Chemistry · Inorganic Chemistry

d- and f-Block Elements formulas for JEE

Every d- and f-Block Elements formula you need for JEE, grouped by concept.

FormulasRevision notes
46 formulas3 concepts
01d-Block (Transition Elements)02Important d-Block Compounds03f-Block Elements (Lanthanoids and Actinoids)
01

d-Block (Transition Elements)

11 formulas

Spin Only Magnetic Moment

μ=n(n+2)\mu = \sqrt{n(n + 2)}

Calculates the magnetic moment of a transition metal ion based on the number of unpaired electrons (n).

applies whenValid for 3d series where the orbital angular momentum contribution is effectively quenched.
magnetic momentspin-onlyparamagnetism

Iodide and Persulphate Catalysis

2I−+S2O82−→I2+2SO42−2I^- + S_2O_8^{2-} \rightarrow I_2 + 2SO_4^{2-}

Overall reaction for the iron(III) catalyzed oxidation of iodide by persulphate.

applies whenCatalyzed by Fe3+.
catalysispersulphateiodide

Iron Catalysis: Step 1

2Fe3++2I−→2Fe2++I22Fe^{3+} + 2I^- \rightarrow 2Fe^{2+} + I_2

Reduction of iron(III) to iron(II) while oxidizing iodide.

applies whenStep 1 of Fe3+ catalysis.
catalysisironmechanism

Iron Catalysis: Step 2

2Fe2++S2O82−→2Fe3++2SO42−2Fe^{2+} + S_2O_8^{2-} \rightarrow 2Fe^{3+} + 2SO_4^{2-}

Oxidation of iron(II) back to iron(III) by persulphate.

applies whenStep 2 of Fe3+ catalysis.
catalysisironmechanism

Acidity of CrO3

CrO3+H2O→H2CrO4CrO_3 + H_2O \rightarrow H_2CrO_4

Chromium(VI) oxide dissolves in water to give chromic acid, demonstrating its acidic character.

oxideacidic characterchromium

Chromium(II) Reducing Action

2Cr2++2H+→2Cr3++H22Cr^{2+} + 2H^+ \rightarrow 2Cr^{3+} + H_2

Chromium(II) acting as a strong reducing agent by liberating hydrogen from dilute acid.

applies whenDilute acid.
redoxchromiumreducing agent

Copper(I) Disproportionation

2Cu+→Cu2++Cu2Cu^+ \rightarrow Cu^{2+} + Cu

Disproportionation of copper(I) ions in aqueous solution due to high negative hydration enthalpy of Cu(II).

applies whenAqueous solution.
redoxdisproportionationcopper

Copper(II) with Iodide

2Cu2++4I−→2CuI+I22Cu^{2+} + 4I^- \rightarrow 2CuI + I_2

Oxidation of iodide to iodine by Cu(II), resulting in the formation of Copper(I) iodide.

redoxcopperiodide

Effective Magnetic Moment (with orbital)

μeff=4S(S+1)+L(L+1)\mu_{eff} = \sqrt{4S(S+1) + L(L+1)}

Calculates the effective magnetic moment including both spin (S) and orbital (L) angular momentum contributions.

applies whenApplicable when orbital contribution is not quenched (e.g., some complex geometries or f-block).
magnetic momentorbital contributionjee-advanced

Mn2+ Magnetic Moment Calculation

μ=5(5+2)=5.92 B.M.\mu = \sqrt{5(5 + 2)} = 5.92 \text{ B.M.}

Calculation of the spin-only magnetic moment for a divalent Mn2+ ion (d5).

applies whenWorked Example 4.8 application.
magnetic momentcalculationmanganese

Acidity of Mn2O7

Mn2O7+H2O→2HMnO4Mn_2O_7 + H_2O \rightarrow 2HMnO_4

Manganese(VII) oxide dissolves in water to give permanganic acid, demonstrating its acidic character.

oxideacidic charactermanganese
02

Important d-Block Compounds

25 formulas

Permanganate iron reaction

5Fe2++MnO4−+8H+→Mn2++4H2O+5Fe3+5Fe^{2+} + MnO_4^- + 8H^+ \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+}

