Comprehensive Study Guide to d and f-Block Elements

1. Definition and Classification of d-Block Elements

• Transition Element Definition: An element whose atom in the ground state or ion in a common oxidation state has an incomplete d-subshell, containing $1$ to $9$ electrons.

• Positioning: They are termed "transition elements" because they lie between the most electropositive s-block elements and the most electronegative p-block elements, representing a transition in properties.

• General Electronic Configuration: $(n-1)d^{1-10}ns^{0-2}$.

• Exclusions: Zinc ($Zn$), Cadmium ($Cd$), and Mercury ($Hg$) are excluded from the definition of transition metals because they have completely filled d-orbitals in their ground and common oxidation states ($M^{2+}$). They do not exhibit typical transition characteristics.

• Non-Typical Transition Elements: Elements of group 3 ($Sc, Y, La, Ac$) and group 12 ($Zn, Cd, Hg$) are classified as non-typical transition elements.

The Four Transition Series and Electronic Configurations

• First Transition (3d) Series: Sc ($21$) to Zn ($30$).   - Scandium ($Sc$): $[Ar] 3d^1 4s^2$   - Titanium ($Ti$): $[Ar] 3d^2 4s^2$   - Vanadium ($V$): $[Ar] 3d^3 4s^2$   - Chromium ($Cr^*$): $[Ar] 3d^5 4s^1$ (Anomalous due to half-filled stability)   - Manganese ($Mn$): $[Ar] 3d^5 4s^2$   - Iron ($Fe$): $[Ar] 3d^6 4s^2$   - Cobalt ($Co$): $[Ar] 3d^7 4s^2$   - Nickel ($Ni$): $[Ar] 3d^8 4s^2$   - Copper ($Cu^*$): $[Ar] 3d^{10} 4s^1$ (Anomalous due to full-filled stability)   - Zinc ($Zn$): $[Ar] 3d^{10} 4s^2$

• Second Transition (4d) Series: Y ($39$) to Cd ($48$).   - Includes Yttrium ($Y$), Zirconium ($Zr$), Niobium ($Nb^*$), Molybdenum ($Mo^*$), Technetium ($Tc$), Ruthenium ($Ru^*$), Rhodium ($Rh^*$), Palladium ($Pd^*$: $[Kr] 4d^{10} 5s^0$), Silver ($Ag^*$), and Cadmium ($Cd$).

• Third Transition (5d) Series: La ($57$), Hf ($72$) to Hg ($80$).   - Includes Lanthanum ($La$), Hafnium ($Hf$), Tantalum ($Ta$), Tungsten ($W$), Rhenium ($Re$), Osmium ($Os$), Iridium ($Ir$), Platinum ($Pt^*$), Gold ($Au^*$), and Mercury ($Hg$).

• Fourth Transition (6d) Series: Ac ($89$), Rf ($104$) to Uub ($112$).

• Anomalous Configurations: Marked with asterisks ($Cr, Cu, Nb, Mo, Ru, Rh, Pd, Ag, Pt, Au$), these are caused by nuclear-electron forces, electron-electron interactions, and the stability of half-filled and fully-filled orbitals.

• General Rule: All transition elements are d-block elements, but not all d-block elements are transition elements.

Physico-Chemical Properties of d-Block Elements

• Atomic Radii (3d Series in pm):   - $Sc: 144, Ti: 132, V: 122, Cr: 117, Mn: 117, Fe: 117, Co: 116, Ni: 115, Cu: 117, Zn: 125$.   - Trend: Decreases with increase in atomic number, reaches a minimum in the middle (around $Fe, Co, Ni$), and increases slightly at the end ($Cu, Zn$).   - Explanation: Increasing nuclear charge reduces size, while the addition of electrons to the inner d-shell (shielding/repulsion) opposes this. Initially, nuclear charge dominates; later, electron repulsion and shielding increase radii.

• Group Trends: Radii increase down a group due to additional shells. However, 2nd and 3rd series elements (e.g., $Zr$ and $Hf$) have nearly identical radii due to Lanthanide Contraction.

• Ionic Radii: For ions with identical charges ($M^{2+}$ or $M^{3+}$), radii decrease slowly across a series due to increasing effective nuclear charge.

