JEE Mains Chemistry · Formula sheet
The d- and f-Block Elements formulas
8 formulas, 13 reference tables and 42 common traps for JEE Mains Chemistry The d- and f-Block Elements, grouped by subtopic.
Electronic Configuration and General Properties
Learn this subtopic in the notesConfigurations of d-block atoms and ions
d electrons in a 3d ion
Ionisation enthalpies across the 3d series
| Metal | First IE (kJ/mol) | Second IE (kJ/mol) | Third IE (kJ/mol) | What it shows |
|---|---|---|---|---|
| Sc | 631 | 1235 | 2389 | Sc³⁺ is d⁰, so +3 is easy and is its only state |
| Ti | 656 | 1309 | 2652 | A steady rise with the nuclear charge |
| V | 650 | 1414 | 2828 | A steady rise with the nuclear charge |
| Cr | 653 | 1592 | 2987 | Low first IE (lone 4s); high second IE (breaks 3d⁵) Highest second IE from Sc to Fe, but its third IE is below Mn's. |
| Mn | 717 | 1509 | 3248 | High third IE: Mn²⁺ is 3d⁵ |
| Fe | 762 | 1561 | 2957 | Low third IE: Fe²⁺ loses one electron to reach 3d⁵ |
| Co | 758 | 1644 | 3232 | Rises again after the dip at Fe |
| Ni | 736 | 1752 | 3393 | Rises again after the dip at Fe |
| Cu | 745 | 1958 | 3554 | Highest second IE of the series: Cu⁺ is 3d¹⁰ |
| Zn | 906 | 1734 | 3833 | Highest first IE: a filled 4s² over a filled 3d¹⁰ |
Melting points, atomisation, density, catalysts and interstitial compounds
| Metal | Atomisation enthalpy (kJ/mol) | Metallic radius (pm) | Density (g/cm³) | Point tested |
|---|---|---|---|---|
| Sc | 326 | 164 | 2.99 | Largest atom of the series |
| Ti | 473 | 147 | 4.51 | Ti⁴⁺ in TiCl₄ is d⁰: the Ziegler–Natta catalyst is diamagnetic |
| V | 515 | 135 | 6.11 | Highest atomisation enthalpy of the 3d series |
| Cr | 397 | 129 | 7.19 | Smallest radius among Sc, Ti, V, Cr, Mn and Zn |
| Mn | 281 | 137 | 7.21 | A dip: 3d⁵ holds its d electrons out of the bonding |
| Fe | 416 | 126 | 7.87 | Catalyst of the Haber process |
| Co | 425 | 125 | 8.90 | Dense, high-melting |
| Ni | 430 | 125 | 8.91 | Catalyst for hydrogenating oils |
| Cu | 339 | 128 | 8.96 | Densest of the listed 3d metals |
| Zn | 126 | 137 | 7.14 | Lowest atomisation enthalpy: soft, low-melting Zn, Cd and Hg have filled d subshells; they are the soft end of each series. |
Common traps
Ions lose 4s before 3d
The 4d series has more exceptions than the 3d
Cr beats Mn on the second IE only
Cr is not the highest second IE of the whole series
A catalyst weakens bonds and uses 4s electrons too
The group-7/group-8 order flips in the 5d series
Oxidation States and Electrode Potentials
Learn this subtopic in the notesWhy Cu²⁺ is the stable copper ion in water
Iodometry of copper(II)
Oxidation states of the 3d metals
| Metal | Oxidation states | Most stable in water | Highest fluoride and oxide |
|---|---|---|---|
| Sc | +3 | +3 | , The only 3d metal with a single oxidation state besides 0. |
| Ti | +2, +3, +4 | +4 | , |
| V | +2, +3, +4, +5 | +4 (as ) and +5 | , |
| Cr | +2, +3, +4, +5, +6 | +3 | , |
| Mn | +2, +3, +4, +5, +6, +7 | +2 | , Highest oxide (+7) and highest fluoride (+4) differ by 3. |
| Fe | +2, +3 (+4 and +6 rare) | +3 in air, +2 without it | , |
| Co | +2, +3, +4 | +2 | , |
| Ni | +2, +3, +4 | +2 | , NiO |
| Cu | +1, +2 | +2 | , CuO |
| Zn | +2 | +2 | , ZnO |
E° values: which ions reduce acid and which oxidise
| Metal | E° of M²⁺/M (V) | E° of M³⁺/M²⁺ (V) | What it means |
|---|---|---|---|
| Ti | −1.63 | −0.37 | Ti²⁺ is a reductant and liberates hydrogen |
| V | −1.18 | −0.26 | V²⁺ is a reductant and liberates hydrogen |
| Cr | −0.90 | −0.41 | Cr²⁺ is a strong reductant: it becomes Cr³⁺, d³ |