Permanganate titration reaction with iron(II) salt (e.g., Mohr's salt) converting Fe2+ to Fe3+.

applies whenAcidic medium.
redoxpermanganatetitrationiron

Permanganate oxalate reaction

5C2O42−+2MnO4−+16H+→333 K2Mn2++8H2O+10CO25C_2O_4^{2-} + 2MnO_4^- + 16H^+ \xrightarrow{333 \text{ K}} 2Mn^{2+} + 8H_2O + 10CO_2

Permanganate titration reaction with oxalate ion/oxalic acid at 333 K.

applies whenAcidic medium, requires heating to 333 K.
redoxpermanganatetitrationoxalate

Chromate to Dichromate Conversion

2CrO42−+2H+→Cr2O72−+H2O2 CrO_4^{2-} + 2H^+ \rightarrow Cr_2O_7^{2-} + H_2O

Equilibrium conversion of yellow chromate to orange dichromate in acidic medium.

applies whenpH < 7
equilibriumchromatedichromatepH dependent

Dichromate to Chromate Conversion

Cr2O72−+2OH−→2CrO42−+H2OCr_2O_7^{2-} + 2 OH^- \rightarrow 2 CrO_4^{2-} + H_2O

Equilibrium conversion of orange dichromate back to yellow chromate in basic medium.

applies whenpH > 7
equilibriumchromatedichromatepH dependent

Dichromate Oxidation of H2S

Cr2O72−+8H++3H2S→2Cr3++7H2O+3SCr_2O_7^{2-} + 8H^+ + 3H_2S \rightarrow 2Cr^{3+} + 7H_2O + 3S

Potassium dichromate oxidizes hydrogen sulphide to elemental sulphur.

applies whenAcidic medium.
redoxdichromatehydrogen sulphide

Dichromate Oxidation of Iodide

Cr2O72−+14H++6I−→2Cr3++7H2O+3I2Cr_2O_7^{2-} + 14H^+ + 6I^- \rightarrow 2Cr^{3+} + 7H_2O + 3I_2

Potassium dichromate oxidizes iodide ions to free iodine.

applies whenAcidic medium.
redoxdichromateiodide

Dichromate Oxidation of Tin(II)

Cr2O72−+14H++3Sn2+→2Cr3++7H2O+3Sn4+Cr_2O_7^{2-} + 14H^+ + 3Sn^{2+} \rightarrow 2Cr^{3+} + 7H_2O + 3Sn^{4+}

Potassium dichromate oxidizes tin(II) salts to tin(IV).

applies whenAcidic medium.
redoxdichromatetin

Equivalent Weight of K2Cr2O7

E=M6E = \frac{M}{6}

Calculation of the equivalent weight of K2Cr2O7 in acidic medium (n-factor = 6).

applies whenAcidic medium.
equivalent weightdichromatejee-advanced

Equivalent Weight of KMnO4 (Acidic)

E=M5E = \frac{M}{5}

Calculation of the equivalent weight of KMnO4 in acidic medium (n-factor = 5).

applies whenAcidic medium.
equivalent weightpermanganatejee-advanced

Equivalent Weight of KMnO4 (Strong Base)

E=M1E = \frac{M}{1}

Calculation of the equivalent weight of KMnO4 in strongly basic medium (n-factor = 1).

applies whenStrongly basic medium.
equivalent weightpermanganatejee-advanced

Equivalent Weight of KMnO4 (Neutral/Weak Base)

E=M3E = \frac{M}{3}

Calculation of the equivalent weight of KMnO4 in neutral or weakly basic medium (n-factor = 3).

applies whenNeutral or faintly alkaline medium.
equivalent weightpermanganatejee-advanced

Permanganate Oxidation of Iodide (Acidic)

10I−+2MnO4−+16H+→2Mn2++8H2O+5I210I^- + 2MnO_4^- + 16H^+ \rightarrow 2Mn^{2+} + 8H_2O + 5I_2

Oxidation of iodide to free iodine by KMnO4 in acidic solution.

