Comprehensive Study Notes on d- and f-Block Elements

Electronic Configurations and Classification of d-Block Elements

• Definition of d-Block Elements:

  • Elements in which the last electron enters the $(n - 1)d$ subshell (d-orbitals of the penultimate shell) are classified as d-block elements.

  • General valence electronic configuration: $(n - 1)d^{1-10} ns^{0-2}$.

  • Situated in Groups 3 to 12 across the 4th, 5th, 6th, and 7th periods of the periodic table, spanning 40 elements total.      

    

• The Four Transition Series:

  • $3d$ Series (First Transition Series): Scandium ($\text{Sc}$, $Z = 21$) to Zinc ($\text{Zn}$, $Z = 30$).

  • $4d$ Series (Second Transition Series): Yttrium ($\text{Y}$, $Z = 39$) to Cadmium ($\text{Cd}$, $Z = 48$).

  • $5d$ Series (Third Transition Series): Lanthanum ($\text{La}$, $Z = 57$), Hafnium ($\text{Hf}$, $Z = 72$) to Mercury ($\text{Hg}$, $Z = 80$).

  • $6d$ Series (Fourth Transition Series): Actinium ($\text{Ac}$, $Z = 89$), Rutherfordium ($\text{Rf}$, $Z = 104$) to Copernicium / Ununbium ($\text{Uub}$, $Z = 112$).

• Detailed Subshell Configurations:

  • $3d$ Series ($3d^{1-10} 4s^{1-2}$):

  • $\text{Sc} \, (Z = 21)$: $4s^2 3d^1$

  • $\text{Ti} \, (Z = 22)$: $4s^2 3d^2$

  • $\text{V} \, (Z = 23)$: $4s^2 3d^3$

  • $\text{Cr} \, (Z = 24)$: $4s^1 3d^5$ (Anomalous stability of half-filled subshell)

  • $\text{Mn} \, (Z = 25)$: $4s^2 3d^5$

  • $\text{Fe} \, (Z = 26)$: $4s^2 3d^6$

  • $\text{Co} \, (Z = 27)$: $4s^2 3d^7$

  • $\text{Ni} \, (Z = 28)$: $4s^2 3d^8$

  • $\text{Cu} \, (Z = 29)$: $4s^1 3d^{10}$ (Anomalous stability of fully-filled subshell)

  • $\text{Zn} \, (Z = 30)$: $4s^2 3d^{10}$          

    

  • $4d$ Series ($4d^{1-10} 5s^{0-2}$):

  • $\text{Y} \, (Z = 39)$: $5s^2 4d^1$

  • $\text{Zr} \, (Z = 40)$: $5s^2 4d^2$

  • $\text{Nb} \, (Z = 41)$: $5s^1 4d^4$

  • $\text{Mo} \, (Z = 42)$: $5s^1 4d^5$

  • $\text{Tc} \, (Z = 43)$: $5s^1 4d^6$

  • $\text{Ru} \, (Z = 44)$: $5s^1 4d^7$

  • $\text{Rh} \, (Z = 45)$: $5s^1 4d^8$

  • $\text{Pd} \, (Z = 46)$: $5s^0 4d^{10}$ (Zero electrons in $5s$ subshell)

  • $\text{Ag} \, (Z = 47)$: $5s^1 4d^{10}$

  • $\text{Cd} \, (Z = 48)$: $5s^2 4d^{10}$          

    

  • $5d$ Series ($5d^{1-10} 6s^{1-2}$):

  • $\text{La} \, (Z = 57)$: $6s^2 5d^1$

  • $\text{Hf} \, (Z = 72)$: $6s^2 5d^2$

  • $\text{Ta} \, (Z = 73)$: $6s^2 5d^3$

  • $\text{W} \, (Z = 74)$: $6s^2 5d^4$

  • $\text{Re} / \text{Rd} \, (Z = 75)$: $6s^2 5d^5$

  • $\text{Os} \, (Z = 76)$: $6s^2 5d^6$

  • $\text{Ir} \, (Z = 77)$: $6s^2 5d^7$

  • $\text{Pt} \, (Z = 78)$: $6s^1 5d^9$

  • $\text{Au} \, (Z = 79)$: $6s^1 5d^{10}$

  • $\text{Hg} \, (Z = 80)$: $6s^2 5d^{10}$          

    