• Ionization Energies (IE):   - IE values of transition elements ($Sc$ to $Zn$) are higher than s-block but generally lower than p-block.   - Trend: IE increases across the series, but the trend is not regular because shielding by d-electrons opposes the increased nuclear charge.   - 5d Series Exception: The first ionization energies of 5d series are higher than 3d and 4d series because the 4f electrons (added after La) provide poor shielding, making outermost electrons experience high nuclear attraction.

• Metallic Character: All are hard, malleable, ductile metals with high thermal and electrical conductivity. Structures: face-centered cubic (fcc), hexagonal close-packed (hcp), and body-centered cubic (bcc).

• Bonding: Transition metals exhibit both covalent (due to unpaired d-orbitals) and metallic bonding.

• Melting and Boiling Points: Very high (except $Cd$ and $Hg$). They increase to a maximum near the middle of the series ($Cr$ in 3d) and then decrease.   - Maxima are correlated with the number of unpaired electrons (highest strength of metallic bonds).   - Low points for $Zn, Cd, Hg$ are due to the absence of unpaired d-electrons.

• Enthalpies of Atomization: High due to closely packed atoms and strong metallic bonds formed by valence electrons.

Oxidation States and Stability

• Variable Valency: Participation of both $(n-1)d$ and $ns$ electrons in bonding allows multiple oxidation states.

• Trends in 3d Series:   - Sc: $+2, +3$   - Ti: $+2, +3, +4$   - V: $+2, +3, +4, +5$   - Cr: $+1, +2, +3, +4, +5, +6$   - Mn: $+2, +3, +4, +5, +6, +7$   - Fe: $+2, +3, +4, +5, +6$   - Co/Ni: $+2, +3, +4$   - Cu: $+1, +2$   - Zn: $+2$

• Commonality: The most common state is $+2$ (loss of 4s electrons), except for scandium.

• Highest States: Found in oxides and fluorides. Maximum oxidation state is $+8$ (shown by $Ru$ and $Os$).

• Group Behavior: Within a group, higher oxidation states become more stable with increasing atomic number (e.g., $Fe$ stays $+2/+3$, whereas $Ru/Os$ reach $+8$).

• Stability Calculation: Stability related to Ionization Energy sum:   - $Ni^{2+}$ is thermodynamically more stable than $Pt^{2+}$ ($IE_1 + IE_2$: $2490$ vs $2660 kJ\,mol^{-1}$).   - $Pt^{4+}$ is more stable than $Ni^{4+}$ ($E_{total}$: $9360$ vs $11290 kJ\,mol^{-1}$).

Electrode Potentials and Aqueous Stability

• Standard Electrode Potential ($E^o$): Measures the tendency for $M^{n+}(aq) + ne^- \rightarrow M(s)$.

• Trends: $E^o$ values for the 3d series are mostly negative (except $Cu^{2+}/Cu$ at $+0.34V$), indicating these metals liberate $H_2$ from dilute acids.

• Enthalpy Calculation for Stability:   - Total enthalpy change ($\Delta H$) depends on:     1. Enthalpy of sublimation ($\Delta H_{sub}$)     2. Ionization energy ($IE$)     3. Enthalpy of hydration ($\Delta H_{hyd}$)   - Formula: $\Delta H = \Delta H_{sub} + IE + \Delta H_{hyd}$   - The oxidation state for which the total energy is most negative is the most stable in solution.

Color and Magnetic Properties

• Formation of Coloured Ions: Due to crystal field splitting of d-orbitals into levels of different energies ($t_{2g}$ and $e_g$).

• Mechanism: Electrons promoted from lower to higher d-levels absorb specific wavelengths of visible light ($\lambda = 380 - 760\,nm$). The transmitted light is the complementary color.   - $Cu(H_2O)_6^{2+}$: Absorbs red, appears blue-green.   - $Co^{2+}$: Absorbs blue-green, appears red.

• Colorless Exceptions: Ions with $d^0$ ($Sc^{3+}, Ti^{4+}$) or $d^{10}$ ($Zn^{2+}, Cd^{2+}, Hg^{2+}, Cu^+$) because no d-d transitions are possible.

• Paramagnetism: Attracted to magnetic fields due to unpaired electrons.

• Magnetic Moment Formula (Spin-only): $\mu_s = \sqrt{n(n+2)}\,BM$ (Bohr Magnetons), where $n$ is the number of unpaired electrons.   - Max magnetism occurs at $d^5$ ($Mn^{2+}, Fe^{3+}$).

