General properties of the transition elements

What are the general properties of the transition elements?

In plain words: a transition metal has d electrons that can take part in bonding and can be lost a few at a time. That one fact explains why the metals are so strong, why iron can be Fe²⁺ or Fe³⁺, why copper sulphate is blue and why iron and nickel speed up industrial reactions.

The d-block sits between the s- and p-blocks. The numbers on this page are NCERT’s, from its Tables 4.2, 4.4 and 4.7 (NCERT pages 94, 99 and 102), unless another source is named.

Physical properties

• Metallic structures. Except Zn, Cd, Hg and Mn, the transition metals have one or more typical metallic structures (hcp, ccp or bcc) at normal temperatures (NCERT Section 4.3.1, page 92).
• NCERT slip (page 92): the key under the lattice-structure table reads “X = a typical metal structure”, but X marks Mn, Zn, Cd and Hg, the exceptions named just above it. Read it as “atypical”.
• Hard, with high melting points. Apart from zinc, cadmium and mercury they are very hard and have low volatility and high melting and boiling points. The reason is that electrons from the (n − 1)d orbitals join the ns electrons in the metallic bonding (NCERT page 92).
• The melting-point trend. Across each series the melting point rises to a maximum at about d^⁵, apart from the anomalous Mn and Tc, and then falls as the atomic number increases (NCERT page 92, Fig. 4.1).
• High enthalpies of atomisation. They peak near the middle of each series, where there is about one unpaired electron per d orbital, which favours strong interatomic interaction; in general, the more valence electrons, the stronger the bonding (NCERT pages 92–93). Metals with very high enthalpies of atomisation tend to be noble in their reactions (NCERT page 93).
• Heavier series. The 4d and 5d metals have higher enthalpies of atomisation than the 3d metals, which helps explain why metal–metal bonds are much more common in compounds of the heavy transition metals (NCERT page 93).

NCERT’s Table 4.4 (page 99) repeats these enthalpies of atomisation with slightly different values for seven of its nine metals (Ti 469, Cr 398, Mn 279, Fe 418, Co 427, Ni 431, Zn 130 kJ mol⁻¹; V 515 and Cu 339 agree). The figure uses Table 4.2’s values, Example 3 Table 4.4’s.

Variation in atomic and ionic sizes of transition metals

Radii in pm and densities in g cm⁻³ for the first series (NCERT Table 4.2, page 94):

• Across a series ions of the same charge get smaller as the atomic number rises. Each new electron enters a d orbital, and a d electron shields the outer electrons poorly, so the net attraction of the nucleus grows. Atomic radii follow the same trend, but the change within a series is small (NCERT Section 4.3.2, page 93). NCERT’s Table 4.2 gives manganese 137 pm, above both its neighbours, yet its own Fig. 4.3 plots Mn on the smooth curve near 129 pm; the Wikipedia “Atomic radii of the elements (data page)” gives 127 pm.
• Down a group the radius rises from the 3d to the 4d series, but the 5d radii are almost the same as the 4d ones, for example Zr 160 pm and Hf 159 pm (NCERT pages 93–94).
• Lanthanoid contraction. Before the 5d series begins, the 4f orbitals fill. One 4f electron shields another even less well than one d electron shields another, so the 4fⁿ orbitals shrink steadily as the nuclear charge rises. This lanthanoid contraction cancels the expected increase in size, so the 4d and 5d elements have similar radii and very similar properties (NCERT pages 93–94).
• Density rises across the series, from titanium to copper, because the metallic radius falls while the atomic mass rises (NCERT page 94).
• NCERT slip (Table 4.2, page 94): the densities printed for scandium (3.43), titanium (4.1) and cobalt (8.7 g cm⁻³) are out of line with measured values: scandium’s is about 15% high and titanium’s 9% low; cobalt’s is 2% low. Beyond the NCERT text, the Wikipedia “Densities of the elements (data page)” gives Sc 2.985, Ti 4.506 and Co 8.90 g cm⁻³. The trend NCERT describes still holds. In an exam, use the values a question gives.
• NCERT slip (Fig. 4.3, page 94): the radius axis is labelled “Radius/nm”, but its numbers, 12 to 19, are tens of picometres: Co and Ni, 125 pm in Table 4.2, sit at about 12.5. In an exam, give radii in pm.