  • $6d$ Series ($6d^{1-10} 7s^{1-2}$):

  • $\text{Ac} \, (Z = 89)$: $7s^2 6d^1$

  • $\text{Rf} \, (Z = 104)$: $7s^2 6d^2$

  • $\text{Db} \, (Z = 105)$: $7s^2 6d^3$

  • $\text{Sg} \, (Z = 106)$: $7s^2 6d^4$

  • $\text{Bh} \, (Z = 107)$: $7s^2 6d^5$

  • $\text{Hs} \, (Z = 108)$: $7s^2 6d^6$

  • $\text{Mt} \, (Z = 109)$: $7s^2 6d^7$

  • $\text{Ds} \, (Z = 110)$: $7s^2 6d^8$

  • $\text{Rg} \, (Z = 111)$: $7s^1 6d^{10}$

  • $\text{Uub} \, (Z = 112)$: $7s^2 6d^{10}$          

    

• Transition Elements Definition vs. Group 12 Exclusion:

  • Transition elements are strictly defined as elements having incompletely filled (partially filled) d-orbitals in their ground state or in any one of their common oxidation states.

  • Group 12 elements ($\text{Zn}, \text{Cd}, \text{Hg}$) have $(n-1)d^{10} ns^2$ configurations in their ground state and $(n-1)d^{10}$ in their common $+2$ ionic states.

  • Because their d-subshells remain completely filled, Group 12 elements are classified as d-block elements but are not transition elements.

  • Out of 40 d-block elements, exactly 37 are transition elements.      

    

• Relationships Across Periodicity:

  • Vertical relationships in groups are driven by identical outer electronic configurations.

  • Horizontal relationships across periods arise from the combined balancing effect of shielding ($\sigma$) and effective nuclear charge ($Z_{\text{eff}}$).      

    

• Spatial Spatial Projection of d-Orbitals:

  • The d-orbitals of transition elements project to the periphery of the atom more than s and p orbitals, making them highly responsive to surrounding ions/ligands and affecting adjacent molecules strongly.      

    

Trends in Atomic Radii, Lanthanoid Contraction, and Density

• Variation in Atomic and Ionic Radii (3d Series):

  • Across a period, atomic and ionic radii generally decrease with increasing atomic number due to increasing nuclear charge.

  • From $\text{Sc}$ to $\text{Cr}$: Effective nuclear charge dominates over screening effect ($Z_{\text{eff}} > \sigma$), causing radius contraction.

  • From $\text{Fe}$ to $\text{Ni}$: The increased nuclear charge is balanced by electron-electron repulsions in the inner d-orbitals ($Z_{\text{eff}} \approx \sigma$), maintaining virtually constant atomic radii.

  • For $\text{Cu}$ and $\text{Zn}$: Shielding effect and inter-electronic repulsions exceed effective nuclear charge ($Z_{\text{eff}} < \sigma$), resulting in a slight expansion in size.      

    

• Radius Trend Comparisons:

  • Covalent Radius Order: $\text{Sc} \ge \text{Ti} \ge \text{V} \ge \text{Cr} \ge \text{Mn} \ge \text{Fe} \approx \text{Co} \approx \text{Ni} \le \text{Cu} \le \text{Zn}$.

  • Metallic Radius Order: $\text{Sc} \ge \text{Ti} \ge \text{V} \ge \text{Cr} < \text{Mn} > \text{Fe} \approx \text{Co} \approx \text{Ni} \le \text{Cu} \le \text{Zn}$.

  • Metallic Radius Anomaly of $\text{Cr}$ vs. $\text{Mn}$: In $\text{Mn}$, only two electrons ($4s^2$) participate in metallic bond formation due to half-filled $3d^5$ core stability. In $\text{Cr}$, three electrons participate in bonding, giving $\text{Cr}$ higher metallic bond strength and a lower metallic radius compared to $\text{Mn}$.      

    

• Ionic Radius Trends:

  • Ionic radii follow atomic radius trends for identical oxidation states.