| Mn | −1.18 | +1.57 | Mn³⁺ is a strong oxidant: it becomes Mn²⁺, d⁵ |
| Fe | −0.44 | +0.77 | Fe³⁺ is a mild oxidant; lower than Mn because Fe³⁺ is d⁵ |
| Co | −0.28 | +1.97 | Co³⁺ is the strongest oxidant of the series in water |
| Ni | −0.25 | No simple Ni³⁺ in water | Ni²⁺ is the stable ion |
| Cu | +0.34 | No Cu³⁺ in water | The only positive M²⁺/M value: Cu gives no hydrogen with dilute acid Cu has the highest M²⁺/M value of the 3d series. |
| Zn | −0.76 | No Zn³⁺ in water | Zn²⁺ (d¹⁰) is the only ion |
Common traps
The d-block trend runs the other way from the p-block
Scandium has no +4
Iron's M³⁺/M²⁺ value is not above manganese's
Count the free ion unless a complex is named
The hydration enthalpy of Cu²⁺ is larger, not smaller
Cu₂I₂ and CuI are one compound
Magnetic Moment and Colour
Learn this subtopic in the notesThe spin-only magnetic moment
Spin-only magnetic moment
Colours of the aqueous 3d ions
| Ion | d configuration | Unpaired electrons (free ion) | Colour in water |
|---|---|---|---|
| 3d⁰ | 0 | Colourless | |
| 3d⁰ | 0 | Colourless | |
| 3d¹ | 1 | Purple | |
| 3d¹ | 1 | Blue | |
| 3d² | 2 | Green | |
| 3d³ | 3 | Violet | |
| 3d³ | 3 | Violet | |
| 3d⁴ | 4 | Violet V²⁺, Cr³⁺ and Mn³⁺ are all violet. | |
| 3d⁴ | 4 | Blue | |
| 3d⁵ | 5 | Pink | |
| 3d⁵ | 5 | Yellow | |
| 3d⁶ | 4 | Green | |
| 3d⁶ | 4 | Blue | |
| 3d⁷ | 3 | Pink | |
| 3d⁸ | 2 | Green | |
| 3d⁹ | 1 | Blue | |
| 3d¹⁰ | 0 | Colourless |
Common traps
Past d⁵ the electrons pair up
Take the 4s electrons off first
Intensely coloured is not paramagnetic
Copper is colourless as Cu⁺
Oxides of Transition Metals
Learn this subtopic in the notesBasic, amphoteric and acidic oxides
| Oxide | Metal oxidation state | Character | With acid or alkali |
|---|---|---|---|
| +3 | Basic | Dissolves in acid to give salts | |
| +4 | Less basic (weakly amphoteric) | Dissolves in acid to give salts | |
| +5 | Amphoteric, mainly acidic | in alkali, in acid The contact-process catalyst, but not a basic oxide. | |
| CrO | +2 | Basic | Dissolves in acid to give |
| +3 | Amphoteric | Reacts with both acid and alkali | |
| +6 | Acidic | With water gives chromic acid, | |
| MnO | +2 | Basic | Dissolves in acid to give |
| +7 | Acidic | With water gives permanganic acid, | |
| ZnO | +2 | Amphoteric | Zincate, , in excess alkali |
Structure of Mn₂O₇ and the mixed oxides
| Oxide | Metal oxidation state | Structure or make-up | Point tested |
|---|---|---|---|
| +7 | Two tetrahedra sharing one O | 6 terminal Mn=O, 1 bridging O, covalent green oil Mn is tetrahedral, not octahedral, and there is no Mn–Mn bond. | |
| +6 | Chains of tetrahedra sharing corners | Acidic, strong oxidant | |
| +2 and +3 | MnO· | Mixed oxide; paramagnetic | |
| +2 and +3 | FeO· | Mixed oxide; magnetite, strongly magnetic | |
| +2 and +3 | CoO· | Mixed oxide | |
| +3 | One oxidation state | Not a mixed oxide |
Common traps
V₂O₄ with acid gives VO²⁺
Ionic character falls as the oxidation state rises
Mn₂O₇ is covalent, not ionic
An M₂O₃ or M₃O₄ formula alone does not decide 'mixed'
Potassium Dichromate and Chromium Compounds
Learn this subtopic in the notesFrom chromite ore to K₂Cr₂O₇, and chromate against dichromate
The chromate–dichromate equilibrium
Acidified dichromate as an oxidising agent
Electron balance with dichromate
The chromyl chloride test and blue CrO₅
Oxidation state of Cr in CrO₅
Common traps
Chromate to dichromate is not a redox change
Only the potassium salt is a primary standard
Electrons per what?