Ionisation enthalpies

Ionisation enthalpy in kJ mol⁻¹ for the first series (NCERT Table 4.2, page 94):

• The trend. Ionisation enthalpy rises along each series as the nuclear charge rises with the filling of the inner d orbitals. The rise is much smaller than along a period of non-transition elements. The first ionisation enthalpy rises gently; the second and third rise much more from one element to the next (NCERT Section 4.3.3, page 95).
• Why the first rises so little. The added 3d electrons shield the 4s electrons from the growing nuclear charge better than outer electrons shield one another, so the atoms shrink slowly and the first ionisation enthalpy creeps up. Its irregularities come from the way removing one electron changes the relative energies of the 4s and 3d orbitals (NCERT page 95).
• Breaks at d^⁵. M²⁺ and M³⁺ ions have dⁿ configurations with no 4s electrons. The steady rise in second ionisation enthalpy breaks at Mn (1509, below Cr’s 1592), and the rise in third ionisation enthalpy breaks at Fe (2962, below Mn’s 3260). In both cases the ion formed is d^⁵ (NCERT page 95).
• Exchange energy. Three terms set an ionisation enthalpy: the attraction of each electron to the nucleus, the repulsion between electrons and the exchange energy. Exchange energy stabilises a configuration and is roughly proportional to the number of pairs of electrons with parallel spins in the degenerate orbitals; by Hund’s rule the lowest state has the most singly filled orbitals with parallel spins (NCERT pages 95–96). Removing an electron that costs exchange energy is harder. So Mn⁺ (3d^⁵4s^¹) ionises more easily than Cr⁺ (d^⁵), and Fe²⁺ (d^⁶) more easily than Mn²⁺ (d^⁵) (NCERT page 96).
• NCERT slip (page 96): NCERT writes “The loss of exchange energy increases the stability.” As written this is the wrong way round: exchange energy stabilises, so losing it makes a configuration less stable, and an ionisation that would lose exchange energy is difficult. NCERT’s conclusions in the same paragraph, about Mn⁺ against Cr⁺ and Fe²⁺ against Mn²⁺, are right. NCERT’s point is that ionising a d^⁵ set would lose exchange energy, so it is difficult; write it that way.
• The +2 state. Forming M²⁺ from the solid needs the enthalpy of atomisation plus the first two ionisation enthalpies. The second is the big term: it is unusually high for Cr and Cu, whose M⁺ ions are d^⁵ and d^¹⁰, and low for Zn, which loses its second 4s electron to become d^¹⁰ (NCERT page 96).
• The third ionisation enthalpy is high for Mn²⁺ (d^⁵) and Zn²⁺ (d^¹⁰), and high values for copper, nickel and zinc explain why they rarely go beyond +2 (NCERT page 96).

Oxidation states

The common oxidation states of the first series (NCERT Table 4.3, page 96; the ones NCERT prints in bold are marked bold):

• Most states in the middle. Manganese shows every state from +2 to +7. At the ends there are fewer: Sc and Ti have too few electrons to lose or share, and Cu and Zn have so many d electrons that few orbitals are left for sharing. Thus scandium(II) is virtually unknown, Ti(IV) is more stable than Ti(III) or Ti(II), and the only oxidation state of zinc is +2 (NCERT Section 4.3.4, page 97). Beyond the NCERT text: rare exceptions exist, such as the zinc(I) compound decamethyldizincocene, reported in 2004 (Wikipedia, “Decamethyldizincocene”).
• The highest stable state equals the sum of the s and d electrons up to manganese: Ti(IV) in TiO₂, V(V) in VO₂⁺, Cr(VI) in CrO₄²⁻, Mn(VII) in MnO₄⁻. After that higher states quickly lose stability: Fe(II, III), Co(II, III), Ni(II), Cu(I, II), Zn(II) (NCERT page 97).
• Steps of one. Transition-metal oxidation states differ by one, as in V(II), V(III), V(IV) and V(V); those of non-transition elements usually differ by two (NCERT page 97).
• Opposite to the p-block. In the p-block the heavier members favour lower states (the inert pair effect). In groups 4 to 10 of the d-block the heavier members favour higher ones: Mo(VI) and W(VI) are more stable than Cr(VI), so dichromate in acid is a strong oxidising agent but MoO₃ and WO₃ are not (NCERT page 97).
• Low states. Ligands that accept π electrons as well as forming σ bonds stabilise low states: nickel in Ni(CO)₄ and iron in Fe(CO)₅ are 0 (NCERT page 97).
• No variable states: scandium (Z = 21) does not exhibit variable oxidation states (NCERT Example 4.3, page 97); give scandium in an exam.