  • Radius decreases progressively as the positive charge on the cation increases:

  • $\text{Fe}^{3+} \, (0.64 \, \text{\AA}) < \text{Fe}^{2+} \, (0.76 \, \text{\AA})$

  • $\text{Ni}^{3+} \, (0.62 \, \text{\AA}) < \text{Ni}^{2+} \, (0.72 \, \text{\AA})$

• Lanthanoid Contraction and Consequences:

  • Progressive filling of $4f$ orbitals prior to $5d$ orbitals leads to poor shielding of nuclear charge.

  • Results in a steady decrease in atomic and ionic radii from $\text{Ce} \, (Z=58)$ to $\text{Lu} \, (Z=71)$.

  • Consequence: Pairs of $4d$ and $5d$ series elements in the same vertical group exhibit almost identical radii and identical chemical behavior (e.g., $\text{Zr} \approx \text{Hf}$, $\text{Nb} \approx \text{Ta}$, $\text{Pd} \approx \text{Pt}$, $\text{Ag} \approx \text{Au}$).      

    

• Density Characteristics:

  • Density increases across the period from $\text{Ti}$ to $\text{Cu}$ due to decrease in metallic radius combined with increase in atomic mass.

  • Order of Density (3d Series): $\text{Sc} < \text{Ti} < \text{V} < \text{Cr} < \text{Mn} < \text{Fe} < \text{Co} < \text{Ni} < \text{Cu} > \text{Zn}$.

  • Highest density in 3d series: Copper ($\text{Cu}$).

  • Highest density in overall d-block: Osmium ($\text{Os}$) and Iridium ($\text{Ir}$) ($\approx 22.61 \, g/cm^3$ and $22.56 \, g/cm^3$).

  • Group density order due to Lanthanoid Contraction:

  • $\text{Ti} < \text{Zr} \ll \text{Hf}$

  • $\text{Cu} < \text{Ag} \ll \text{Au}$        

    

Ionization Enthalpy, Oxidation States, and Reactivity

• Ionization Enthalpy (IE):

  • General IP Trend across d-block series: $3d < 5d > 4d$. High IP of $5d$ series elements is due to Lanthanoid Contraction.

  • IP Trend for 3d Series: $\text{Sc} < \text{Ti} > \text{V} < \text{Cr} < \text{Mn} < \text{Fe} > \text{Co} > \text{Ni} < \text{Cu} < \text{Zn}$.

  • Factors causing irregularities in IP:

  1. Exceptional ground-state electronic configurations.

  2. Irregular size and effective nuclear charge ($Z_{\text{eff}}$) variations.

  3. Electron shift from $ns$ to $(n-1)d$ upon first ionization alters exchange energy stability.

• Variable Oxidation States:

  • Caused by small energy differences between $(n-1)d$ and $ns$ subshells, allowing electrons from both levels to form chemical bonds.      

    

  • Key Oxidation State Characteristics:

  • Scandium ($\text{Sc}$) shows only $+3$; Zinc ($\text{Zn}$) shows only $+2$.

  • Most common oxidation state across d-block: $+2$.

  • Highest oxidation state in 3d series: $+7$ (Manganese in $\text{KMnO}_4$).

  • Highest oxidation state in entire d-block: $+8$ (Osmium in $\text{OsO}_4$, Ruthenium in $\text{RuO}_4$).

  • Low or Zero oxidation states occur in complexes with $\pi$-acceptor ligands (e.g., $[\text{Ni}(\text{CO})_4]$, $[\text{Fe}(\text{CO})_5]$).

  • High oxidation states are stabilized by Fluorine and Oxygen due to their high electronegativity and small ionic radii. Oxygen can form $\text{p}\pi\text{--d}\pi$ double bonds, enabling higher oxidation states than Fluorine (maximum halide state is $+6$ in $\text{CrF}_6$).          

    

        

    

  • Bonding Character:

  • Compounds in lower oxidation states are ionic in nature.

  • Compounds in higher oxidation states are covalent in nature.          