Formation of Complexes, Alloys, and Interstitials

• Complex Formation: Transition metals form complexes (e.g., $[Fe(CN)_6]^{4-}, [Cu(NH_3)_4]^{2+}$) due to small cation size, high nuclear charge, and availability of vacant d-orbitals.

• Interstitial Compounds: Small atoms ($H, B, C, N$) get trapped in metal lattice voids. Characteristics: Non-stoichiometric, very hard, high density, same chemical but different physical properties. Examples: $VSe_{0.98}, Fe_{0.94}O$, Titanium nitride.

• Catalytic Properties: Good catalysts (e.g., $Pt, Fe, V_2O_5, Ni$) due to vacant d-orbitals, variable oxidation states, and the ability to form reaction intermediates.

• Alloy Formation: Metal atoms can easily replace each other in the lattice because their atomic radii are very similar. Examples: Stainless steel, Invar, Brass.

Chromium Compounds: Potassium Dichromate ($K_2Cr_2O_7$)

• Preparation from Chromite Ore ($FeCr_2O_4$):   1. Preparation of Sodium Chromate: $4FeCr_2O_4 + 8Na_2CO_3 + 7O_2 \rightarrow 2Fe_2O_3 + 8CO_2 + 8Na_2CrO_4$.   2. Conversion to Dichromate: $2Na_2CrO_4 + H_2SO_4 \rightarrow Na_2Cr_2O_7 + Na_2SO_4 + H_2O$.   3. Conversion to Potassium Dichromate: $Na_2Cr_2O_7 + 2KCl \rightarrow K_2Cr_2O_7 + 2NaCl$.

• Properties: Orange-red crystals, melts at $699\,K$. Used as a primary standard.

• Chemical Reactions:   - Heat: $4K_2Cr_2O_7 \xrightarrow{\Delta} 4K_2CrO_4 + 2Cr_2O_3 + 3O_2$.   - Alkali: Chromate-dichromate equilibrium: $2CrO_4^{2-} + 2H^+ \rightleftharpoons Cr_2O_7^{2-} + H_2O$.   - Oxidizing Nature (Acidic): $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O$ ($E^o = +1.31V$).     - Oxidises $Fe^{2+}$ to $Fe^{3+}$, $I^-$ to $I_2$, $H_2S$ to $S$, and $SO_3^{2-}$ to $SO_4^{2-}$.

• Chromyl Chloride Test: Heating with chloride salt and conc. $H_2SO_4$ yields orange-red vapours ($CrO_2Cl_2$).

• Structure: Chromate ($CrO_4^{2-}$) is tetrahedral. Dichromate ($Cr_2O_7^{2-}$) consists of two tetrahedra sharing one oxygen (Cr-O-Cr bond angle approx. $126^o$ per diagram, text says structure shows $131^o$ between O-Cr-O and O-O distances).

Manganese Compounds: Potassium Permanganate ($KMnO_4$)

• Preparation from Pyrolusite ($MnO_2$):   1. Fusion with $KOH$ and air: $2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O$.   2. Oxidation of green $K_2MnO_4$ using chemical ($Cl_2, O_3, CO_2$) or electrolytic methods.

• Properties: Dark purple crystals, soluble in water.

• Reaction in Different Media:   - Acidic: $MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$.   - Neutral/Faintly Alkaline: $MnO_4^- + 2H_2O + 3e^- \rightarrow MnO_2 + 4OH^-$.   - Strongly Alkaline: $MnO_4^- + e^- \rightarrow MnO_4^{2-}$.

• Oxidizing Actions: Oxidizes oxalic acid to $CO_2$, ferrous to ferric, and ammonia to nitrogen.

• Permanganate Structure: $Mn$ is in $+7$ oxidation state with $sp^3$ hybridization (tetrahedral shape).

Iron and its Compounds

• Ores: Haematite ($Fe_2O_3$), Magnetite ($Fe_3O_4$), Limonite ($Fe_2O_3 \cdot 3H_2O$), Iron pyrites ($FeS_2$).

• Extraction (Blast Furnace):   - Roasting: $4FeO + O_2 \rightarrow 2Fe_2O_3$.   - Smelting: Reduction by $CO$ ($Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2$).