Trends in the M^²⁺/M standard electrode potentials

• The numbers. E^⊖(M²⁺/M) is −1.63 V for Ti, −1.18 for V, −0.90 for Cr, −1.18 for Mn, −0.44 for Fe, −0.28 for Co, −0.25 for Ni, +0.34 for Cu and −0.76 V for Zn (NCERT Table 4.2, page 94; see the figure above). The more negative this standard reduction potential, the stronger the corresponding metal’s thermodynamic tendency to reduce a common comparison oxidant. It is not a reaction-rate prediction; actual potentials depend on activities.
• The trend is towards less negative values across the series, because the sum of the first and second ionisation enthalpies generally rises (NCERT Section 4.3.5, page 98).
• Copper is the only positive one. This accounts for its inability to liberate H₂ from acids; only oxidising acids, nitric and hot concentrated sulphuric, react with copper, the acids being reduced (NCERT page 98). The large energy needed to turn Cu(s) into Cu²⁺(aq) is not repaid by its hydration enthalpy (NCERT page 98). Strictly, dissolved oxygen can also let copper dissolve slowly in a non-oxidising acid (reasoned from the E^⊖ values).
• Mn, Ni and Zn are more negative than the trend: Mn²⁺ has a stable half-filled d^⁵ set and Zn²⁺ a full d^¹⁰ set, while nickel’s value goes with its most negative hydration enthalpy (NCERT pages 98–99). Nickel’s −0.25 V is barely above cobalt’s −0.28 V, though the series then climbs steeply to copper’s +0.34 V. In Table 4.4 nickel and copper share that value, −2121 kJ mol⁻¹ (NCERT page 99).

Trends in the M^³⁺/M^²⁺ standard electrode potentials

E^⊖(M³⁺/M²⁺) is −0.37 V for Ti, −0.26 for V, −0.41 for Cr, +1.57 for Mn, +0.77 for Fe and +1.97 V for Co (NCERT Table 4.2, page 94).

• High for Mn: Mn²⁺ (d^⁵) is particularly stable, and removing a third electron from Mn (Mn²⁺ → Mn³⁺, d^⁵ to d^⁴) takes a much larger third ionisation enthalpy (NCERT Section 4.3.6, page 99). NCERT adds that this “also explains why the +3 state of Mn is of little importance” (Example 4.7, page 101); give that in an exam. Strictly, the large value makes simple aqueous Mn(III) strongly oxidising, while Mn(III) is still found in solids such as MnF₃ and Mn₂O₃ (reasoned from NCERT Tables 4.5 and 4.6, pages 99–100).
• Low for Fe: Fe³⁺ is d^⁵, so it is extra stable (NCERT page 99).
• Higher than its neighbours for V: −0.26 V is less negative than Ti’s −0.37 and Cr’s −0.41 V, because V²⁺ has a half-filled t_2g level and resists oxidation (NCERT page 99).
• NCERT slip (page 99): NCERT calls vanadium’s value “comparatively low” yet relates it to the stability of V²⁺. A stable M²⁺ makes E^⊖(M³⁺/M²⁺) higher, and Table 4.2’s −0.26 V is indeed above its neighbours’. In an answer, give NCERT’s reason, the half-filled t_2g level of V²⁺.
• Sc and Zn. NCERT explains a low value for Sc by the noble gas configuration of Sc³⁺, and the highest value for Zn by the loss of an electron from Zn²⁺’s stable d^¹⁰ set (NCERT page 99). Table 4.2 itself prints no value for either.
• Same d^⁴, opposite behaviour. Cr²⁺ is reducing, because going to Cr³⁺ takes d^⁴ to d^³ with a half-filled t_2g level; Mn³⁺ is oxidising, because going to Mn²⁺ takes d^⁴ to the half-filled d^⁵ (NCERT Example 4.4, page 98).