    

Standard Electrode Potentials and Redox Thermodynamics

• Born-Haber Cycle for Transition Metals ($M(s) \rightarrow M^+(aq) + e^-$):

  • Total Enthalpy Change: $\Delta_T H = \Delta_{\text{sub}} H + \Delta_i H + \Delta_{\text{hyd}} H$

  • Sublimation Enthalpy ($\Delta_{\text{sub}} H$): Endothermic ($> 0$).

  • Ionization Enthalpy ($\Delta_i H$): Endothermic ($> 0$).

  • Hydration Enthalpy ($\Delta_{\text{hyd}} H$): Exothermic ($< 0$).      

    

• Standard Reduction Potentials $E^\circ(M^{2+}/M)$ of 3d Series:

  • $\text{Ti}^{2+}/\text{Ti}$: $-1.63 \, \text{V}$

  • $\text{V}^{2+}/\text{V}$: $-1.18 \, \text{V}$

  • $\text{Cr}^{2+}/\text{Cr}$: $-0.91 \, \text{V}$

  • $\text{Mn}^{2+}/\text{Mn}$: $-1.18 \, \text{V}$

  • $\text{Fe}^{2+}/\text{Fe}$: $-0.44 \, \text{V}$

  • $\text{Co}^{2+}/\text{Co}$: $-0.28 \, \text{V}$

  • $\text{Ni}^{2+}/\text{Ni}$: $-0.25 \, \text{V}$

  • $\text{Cu}^{2+}/\text{Cu}$: $+0.34 \, \text{V}$

  • $\text{Zn}^{2+}/\text{Zn}$: $-0.76 \, \text{V}$

• Key Redox Observations:

  • Copper ($\text{Cu}$) has a positive $E^\circ(M^{2+}/M)$ value ($+0.34 \, \text{V}$) because its high enthalpy of atomization and ionization enthalpy are not compensated by its hydration enthalpy. Consequently, copper cannot liberate $\text{H}_2$ gas from dilute non-oxidizing acids ($\text{HCl}$); it reacts only with oxidizing acids like $\text{HNO}_3$ and concentrated $\text{H}_2\text{SO}_4$      

    

  • $\text{Mn}^{2+}$ ($3d^5$) and $\text{Zn}^{2+}$ ($3d^{10}$) have abnormally negative $E^\circ$ values due to extra stability of half-filled and fully-filled d-subshells.

  • $\text{Ni}^{2+}$ has a more negative $E^\circ$ than expected due to its extremely high negative enthalpy of hydration.

  • Chromium ($\text{Cr}$) is unreactive despite its highly negative reduction potential due to passivation by a protective surface layer of $\text{Cr}_2\text{O}_3$

• Standard Reduction Potentials $E^\circ(M^{3+}/M^{2+})$:

  • $\text{Ti}^{3+}/\text{Ti}^{2+}$: $+0.37 \, \text{V}$

  • $\text{V}^{3+}/\text{V}^{2+}$: $+0.26 \, \text{V}$

  • $\text{Cr}^{3+}/\text{Cr}^{2+}$: $-0.41 \, \text{V}$

  • $\text{Mn}^{3+}/\text{Mn}^{2+}$: $+1.57 \, \text{V}$

  • $\text{Fe}^{3+}/\text{Fe}^{2+}$: $+0.77 \, \text{V}$

  • $\text{Co}^{3+}/\text{Co}^{2+}$: $+1.97 \, \text{V}$

  • $\text{Sc}^{3+}$ is extraordinarily stable ($3d^0$ noble gas core).

  • High positive values for $\text{Mn}^{3+}$ ($+1.57 \, \text{V}$) and $\text{Co}^{3+}$ ($+1.97 \, \text{V}$) indicate that they act as strong oxidizing agents.

Magnetic Properties of d-Block Elements

• Types of Magnetic Behavior:

  • Diamagnetism: Slightly repelled by magnetic fields; observed when all electrons are paired ($n = 0$, e.g., $3d^0$, $3d^{10}$ ions like $\text{Sc}^{3+}, \text{Ti}^{4+}, \text{Zn}^{2+}$).

  • Paramagnetism: Attracted by magnetic fields; caused by unpaired electrons ($n \ge 1$).

  • Ferromagnetism: Alignment of magnetic domains in solid state resulting in permanent magnetization (e.g., $\text{Fe}, \text{Co}, \text{Ni}$).      