The green paper is not proof of SO₂ alone
CrO₅ is +6, not +10
The formula is CrO₂Cl₂
Potassium Permanganate and Manganese Compounds
Learn this subtopic in the notesMaking KMnO₄: manganate, permanganate and disproportionation
Disproportionation of manganate
Permanganate as an oxidant: acid against neutral
Two media, two products
Common traps
Manganate +6, permanganate +7
Peroxodisulphate goes all the way to permanganate
Permanganate oxidises; it never reduces
Count the water of crystallisation when the question does
Lanthanoids and Actinoids
Learn this subtopic in the notesLanthanoid configurations and 4f counts
| Element (Z) | Atom | M³⁺ ion | Other common ion |
|---|---|---|---|
| La (57) | [Xe]5d¹6s² | 4f⁰, colourless | Shows only +3 |
| Ce (58) | [Xe]4f¹5d¹6s² | 4f¹ | Ce⁴⁺, 4f⁰ |
| Pr (59) | [Xe]4f³6s² | 4f² | Pr⁴⁺, 4f¹ |
| Nd (60) | [Xe]4f⁴6s² | 4f³ | Nd²⁺ 4f⁴; Nd⁴⁺ 4f² |
| Pm (61) | [Xe]4f⁵6s² | 4f⁴ | Shows only +3 |
| Sm (62) | [Xe]4f⁶6s² | 4f⁵ | Sm²⁺, 4f⁶ |
| Eu (63) | [Xe]4f⁷6s² | 4f⁶ | Eu²⁺, 4f⁷ Eu²⁺ and Gd³⁺ are the two 4f⁷ ions. |
| Gd (64) | [Xe]4f⁷5d¹6s² | 4f⁷ | Shows only +3 |
| Tb (65) | [Xe]4f⁹6s² | 4f⁸ | Tb⁴⁺, 4f⁷ |
| Dy (66) | [Xe]4f¹⁰6s² | 4f⁹ | Dy⁴⁺, 4f⁸ |
| Ho (67) | [Xe]4f¹¹6s² | 4f¹⁰ | Shows only +3 |
| Er (68) | [Xe]4f¹²6s² | 4f¹¹ | Shows only +3 |
| Tm (69) | [Xe]4f¹³6s² | 4f¹² | Tm²⁺, 4f¹³ |
| Yb (70) | [Xe]4f¹⁴6s² | 4f¹³ | Yb²⁺, 4f¹⁴ |
| Lu (71) | [Xe]4f¹⁴5d¹6s² | 4f¹⁴, colourless | Shows only +3 |
Lanthanoid ions outside the +3 state
| Ion | 4f configuration | Why it exists | Behaviour |
|---|---|---|---|
| Ce⁴⁺ | 4f⁰ | Noble-gas (Xe) core | Strong oxidant; E° = +1.74 V back to Ce³⁺ The noble-gas core favours forming Ce⁴⁺, but Ce³⁺ is still the more stable state in water. |
| Tb⁴⁺ | 4f⁷ | Half-filled 4f | Stronger oxidant than Ce⁴⁺; found in |
| Pr⁴⁺, Nd⁴⁺, Dy⁴⁺ | 4f¹, 4f², 4f⁸ | Stabilised only in the solid oxide | Found only as ; oxidants |
| Eu²⁺ | 4f⁷ | Half-filled 4f after losing 6s² | Strong reductant; turns into Eu³⁺ |
| Yb²⁺ | 4f¹⁴ | Full 4f after losing 6s² | Reductant; diamagnetic |
| Sm²⁺ | 4f⁶ | Close to 4f⁷ | Reductant |
| Ln³⁺ (all) | 4f¹ to 4f¹⁴ | Loss of 6s² and one more electron | The stable state of every lanthanoid |
Actinoids compared with lanthanoids
| Property | Lanthanoids | Actinoids |
|---|---|---|
| Subshell being filled | 4f, deeply buried | 5f, less buried, reaches further out |
| f electrons in bonding | Very little | To a far greater extent |
| Oxidation states | Mostly +3; a few +2 and +4 | +3 common; up to +7 (Np) in the first half |
| Contraction along the series | Lanthanoid contraction | Actinoid contraction: larger from element to element |
| Radioactivity | Only Pm | All of them |
| Example configuration | Gd [Xe]4f⁷5d¹6s² | Cm [Rn]5f⁷6d¹7s² |
Common traps
The 5d electron in Gd and Lu does not change the ion
Isoelectronic means the same total, Z minus charge
A noble-gas core does not make Ce⁴⁺ the stable state
4f⁷ does not stop Eu²⁺ reducing
Name the right contraction