applies whenAcidic medium.
redoxpermanganateiodide

Permanganate Oxidation of Iodide (Neutral)

2MnO4−+H2O+I−→2MnO2+2OH−+IO3−2MnO_4^- + H_2O + I^- \rightarrow 2MnO_2 + 2OH^- + IO_3^-

Oxidation of iodide to iodate by KMnO4 in neutral or faintly alkaline solution.

applies whenNeutral or faintly alkaline medium.
redoxpermanganateiodate

Permanganate Oxidation of Manganous Salt

2MnO4−+3Mn2++2H2O→5MnO2+4H+2MnO_4^- + 3Mn^{2+} + 2H_2O \rightarrow 5MnO_2 + 4H^+

Oxidation of manganous salt to MnO2 by KMnO4, catalyzed by zinc sulphate or zinc oxide.

applies whenNeutral or faintly alkaline medium; presence of ZnSO4 or ZnO.
redoxpermanganatemanganese

Permanganate Oxidation of Nitrite

5NO2−+2MnO4−+6H+→2Mn2++5NO3−+3H2O5NO_2^- + 2MnO_4^- + 6H^+ \rightarrow 2Mn^{2+} + 5NO_3^- + 3H_2O

Oxidation of nitrite to nitrate by KMnO4.

applies whenAcidic medium.
redoxpermanganatenitrite

Permanganate Oxidation of Sulphide

5S2−+2MnO4−+16H+→2Mn2++8H2O+5S5S^{2-} + 2MnO_4^- + 16H^+ \rightarrow 2Mn^{2+} + 8H_2O + 5S

Oxidation of hydrogen sulphide to elemental sulphur by KMnO4.

applies whenAcidic medium.
redoxpermanganatesulphide

Permanganate Oxidation of Sulphite

5SO32−+2MnO4−+6H+→2Mn2++3H2O+5SO42−5SO_3^{2-} + 2MnO_4^- + 6H^+ \rightarrow 2Mn^{2+} + 3H_2O + 5SO_4^{2-}

Oxidation of sulphurous acid or sulphite to sulphate by KMnO4.

applies whenAcidic medium.
redoxpermanganatesulphite

Permanganate Oxidation of Thiosulphate

8MnO4−+3S2O32−+H2O→8MnO2+6SO42−+2OH−8MnO_4^- + 3S_2O_3^{2-} + H_2O \rightarrow 8MnO_2 + 6SO_4^{2-} + 2OH^-

Quantitative oxidation of thiosulphate to sulphate by KMnO4.

applies whenNeutral or faintly alkaline medium.
redoxpermanganatethiosulphate

Thermal Decomposition of KMnO4

2KMnO4→ΔK2MnO4+MnO2+O22KMnO_4 \xrightarrow{\Delta} K_2MnO_4 + MnO_2 + O_2

Heating potassium permanganate at 513 K produces K2MnO4, MnO2, and O2.

applies whenTemperature at 513 K.
decompositionpermanganatethermal

Preparation of Dichromate: Step 1

4FeCr2O4+8Na2CO3+7O2→8Na2CrO4+2Fe2O3+8CO24 FeCr_2O_4 + 8 Na_2CO_3 + 7 O_2 \rightarrow 8 Na_2CrO_4 + 2 Fe_2O_3 + 8 CO_2

Fusion of chromite ore with sodium carbonate in the presence of air to form sodium chromate.

applies whenFusion in free access of air.
preparationdichromatechromite ore

Preparation of Dichromate: Step 2

2Na2CrO4+2H+→Na2Cr2O7+2Na++H2O2 Na_2CrO_4 + 2 H^+ \rightarrow Na_2Cr_2O_7 + 2 Na^+ + H_2O

Acidification of sodium chromate extract to form sodium dichromate.

applies whenAcidic medium.
preparationdichromateacidification

Preparation of Dichromate: Step 3

Na2Cr2O7+2KCl→K2Cr2O7+2NaClNa_2Cr_2O_7 + 2 KCl \rightarrow K_2Cr_2O_7 + 2 NaCl

Crystallization of potassium dichromate via displacement with KCl.