    

• Spin-Only Magnetic Moment Formula:   $\mu = \sqrt{n(n + 2)} \, \text{B.M.}$   where $n$ = number of unpaired electrons, and $\text{B.M.}$ = Bohr Magneton.      

  

• Magnetic Properties Table (3d Divalent & Trivalent Ions):

  • $\text{Sc}^{3+} \, (3d^0)$: $n = 0$, $\mu = 0 \, \text{B.M.}$ (Diamagnetic)

  • $\text{Ti}^{3+} \, (3d^1)$: $n = 1$, $\mu = 1.73 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Ti}^{2+} \, (3d^2)$: $n = 2$, $\mu = 2.84 \, \text{B.M.}$ (Paramagnetic)

  • $\text{V}^{2+} \, (3d^3)$: $n = 3$, $\mu = 3.87 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Cr}^{2+} \, (3d^4)$: $n = 4$, $\mu = 4.90 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Mn}^{2+} \, (3d^5)$: $n = 5$, $\mu = 5.92 \, \text{B.M.}$ (Maximum Paramagnetism)

  • $\text{Fe}^{2+} \, (3d^6)$: $n = 4$, $\mu = 4.90 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Co}^{2+} \, (3d^7)$: $n = 3$, $\mu = 3.87 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Ni}^{2+} \, (3d^8)$: $n = 2$, $\mu = 2.84 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Cu}^{2+} \, (3d^9)$: $n = 1$, $\mu = 1.73 \, \text{B.M.}$ (Paramagnetic)

  • $\text{Zn}^{2+} \, (3d^{10})$: $n = 0$, $\mu = 0 \, \text{B.M.}$ (Diamagnetic)      

    

Formation of Coloured Ions and Charge Transfer Spectra

• Mechanisms of Color Formation:

  1. d-d Transition: Excitation of an unpaired electron from lower energy $t_{2g}$ orbitals to higher energy $e_g$ orbitals upon absorbing visible light ($4000\text{--}7000 \, \text{\AA}$).

  • Anhydrous $\text{CuSO}_4$ is white (no crystal field splitting without ligands); hydrated $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$ is blue.

  • Anhydrous $\text{TiCl}_3$ is white; hydrated $\text{TiCl}_3 \cdot 6\text{H}_2\text{O}$ is violet.            

    

  1. Charge Transfer Spectra: In $d^0$ or $d^{10}$ species where d-d transition cannot occur:

  • Ligand to Metal Charge Transfer (LMCT): Electron transfer from ligand orbital to empty metal d-orbital. High positive charge on metal cation, low charge on ligand (e.g., $\text{KMnO}_4$ purple, $\text{K}_2\text{Cr}_2\text{O}_7$ orange, $\text{K}_2\text{CrO}_4$ yellow).

  • Metal to Ligand Charge Transfer (MLCT): Electron transfer from low-charge metal cation to ligand (e.g., $\text{Cu}_2\text{O}$ ruby red).            

    

  1. Polarization: Color darkness $\propto$ Polarization (Fajans' Rule). Larger anion size increases polarization and color intensity ($\text{AgCl}$ white $< \text{AgBr}$ light yellow $< \text{AgI}$ yellow).            

     

• Aqueous Solution Colors of 3d Ions:

  • $\text{V}^{4+}$: Light Blue / Blue-Green

  • $\text{V}^{3+}$: Green

  • $\text{Mn}^{2+}$: Pink

  • $\text{Fe}^{3+}$: Yellowish-brown

  • $\text{Co}^{2+}$: Pink / Red

  • $\text{Ni}^{2+}$: Bright Green

  • $\text{Cu}^{2+}$: Blue      

    

Complexation, Catalytic Activity, Interstitial Compounds, and Alloys

• Complex Formation:

  • Transition metals form complex ions easily due to small cation size, high effective nuclear charge ($Z_{\text{eff}}$), and available vacant $(n-1)d$ orbitals of suitable energy.

  • Cobalt forms more complexes than any other transition metal.