Trends in stability of higher oxidation states

• Halides. The highest states appear in the tetrahalides TiX₄, in VF₅ and, in NCERT’s list, CrF₆. Manganese’s +7 has no simple halide, but MnO₃F is known. Among the ordinary compounds in NCERT’s restricted list, the trihalides beyond Mn are FeX₃ and CoF₃ (NCERT Section 4.3.7 and Table 4.5, page 99).
• NCERT slip (page 99), CrF₆: beyond the NCERT text, a 2014 matrix-isolation reinvestigation assigned earlier purported CrF₆ spectra to CrF₅, so CrF₆ should not be presented as a securely established ordinary compound (Schlöder and colleagues, Inorganic Chemistry, 2014); in an exam, give NCERT’s CrF₆.
• Fluorine stabilises high states through a higher lattice energy (CoF₃) or higher bond enthalpies in covalent compounds (VF₅). V(V) forms only VF₅; its other halides hydrolyse to the oxohalides VOX₃. NCERT notes the “instability” of fluorides “in the low oxidation states e.g., VX₂” (X = Cl, Br or I; page 99). Beyond the NCERT text: this is not a universal exclusion, since VF₂ has been prepared and characterised (Shafer, Materials Research Bulletin, 1969).
• NCERT slip (Table 4.5 against the text, pages 99–100): the table’s key gives VX₂ for all four halogens and CuX₂ for F and Cl only. The text names VX₂ only for Cl, Br and I (page 99), and says all copper(II) halides are known except the iodide (page 100). On copper the text is right (CuBr₂ is known); on vanadium the table is borne out by VF₂ (beyond the NCERT text, above). In an exam, answer from NCERT’s text.
• Copper(II) halides are all known except the iodide, because Cu²⁺ oxidises I⁻: 2Cu²⁺ + 4I⁻ → Cu₂I₂ + I₂ (NCERT page 100).
• Copper(I) in water disproportionates, 2Cu⁺ → Cu²⁺ + Cu. Cu²⁺(aq) is more stable than Cu⁺(aq) because its far more negative hydration enthalpy more than pays for copper’s second ionisation enthalpy (NCERT page 100).
• Oxides. The highest oxidation number in the oxides equals the group number from Sc₂O₃ to Mn₂O₇. In the ordinary textbook oxide series, iron ends at Fe₂O₃; ferrates(VI), FeO₄²⁻, form in alkali but decompose to Fe₂O₃ and O₂. Oxocations stabilise V(V) as VO₂⁺, V(IV) as VO²⁺ and Ti(IV) as TiO²⁺ (NCERT Table 4.6, page 100).
• Oxygen beats fluorine. The highest manganese fluoride is MnF₄, but the highest oxide is Mn₂O₇, because oxygen can form multiple bonds to the metal. In Mn₂O₇ each Mn is surrounded tetrahedrally by oxygens, with an Mn–O–Mn bridge; tetrahedral [MO₄]ⁿ⁻ ions are known for V(V), Cr(VI), Mn(V), Mn(VI) and Mn(VII) (NCERT page 100).
• Standard oxidising power in acidic aqueous conditions rises VO₂⁺ < Cr₂O₇²⁻ < MnO₄⁻, because the lower species they are reduced to grow more stable in that order (NCERT Example 4.5, page 100).
• Disproportionation happens when a state becomes less stable than one higher and one lower state. Manganese(VI) does this in acid: 3MnO₄²⁻ + 4H⁺ → 2MnO₄⁻ + MnO₂ + 2H₂O (NCERT Example 4.9, page 105).

Chemical reactivity and E⊖ values

• Reactivity varies widely. Many transition metals dissolve in mineral acids; a few are noble and are unaffected by single acids (NCERT Section 4.3.8, page 101).
• The usual first-series metals, except copper, have a thermodynamic tendency to reduce acid under the stated standard-like conditions, though sometimes slowly: titanium and vanadium are in practice passive to dilute non-oxidising acids at room temperature (NCERT page 101).
• M^²⁺/M values become less negative across the series, so the tendency to form M²⁺ falls (NCERT page 101). They are irregular because the sum of the first two ionisation enthalpies varies irregularly, and so do the sublimation enthalpies, which for a metal are its enthalpies of atomisation (NCERT Example 4.6, page 101).
• NCERT slip (Example 4.6, page 101): the solution says the sublimation enthalpies are “relatively much less for manganese and vanadium”. Manganese fits (281 kJ mol⁻¹), but NCERT’s own Table 4.2 gives vanadium the highest enthalpy of atomisation in the series, 515 kJ mol⁻¹. In an answer, name manganese only. The same list also prints Cr as −0.91 V; Tables 4.2 and 4.4 give −0.90 V.
• M^³⁺/M^²⁺ values show that Mn³⁺ and Co³⁺ are the strongest oxidising agents in water, while Ti²⁺, V²⁺ and Cr²⁺ are strong reducing agents that liberate hydrogen from dilute acid: 2Cr²⁺ + 2H⁺ → 2Cr³⁺ + H₂ (NCERT page 101).

