orbitals → stable complexes
CatalysisVariable valency + surface activity → industrial and biological catalysts
NonstoichiometryVariable composition due to variable oxidation state (e.g. FeO)
M–M bondingRare in 1st row; common in 2nd/3rd row; forms cluster compounds

References & Further Reading: J.D. Lee, Concise Inorganic Chemistry, 5th Ed., Blackwell Science; Atkins, Shriver & Atkins' Inorganic Chemistry; IUPAC Recommendations for Nomenclature of Inorganic Chemistry (2005). All molecular geometries, bond angles, and oxidation states are consistent with IUPAC guidelines and experimental crystallographic data.

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