  • Examples: $[\text{Ag}(\text{NH}_3)_2]^+$ (Linear, C.N.=2), $[\text{Cu}(\text{NH}_3)_4]^{2+}$ (Square Planar, C.N.=4), $[\text{Ni}(\text{CN})_4]^{2-}$ (C.N.=4), $[\text{Fe}(\text{CN})_6]^{4-}$ (Octahedral, C.N.=6), $[\text{Co}(\text{NH}_3)_6]^{3+}$ (Octahedral, C.N.=6).

• Catalytic Properties:

  • Transition metals act as excellent catalysts due to variable oxidation states (Intermediate Compound Theory) and large surface adsorption area (Adsorption Theory).

  • Major Industrial Catalysts:

  • $\text{TiCl}_4 + \text{Al}(\text{C}_2\text{H}_5)_3$: Ziegler-Natta catalyst (Ethylene polymerization).

  • $\text{V}_2\text{O}_5$: Contact process ($\text{SO}_2 \rightarrow \text{SO}_3$).

  • $\text{Fe}$: Haber-Bosch process ($\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$).

  • $\text{PdCl}_2$: Wacker process (Acetaldehyde production).

  • $\text{Pd}$: Alkane/alkyne hydrogenation.

  • $\text{Pt} / \text{PtO}$: Adams' catalyst (Selective reduction).

  • $\text{Pt} / \text{Rh}$: Ostwald process ($\text{NH}_3 \rightarrow \text{NO}$).

  • $\text{Cu}$: Alcohol oxidation.      

    

• Interstitial Compounds:

  • Small non-metallic atoms ($\text{H}, \text{B}, \text{C}, \text{N}$) occupy interstitial voids in the metallic crystal lattice.

  • Characteristics: Non-stoichiometric (e.g., $\text{VH}_{0.56}, \text{TiH}_{1.5}$), neither purely ionic nor covalent, extremely hard (Cementite $\text{Fe}_3\text{C}$ used for railway tracks), chemically inert, retaining metallic conductivity, with melting points higher than pure metals.

  • Alkali metals do not form interstitial compounds due to soft metallic lattices.      

    

• Alloy Formation:

  • Transition metals readily form alloys due to similar atomic radii (radius difference $< 15\%$).      

    

  • Alloys containing Mercury ($\text{Hg}$) are called Amalgams. Iron, Cobalt, and Nickel do not form amalgams; thus liquid mercury is stored in iron containers.

  • Important Alloy Compositions:

  • Brass: $\text{Cu} + \text{Zn}$

  • Bronze / Bell Metal: $\text{Cu} + \text{Sn}$

  • Rolled Gold: $\text{Cu} + \text{Al}$

  • Invar: $\text{Fe} + \text{Ni}$

  • Alnico: $\text{Fe} + \text{Al} + \text{Ni} + \text{Co}$ (For permanent magnets)

  • Stainless Steel: $\text{Fe} + \text{Ni} + \text{Cr}$

  • Tungsten Steel: $\text{Fe} + \text{Ni} + \text{W}$

  • German Silver: $\text{Ni} + \text{Cu} + \text{Zn}$ ($0\%$ Silver)

  • 20 ct Gold: $\text{Au} + \text{Cu}$

  • 24 ct Gold: $100\% \, \text{Au}$

• Melting Points and Enthalpy of Atomization:

  • High MP and Enthalpy of Atomization ($\Delta_a H$) due to strong interatomic metallic bonding.

  • Peak MP occurs in the middle of each series ($\text{Cr}\text{--}\text{Mo}\text{--}\text{W}$ family).

  • Highest MP: Tungsten ($\text{W}$, $\approx 3422 ^\circ\text{C}$); Lowest MP: Mercury ($\text{Hg}$, $-38.83 ^\circ\text{C}$).

  • Manganese ($\text{Mn}$) has an abnormally low MP ($1246 ^\circ\text{C}$) due to stable $3d^5 4s^2$ configuration and complex crystal packing.      