Magnetic properties

• Kinds of magnetism. Diamagnetic substances are repelled by a magnetic field and paramagnetic ones attracted; substances attracted very strongly are ferromagnetic, and NCERT calls ferromagnetism “an extreme form of paramagnetism” (NCERT Section 4.3.9, pages 101–102); give that in an exam. Beyond the NCERT text: in a ferromagnet the moments align with each other spontaneously in domains, which lets it form a permanent magnet (Wikipedia, “Ferromagnetism”), so it is more than strong paramagnetism. Many transition-metal ions are paramagnetic (NCERT page 102).
• Unpaired electrons cause paramagnetism. For the compounds of the first series, NCERT says, the orbital contribution is effectively quenched and hence of no significance (page 102), so the moment is found from the number of unpaired electrons, n, by the spin-only formula, in Bohr magnetons (BM). Strictly, the quenching is only partial for some ions, as the observed values below show (reasoned):

One unpaired electron gives 1.73 BM, and the moment rises with n, so the observed magnetic moment gives a useful indication of the number of unpaired electrons (NCERT page 102).

Calc.: the spin-only value from the formula. Obs.: the observed value from NCERT Table 4.7 (page 102), mostly for hydrated ions.

From Fe²⁺ to Cu²⁺ the observed moments exceed the spin-only ones: the orbital contribution is not wholly quenched (reasoned from NCERT Table 4.7, page 102). Even so, when a problem asks for the magnetic moment of a first-series ion, give the spin-only value, as NCERT Example 4.8 (page 102) does for the divalent ion of Z = 25, Mn²⁺: √35 = 5.92 BM; a measured moment can differ from it (reasoned).

• NCERT slips (Table 4.7, page 102): the third ion is printed “Tl²⁺”, a misprint for Ti²⁺ (3d^²); the spin-only value for two unpaired electrons is printed 2.84 BM, but √8 = 2.83; and the observed range for Ni²⁺ is printed “2.9 – 3, 4”, meaning 2.9–3.4. In an exam, choose the option closest to 2.83 BM.

Formation of coloured ions

• d–d transitions. When an electron is excited from a lower-energy d orbital to a higher-energy one, the energy absorbed corresponds to light, usually in the visible region. We see the complementary colour of the light absorbed, and the ligand decides which frequency is absorbed (NCERT Section 4.3.10, page 103).
• Textbook colours in aqueous media (NCERT Table 4.8, page 103). Strictly, these colours depend on ligands, acidity and speciation (reasoned): the blue V(IV) species, for example, is the oxocation VO²⁺, not a bare V⁴⁺ ion (reasoned from NCERT page 100, where oxocations stabilise V(IV) as VO²⁺):

• d^⁰ and d^¹⁰ ions cannot show ordinary d–d transitions: with an empty or a full d set no d–d transition is possible (reasoned from NCERT page 103). This rules out only d–d colour: permanganate is Mn(VII), d^⁰, yet intensely purple, a colour NCERT says needs molecular orbital theory (page 107).
• NCERT slip (Table 4.8, page 103): the cobalt row is run together as “3d^⁶3d^⁷, Co³⁺Co²⁺, bluepink”. Read it as two rows: Co³⁺, 3d^⁶, blue; Co²⁺, 3d^⁷, pink, as above.

Formation of complex compounds

• Complexes are species in which a metal ion binds a number of anions or neutral molecules, such as [Fe(CN)₆]³⁻, [Fe(CN)₆]⁴⁻, [Cu(NH₃)₄]²⁺ and [PtCl₄]²⁻ (NCERT Section 4.3.11, page 103).
• Why so many: transition-metal ions are comparatively small, carry high charges and have d orbitals available for bonding (NCERT page 104). NCERT’s Unit 5, on coordination compounds, treats them in detail.