• Varieties:   - Cast Iron (Pig Iron): Most impure, $2.5-4\%$ Carbon.   - Wrought Iron: Purest form, $0.12-0.25\%$ Carbon.   - Steel: $0.2-1.5\%$ Carbon. Categories: Mild ($0.2-0.5\%$) and Hard ($0.5-1.5\%$).

• Heat Treatment of Steel:   - Annealing: Slow cooling from redness (softens).   - Quenching: Rapid cooling (hardens).   - Tempering: Heating below redness to remove brittleness.   - Case-hardening: Carbon thin coating.   - Nitriding: Heating in $NH_3$ to form iron nitride layer.

• Important Compounds:   - Ferrous Sulphate ($FeSO_4 \cdot 7H_2O$): Green vitriol.   - Mohr’s Salt ($(NH_4)_2SO_4 \cdot FeSO_4 \cdot 6H_2O$): Stable primary standard.   - Ferric Chloride ($FeCl_3$): Forms dimer $Fe_2Cl_6$ in vapour state; used as a styptic.

Copper, Silver, Gold, Zinc, and Mercury

• Copper ($Cu$):   - Ores: Chalcopyrite ($CuFeS_2$), Cuprite ($Cu_2O$).   - Extraction: Roasting to "matte" ($Cu_2S + FeS$), then Bessemerisation to "blister copper" ($98\%$ pure).   - Compounds: Blue Vitriol ($CuSO_4 \cdot 5H_2O$). Bordeaux mixture is $CuSO_4 +$ Lime (fungicide).

• Silver ($Ag$):   - Ores: Argentite ($Ag_2S$). Extraction: Mac-Arthur-Forrest Cyanide process.   - Photography: $AgBr$ in gelatin; developed by hydroquinone; fixed by Hypo ($Na_2S_2O_3$).

• Gold ($Au$):   - Purity: Carats ($24$ carat is $100\%$). $14$ carat is $58.3\%$ gold.   - Soluble only in Aqua Regia ($3HCl:1HNO_3$).

• Zinc ($Zn$):   - Ores: Zinc blende ($ZnS$), Calamine ($ZnCO_3$).   - ZnO is called Philosopher’s Wool. Constituent of Lithopone ($ZnS + BaSO_4$).

• Mercury ($Hg$):   - Ore: Cinnabar ($HgS$).   - Forms amalgams with metals (except $Fe, Pt$).   - Mercurous ion exists as a dimer $Hg_2^{2+}$.   - Nessler’s Reagent: Alkaline solution of $K_2[HgI_4]$ (tests for $NH_4^+$).   - Calomel: Mercurous chloride ($Hg_2Cl_2$).

f-Block Elements: Lanthanides and Actinides

• Definition: Inner transition elements where electrons fill $(n-2)f$ orbitals.

• General Configuration: $(n-2)f^{0-14}(n-1)d^{0-1}ns^2$.

• Lanthanides ($Z=58-71$):   - Most stable state is $+3$.   - Lanthanide Contraction: Regular decrease in atomic/ionic radii. Cause: Poor shielding by f-electrons. Consequence: Chemical similarity of $Zr/Hf$, decrease in basicity ($La(OH)_3$ to $Lu(OH)_3$).   - Magnetism: Calculate including both spin ($S$) and orbital ($L$) contributions: $\mu_{eff} = \sqrt{4S(S+1) + L(L+1)}$.

• Actinides ($Z=90-103$):   - Radioactive; synthetic (man-made) beyond Uranium (transuranics).   - Show higher oxidation states ($Np, Pu$ to $+7$) due to small energy gap between $5f, 6d$, and $7s$.   - Greater tendency for complex formation than lanthanides.

Miscellaneous Reagents and Facts

• Fenton’s Reagent: $FeSO_4 + H_2O_2$.

• Schweitzer’s Reagent: $[Cu(NH_3)_4]SO_4$.

• Etard Reagent: $CrO_2Cl_2$.

• Zeigler Natta Catalyst: $TiCl_4 + (C_2H_5)_3Al$.

• Wilkinson’s Catalyst: $[Ph_3P]_3RhCl$.

• Lightest/Heaviest: Sc is lightest; Os is denses/heaviest transition metal.

• Iron Pyrites: Known as "Fool's Gold" ($FeS_2$; transcript also notes $CuFeS_2$).