    

Oxides, Chromates, Dichromates, and Permanganates

• 3d Metal Oxides Acid-Base Nature:

  • $\text{Sc}_2\text{O}_3$: Basic

  • $\text{TiO}, \text{Ti}_2\text{O}_3$: Basic; $\text{TiO}_2$: Amphoteric

  • $\text{VO}, \text{V}_2\text{O}_3$: Basic; $\text{VO}_2$: Amphoteric; $\text{V}_2\text{O}_5$: Amphoteric

  • $\text{CrO}$: Basic; $\text{Cr}_2\text{O}_3, \text{CrO}_2$: Amphoteric; $\text{CrO}_3$: Acidic

  • $\text{MnO}, \text{Mn}_2\text{O}_3$: Basic; $\text{MnO}_2, \text{Mn}_3\text{O}_4$: Amphoteric; $\text{Mn}_2\text{O}_7$: Acidic covalent green oil

  • $\text{FeO}, \text{Fe}_2\text{O}_3, \text{Fe}_3\text{O}_4, \text{CoO}, \text{NiO}, \text{CuO}, \text{ZnO}$: Basic

• Potassium Dichromate ($\text{K}_2\text{Cr}_2\text{O}_7$):

  • Prepared from Chromite ore ($\text{FeCr}_2\text{O}_4$):

  1. $4\text{FeCr}_2\text{O}_4 + 8\text{Na}_2\text{CO}_3 + 7\text{O}_2 \rightarrow 8\text{Na}_2\text{CrO}_4 + 2\text{Fe}_2\text{O}_3 + 8\text{CO}_2$

  2. $2\text{Na}_2\text{CrO}_4 + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{Cr}_2\text{O}_7 + \text{Na}_2\text{SO}_4 + \text{H}_2\text{O}$

  3. $\text{Na}_2\text{Cr}_2\text{O}_7 + 2\text{KCl} \rightarrow \text{K}_2\text{Cr}_2\text{O}_7 + 2\text{NaCl}$

  • pH Equilibrium: $2\text{CrO}_4^{2-} \, (\text{yellow}) + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} \, (\text{orange}) + \text{H}_2\text{O} \quad (\text{pH} < 4)$.      

    

  • Dichromate Reactions:

  • Thermal Decomposition: $4\text{K}_2\text{Cr}_2\text{O}_7 \xrightarrow{\Delta} 4\text{K}_2\text{CrO}_4 + 2\text{Cr}_2\text{O}_3 + 3\text{O}_2\uparrow$

  • Conc. $\text{H}_2\text{SO}_4$: $2\text{K}_2\text{Cr}_2\text{O}_7 + 8\text{H}_2\text{SO}_4 \rightarrow 2\text{K}_2\text{SO}_4 + 2\text{Cr}_2(\text{SO}_4)_3 \, (\text{green}) + 8\text{H}_2\text{O} + 3\text{O}_2$

  • Reaction with $\text{H}_2\text{O}_2$: $\text{K}_2\text{Cr}_2\text{O}_7 + \text{H}_2\text{SO}_4 + 4\text{H}_2\text{O}_2 \rightarrow 2\text{CrO}_5 \, (\text{blue layer}) + \text{K}_2\text{SO}_4 + 5\text{H}_2\text{O}$.

  • Chromium Peroxide ($\text{CrO}_5$) Butterfly structure: 1 oxo and 2 peroxo ligands, Oxidation State = $+6$, $sp^3d$ hybridization, trigonal bipyramidal.          

    

        

    

• Potassium Permanganate ($\text{KMnO}_4$):

  • Preparation: Fusion of $\text{MnO}_2$ with $\text{KOH}$ and $\text{O}_2/\text{KNO}_3$ yields dark green manganate ($\text{K}_2\text{MnO}_4$), which disproportionates in acid/neutral medium or undergoes electrolytic oxidation to give purple permanganate ($\text{MnO}_4^-$).      

    

  • Ions Comparison:

  • Permanganate ($\text{MnO}_4^-$): Tetrahedral, $d^3s$, $\text{Mn}^{+7} \, (3d^0)$, diamagnetic, intense purple (LMCT).

  • Manganate ($\text{MnO}_4^{2-}$): Tetrahedral, $d^3s$, $\text{Mn}^{+6} \, (3d^1)$, paramagnetic ($n=1$), green.          