Catalytic properties

• Why they catalyse: they can adopt several oxidation states and form complexes. Examples are vanadium(V) oxide in the Contact Process, finely divided iron in Haber’s Process and nickel in catalytic hydrogenation (NCERT Section 4.3.12, page 104).
• At a surface, reactant molecules bond to the metal atoms (the first series uses 3d and 4s electrons), which concentrates the reactants at the surface and weakens their bonds, lowering the activation energy (NCERT page 104).
• By changing oxidation state. Iron(III) catalyses the reaction of iodide with persulphate, 2I⁻ + S₂O₈²⁻ → I₂ + 2SO₄²⁻, in two steps (NCERT page 104):
  • 2Fe³⁺ + 2I⁻ → 2Fe²⁺ + I₂
  • 2Fe²⁺ + S₂O₈²⁻ → 2Fe³⁺ + 2SO₄²⁻

Formation of interstitial compounds

• What they are: compounds formed when small atoms such as H, C or N are trapped inside the crystal lattice of a metal. They are usually non-stoichiometric and neither typically ionic nor covalent: TiC, Mn₄N, Fe₃H, VH_0.56, TiH_1.7. Their formulas do not correspond to any normal oxidation state of the metal (NCERT Section 4.3.13, page 104). Their bonding has mixed metallic, covalent and ionic character, so integer ionic valences describe it poorly (reasoned from NCERT page 104: neither typically ionic nor covalent, yet they retain metallic conductivity).
• Properties (NCERT page 104): (i) high melting points, higher than those of the pure metals; (ii) very hard, some borides approaching diamond in hardness; (iii) they retain metallic conductivity; (iv) they are chemically inert. Give these in an exam. Strictly, melting behaviour and chemical resistance depend on the compound; these are trends, not guarantees for every metal hydride or interstitial phase (reasoned).

Alloy formation

• An alloy is “a blend of metals prepared by mixing the components” (NCERT Section 4.3.14, page 104). In a homogeneous solid solution the atoms of one metal are spread at random among those of the other; such alloys form between atoms whose metallic radii are within about 15 percent of each other (NCERT page 104). Strictly, an alloy can contain a non-metal, as carbon in steel shows, and the 15 percent rule favours a substitutional solid solution without guaranteeing one; crystal structure, bonding and composition also matter (reasoned).
• Transition metals alloy readily because their radii and other properties are similar, and their alloys are hard and often have high melting points. Chromium, vanadium, tungsten, molybdenum and manganese are used to make steels and stainless steel; brass (copper–zinc) and bronze (copper–tin) join a transition metal to a non-transition metal (NCERT page 104).

Solved examples

Common mistakes to avoid

Quick revision summary

• Transition metals are hard, with high melting points and enthalpies of atomisation, because (n − 1)d electrons join the metallic bonding; Zn, Cd and Hg are the soft exceptions.
• Radii fall slightly across a series; 4d and 5d radii are almost equal because of the lanthanoid contraction; density rises from Ti to Cu.
• Ionisation enthalpies rise slowly across; breaks at d^⁵ (Mn for the second, Fe for the third) come from exchange energy.
• Oxidation states differ in steps of one; Mn shows +2 to +7; heavier members favour higher states.
• E⊖(M^²⁺/M) grows less negative across; only Cu is positive; Mn^³⁺ and Co^³⁺ oxidise, Ti^²⁺, V^²⁺ and Cr^²⁺ reduce.
• Oxygen stabilises higher states than fluorine (Mn_₂O_₇ against MnF_₄); Cu^⁺ disproportionates in water.
• Paramagnetism from unpaired electrons, spin-only μ = √(n(n + 2)) BM; colour from d–d transitions; complexes, catalysis, interstitial compounds and alloys.

Questions students ask

Why is mercury a liquid at room temperature?

Mercury is a liquid at room temperature because its metallic bonding is unusually weak: it melts at −38.83 °C (234.32 K), the lowest melting point of any stable metal, and is the only metal known to be liquid under standard conditions (beyond the NCERT text; Wikipedia, “Mercury (element)”). Wikipedia puts this down to the lanthanoid contraction and relativistic effects, which draw its outer 6s electrons in towards the nucleus and weaken the bonding. NCERT names zinc, cadmium and mercury as the exceptions to the hardness and high melting points of the transition metals (NCERT page 92), and mercury is the extreme one.