Cm has eight unpaired electrons
Qualitative Analysis of Ions
Learn this subtopic in the notesCation groups and their group reagents
| Group | Cations | Group reagent | Precipitated as |
|---|---|---|---|
| Zero | No group reagent; heat with NaOH | Ammonia gas, confirmed with Nessler's reagent | |
| I | Dilute HCl | White | |
| II | , , , | in dilute HCl | Sulphides: PbS and CuS black, CdS and yellow Pb²⁺ shows up in group I and again in group II, because PbCl₂ is partly soluble. |
| III | , , | with | Hydroxides: reddish-brown, white, green |
| IV | , , , | in | Sulphides: ZnS white, MnS buff, CoS and NiS black |
| V | , , | in | White carbonates |
| VI | No group reagent; ammonium phosphate | White |
Confirmatory tests and the colours they give
| Ion | Reagent | Observation | Product |
|---|---|---|---|
| in acetic acid | Chocolate-brown precipitate | ||
| Prussian blue precipitate | |||
| KSCN | Blood-red colour | ||
| , after neutralising | White or bluish-white precipitate | ||
| Dimethylglyoxime in | Brilliant red precipitate | , five-membered chelate rings | |
| in acetic acid | Yellow precipitate | ||
| NaOH, then left in air | White precipitate turning brown | ||
| Ammonium phosphate in | White crystalline precipitate | ||
| Nessler's reagent, in KOH | Brown precipitate | Iodide of Millon's base | |
| Ammonium molybdate in | Canary-yellow precipitate | ||
| Sodium nitroprusside | Violet colour |
Borax beads, anion tests and Mohr's salt
| Test | Conditions | Observation | Reason |
|---|---|---|---|
| Borax bead: Cu | Oxidising flame | Green when hot, blue when cold | Copper metaborate; red and opaque in the reducing flame |
| Borax bead: Fe | Oxidising and reducing flame | Yellowish-brown hot, yellow cold (oxidising); green (reducing) | Iron(III) metaborate; iron(II) in the reducing flame |
| Borax bead: Ni | Oxidising flame | Violet when hot, reddish-brown when cold | Nickel metaborate |
| Borax bead: Mn | Oxidising flame | Violet (amethyst), hot and cold | Manganese metaborate; colourless in the reducing flame |
| Borax bead: Co | Either flame | Blue, hot and cold | Cobalt metaborate |
| Borax bead: Cr | Either flame | Green, hot and cold | Chromium metaborate |
| Brown ring () | Fresh , then conc. down the side | Brown ring where the layers meet | , Fe +1 The complex is nitrosoferrous sulphate. |
| Acetate () | Neutral , then boil | Deep red colour, then a brown-red precipitate | Basic ferric acetate, Fe +3 |
| Chloride () | in dilute , then | Curdy white precipitate that dissolves | AgCl, then |
| Mohr's salt preparation | Dilute added; no prolonged heating | Pale green crystals | Acid stops hydrolysis; heating would oxidise |
Common traps
Mn²⁺ is group IV, Fe³⁺ is group III
Acid decides which sulphides come down
The dimethylglyoxime rings are five-membered
Nessler's reagent has no nitrogen
Iron in the brown ring is +1
The acetate test needs NEUTRAL ferric chloride
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