applies whenBased on lower solubility of potassium dichromate.
preparationdichromatecrystallization

Disproportionation of Manganate (Example 4.9)

3MnO42−+4H+→2MnO4−+MnO2+2H2O3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- + MnO_2 + 2H_2O

Green manganate disproportionates in a neutral or acidic solution to give permanganate and manganese dioxide.

applies whenNeutral or acidic medium.
preparationpermanganatedisproportionation

Preparation of Permanganate: Fusion

2MnO2+4KOH+O2→2K2MnO4+2H2O2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O

Fusion of MnO2 with an alkali metal hydroxide and an oxidizing agent to produce manganate.

applies whenAlkaline oxidative fusion.
preparationpermanganatefusion

Lab Preparation of Permanganate

2Mn2++5S2O82−+8H2O→2MnO4−+10SO42−+16H+2Mn^{2+} + 5S_2O_8^{2-} + 8H_2O \rightarrow 2MnO_4^- + 10SO_4^{2-} + 16H^+

Oxidation of manganese(II) salt by peroxodisulphate in the laboratory.

applies whenLaboratory conditions.
preparationpermanganateperoxodisulphate
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03

f-Block Elements (Lanthanoids and Actinoids)

10 formulas

Lande g-factor

g=1+J(J+1)+S(S+1)−L(L+1)2J(J+1)g = 1 + \frac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)}

Calculates the Lande g-factor for f-block magnetic moment calculations.

applies whenUsed alongside the J-based magnetic moment formula.
lande g-factorquantum numbersjee-advanced

Lanthanoid Magnetic Moment

μ=gJ(J+1)\mu = g \sqrt{J(J+1)}

Formula for the magnetic moment of f-block elements involving total angular momentum quantum number J.

applies whenUsed for lanthanoids and actinoids where spin-orbit coupling is significant.
magnetic momentlanthanoidsf-blockjee-advanced

Lanthanoid Reaction with Acid

2Ln+6H+→2Ln3++3H22Ln + 6H^+ \rightarrow 2Ln^{3+} + 3H_2

Lanthanoids liberate hydrogen gas from dilute acids.

applies whenDilute acids.
lanthanoidsreactionacid

Lanthanoid Reaction with Carbon

Ln+2C→2773 KLnC2Ln + 2C \xrightarrow{2773 \text{ K}} LnC_2

Lanthanoids react with carbon at high temperature to form carbides.

applies whenHeated to 2773 K.
lanthanoidsreactioncarbon

Lanthanoid Reaction with Halogens

2Ln+3X2→2LnX32Ln + 3X_2 \rightarrow 2LnX_3

Lanthanoids burn in halogens to form trihalides.

lanthanoidsreactionhalogens

Lanthanoid Reaction with Nitrogen

2Ln+N2→Δ2LnN2Ln + N_2 \xrightarrow{\Delta} 2LnN

Lanthanoids react with nitrogen upon heating to form nitrides.

applies whenRequires heating.
lanthanoidsreactionnitrogen

Lanthanoid Reaction with Oxygen

4Ln+3O2→2Ln2O34Ln + 3O_2 \rightarrow 2Ln_2O_3

Lanthanoids burn in oxygen to form corresponding oxides.

applies whenCombustion.
lanthanoidsreactionoxygen

Lanthanoid Standard Reduction

Ln3+(aq)+3e−→Ln(s)Ln^{3+}(aq) + 3e^- \rightarrow Ln(s)

Standard reduction half-reaction for lanthanoid ions.

applies whenAqueous solution.
lanthanoidsredoxreduction potential

Lanthanoid Reaction with Sulphur

2Ln+3S→ΔLn2S32Ln + 3S \xrightarrow{\Delta} Ln_2S_3

Lanthanoids react with sulphur upon heating to form sulphides.

applies whenRequires heating.
lanthanoidsreactionsulphur

Lanthanoid Reaction with Water

2Ln+6H2O→2Ln(OH)3+3H22Ln + 6H_2O \rightarrow 2Ln(OH)_3 + 3H_2

Lanthanoids react with water to yield hydroxides and hydrogen gas.

lanthanoidsreactionwater
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