What is a Bohr magneton (BM), the unit of the spin-only magnetic moment?

A Bohr magneton (BM, μ_B) is the natural unit of an electron’s magnetic moment, eh/(4πm_e) = 9.274 × 10^⁻²⁴ J T^⁻¹ (beyond the NCERT text; Wikipedia, “Bohr magneton”; NIST CODATA 2022), and NCERT gives spin-only moments in it (NCERT page 102). An unpaired electron’s spin moment along a field is about 1 BM, but the effective moment that magnetic measurements give is √3 = 1.73 BM, because it grows with the total spin as √(S(S + 1)), not as S (Wikipedia, “Magnetochemistry”). Neither the JEE Main 2027 nor the NEET (UG) 2026 syllabus names the Bohr magneton, but Unit 11 of both lists the “magnetic properties” of the first-row transition elements.

What is the difference between the spin-only and the observed magnetic moment?

The spin-only magnetic moment, μ = √(n(n + 2)) BM, counts only the spin of the unpaired electrons, while the observed moment also includes their orbital motion; in first-series compounds the orbital part is effectively quenched, so the two are close (NCERT page 102). Close is not equal: Cu²⁺, one unpaired electron and 1.73 BM spin-only, is observed at 1.8–2.2 BM (NCERT Table 4.7, page 102). Beyond the NCERT text, when spin–orbit coupling is negligible the moment is √(4S(S + 1) + L(L + 1)) BM, the spin-only formula when L = 0; for the heavier transition metals, the lanthanoids and the actinoids that coupling cannot be ignored (Wikipedia, “Magnetochemistry”).

What is the difference between homogeneous and heterogeneous catalysis?

In homogeneous catalysis the catalyst is in the same phase as the reactants, usually dissolved with them; in heterogeneous catalysis it is in a different phase, usually a solid on whose surface gases or liquids react (beyond the NCERT text; Wikipedia, “Catalysis”). NCERT’s transition-metal catalysts show both kinds (reasoned): iron(III) ions catalysing the reaction of iodide with persulphate in solution act homogeneously, while vanadium(V) oxide in the Contact Process, finely divided iron in Haber’s Process and nickel in catalytic hydrogenation are solid, heterogeneous catalysts (NCERT page 104).

How are transition metals different from the alkali metals of group 1?

Transition metals differ from the alkali metals in most properties: the alkali metals are very reactive, have low ionisation enthalpies, form only 1+ ions, in mostly ionic compounds, and do not occur free in nature (NCERT Class 11 Chemistry, Unit 3, page 84). The transition metals are mostly hard, with high melting points (NCERT page 92), much less reactive, and show variable oxidation states, coloured ions, paramagnetism and catalytic activity (NCERT Class 11 Chemistry, Unit 3, page 84). Electrode potentials show the gap: E^⊖(Na⁺/Na) is −2.71 V, against −0.44 V for Fe²⁺/Fe and +0.34 V for Cu²⁺/Cu (NCERT Unit 2, Table 2.1, page 37).

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. In the series Sc to Zn, the enthalpy of atomisation of zinc is the lowest, 126 kJ mol⁻¹. Why? (NCERT Intext Question 4.2.)

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   High enthalpies of atomisation come from (n − 1)d electrons joining the ns electrons in metallic bonding, the more unpaired electrons the stronger the bonding (NCERT pages 92 and 95). Zinc is 3d^¹⁰4s^²: its d set is full, so only the two 4s electrons bond the atoms together, and the bonding is weakest of the series (reasoned).

2. Q2. Calculate the spin-only magnetic moment of the M²⁺(aq) ion of the element with Z = 27. (NCERT Intext Question 4.8.)

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   Z = 27 is cobalt, [Ar] 3d^⁷4s^², so Co²⁺ is 3d^⁷, with 3 unpaired electrons. μ = √(3 × 5) = √15 = 3.87 BM.

3. Q3. Which metal of the 3d series shows the largest number of oxidation states, and why? (NCERT Intext Question 4.3.)

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   Manganese, from +2 to +7 (NCERT page 97). It has 3d^⁵4s^², seven electrons that can be lost or shared, and it is in the middle of the series, where there are enough electrons and enough d orbitals for bonding.