Inorganic ChemistryHigh Yield (2-3 Qs in JEE)

d- & f-Block Elements Formulas

Transition element trends, variable oxidation states, lanthanide contraction, catalytic properties, and potassium permanganate/dichromate reactions.

8 Formulas•589+ Questions in Bank

Core Formulas & Mathematical Identities

Oxidation States & Redox Equivalent Weights

\text{KMnO}_4 (\text{Acidic}): \text{Mn}^{7+} + 5e^- \to \text{Mn}^{2+} \implies n = 5, \quad \text{K}_2\text{Cr}_2\text{O}_7 (\text{Acidic}): \text{Cr}_2^{6+} + 6e^- \to 2\text{Cr}^{3+} \implies n = 6

Stoichiometric electron transfer in analytical volumetric titrations.

Examiner Tip: Equivalent weight = Molar mass / n-factor (M/5 for acidic KMnO₄, M/6 for acidic K₂Cr₂O₇).

Lanthanide Contraction Phenomenon

r(\text{Zr}) \approx r(\text{Hf}) \approx 1.60 \text{ \AA}, \quad r(\text{Nb}) \approx r(\text{Ta})

Poor shielding effect of 4f electrons causes abnormal similarity in 4d and 5d series atomic and ionic sizes.

Examiner Tip: Causes extreme difficulty in chemical separation of Zr and Hf.

Chromate-Dichromate Equilibrium

2 \text{CrO}_4^{2-} \; (\text{Yellow}) + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} \; (\text{Orange}) + \text{H}_2\text{O}

pH-dependent equilibrium: yellow chromate in base, orange dichromate in acid.

Examiner Tip: Oxidation state of Chromium remains +6 throughout the interconversion.

Standard Electrode Potentials & Thermodynamic Cycle

E^\circ_{M^{2+}/M} \propto -(\Delta H_{\text{sub}} + \text{IE}_1 + \text{IE}_2 + \Delta H_{\text{hyd}}), \quad E^\circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34\,\text{V} > 0

Standard reduction potential determined by balance between sublimation, ionization enthalpies and hydration enthalpy. Cu cannot liberate H₂ from dilute acids.

Examiner Tip: E°(Mn³⁺/Mn²⁺) = +1.57 V is unusually high because Mn²⁺ achieves stable half-filled 3d⁵ configuration.

Chromyl Chloride Test (Confirmatory Test for Cl⁻)

\text{K}_2\text{Cr}_2\text{O}_7 + 4\text{NaCl} + 6\text{H}_2\text{SO}_4 \to 2\text{CrO}_2\text{Cl}_2\uparrow \; (\text{Red Vapor}) \xrightarrow{\text{NaOH}} \text{Na}_2\text{CrO}_4 \xrightarrow{\text{Pb(OAc)}_2} \text{PbCrO}_4\downarrow \; (\text{Yellow})

Qualitative test for ionic chlorides. Covalent chlorides and AgCl, Hg₂Cl₂, HgCl₂, PbCl₂ do NOT respond to this test.

Examiner Tip: Fluorides, bromides, and iodides do not form volatile chromyl halides.

KMnO₄ in Neutral & Strongly Alkaline Media

\text{Neutral/Weak Base: } \text{MnO}_4^- + 3e^- + 2\text{H}_2\text{O} \to \text{MnO}_2\downarrow + 4\text{OH}^- \; (n=3), \quad \text{Strong Base: } \text{MnO}_4^- + e^- \to \text{MnO}_4^{2-} \; (n=1)

In neutral/faintly alkaline medium, KMnO₄ oxidizes iodide to iodate (I⁻ → IO₃⁻) and thiosulfate to sulfate (S₂O₃²⁻ → SO₄²⁻).

Examiner Tip: In acidic medium, I⁻ is oxidized to I₂ (not IO₃⁻).

Interstitial Compounds & Catalytic Properties

\text{Compounds: } \text{TiC}, \; \text{Mn}_4\text{N}, \; \text{Fe}_3\text{H}, \; \text{VH}_{0.56} \implies \text{Higher M.P., Hardness, Metallic Conduction}

Transition metals trap small non-metal atoms (H, B, C, N) inside octahedral/tetrahedral voids of the metallic lattice without changing lattice type.

Examiner Tip: Transition elements are excellent catalysts (V₂O₅, finely divided Fe, Raney Ni) due to variable oxidation states and surface d-orbital adsorption.

Actinoid Contraction & Variable Oxidation States

\text{Contraction: } 5f > 4f \implies \text{Actinoid Contraction} > \text{Lanthanoid Contraction}, \quad \text{Max ON: } \text{Np, Pu } (+7)

Poorer shielding of 5f electrons causes steeper radius decrease across actinoid series than 4f across lanthanoids.

Examiner Tip: 5f, 6d, and 7s energy levels are extremely close in energy, allowing actinoids to exhibit variable oxidation states from +3 up to +7.

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in d- & f-Block Elements

•Lanthanide contraction causes 4d and 5d elements to have nearly identical atomic radii (e.g. Zr ≈ Hf, Nb ≈ Ta).
•KMnO₄ acts as oxidizing agent in acidic medium (change in ON = 5: Mn⁷⁺ -> Mn²⁺), but in basic medium change is 1 (Mn⁷⁺ -> Mn⁶⁺).

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