    

        

    

        

    

  • $\text{KMnO}_4$ Half-Cell Potential Equations:

  • Acidic Medium ($E^\circ = 1.52 \, \text{V}$): $\text{MnO}_4^- + 8\text{H}^+ + 5e^- \rightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O}$

  • Neutral / Alkaline Medium ($E^\circ = 1.69 \, \text{V}$): $\text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \rightarrow \text{MnO}_2 + 4\text{OH}^-$

  • Strongly Alkaline Medium ($E^\circ = 0.56 \, \text{V}$): $\text{MnO}_4^- + e^- \rightarrow \text{MnO}_4^{2-}$

  • Key Redox Reactions of $\text{KMnO}_4$:

  • Acidic: $\text{I}^- \rightarrow \text{I}_2$; $\text{Fe}^{2+} \rightarrow \text{Fe}^{3+}$; $\text{C}_2\text{O}_4^{2-} \rightarrow \text{CO}_2$; $\text{S}^{2-} \rightarrow \text{S}$; $\text{SO}_3^{2-} \rightarrow \text{SO}_4^{2-}$; $\text{NO}_2^- \rightarrow \text{NO}_3^-$.

  • Neutral / Faintly Alkaline: $\text{I}^- \rightarrow \text{IO}_3^-$; $\text{S}_2\text{O}_3^{2-} \rightarrow \text{SO}_4^{2-}$; $\text{Mn}^{2+} \xrightarrow{\text{Zn}^{2+}} \text{MnO}_2$.

Inner Transition Elements: Lanthanoids (4f Series)

• General Configuration: $[\text{Xe}] 4f^{1-14} 5d^{0-1} 6s^2$

• Elements: Cerium ($\text{Ce}, Z=58$) to Lutetium ($\text{Lu}, Z=71$). Lanthanum ($\text{La}, Z=57$) is the d-block prototype.

• Electronic Configurations & Trivalent Radii:

  • $\text{La} \, (57)$: $5d^1 6s^2 \rightarrow \text{La}^{3+} \, (4f^0)$, radius $106 \, \text{pm}$

  • $\text{Ce} \, (58)$: $4f^1 5d^1 6s^2 \rightarrow \text{Ce}^{3+} \, (4f^1)$, radius $103 \, \text{pm}$

  • $\text{Pr} \, (59)$: $4f^3 6s^2 \rightarrow \text{Pr}^{3+} \, (4f^2)$, radius $101 \, \text{pm}$

  • $\text{Nd} \, (60)$: $4f^4 6s^2 \rightarrow \text{Nd}^{3+} \, (4f^3)$, radius $99 \, \text{pm}$

  • $\text{Pm} \, (61)$: $4f^5 6s^2 \rightarrow \text{Pm}^{3+} \, (4f^4)$, radius $98 \, \text{pm}$ (Synthetic Radioactive)

  • $\text{Sm} \, (62)$: $4f^6 6s^2 \rightarrow \text{Sm}^{3+} \, (4f^5)$, radius $96 \, \text{pm}$

  • $\text{Eu} \, (63)$: $4f^7 6s^2 \rightarrow \text{Eu}^{3+} \, (4f^6)$, radius $95 \, \text{pm}$

  • $\text{Gd} \, (64)$: $4f^7 5d^1 6s^2 \rightarrow \text{Gd}^{3+} \, (4f^7)$, radius $94 \, \text{pm}$

  • $\text{Tb} \, (65)$: $4f^9 6s^2 \rightarrow \text{Tb}^{3+} \, (4f^8)$, radius $92 \, \text{pm}$

  • $\text{Dy} \, (66)$: $4f^{10} 6s^2 \rightarrow \text{Dy}^{3+} \, (4f^9)$, radius $91 \, \text{pm}$

  • $\text{Ho} \, (67)$: $4f^{11} 6s^2 \rightarrow \text{Ho}^{3+} \, (4f^{10})$, radius $89 \, \text{pm}$

  • $\text{Er} \, (68)$: $4f^{12} 6s^2 \rightarrow \text{Er}^{3+} \, (4f^{11})$, radius $88 \, \text{pm}$

  • $\text{Tm} \, (69)$: $4f^{13} 6s^2 \rightarrow \text{Tm}^{3+} \, (4f^{12})$, radius $87 \, \text{pm}$

  • $\text{Yb} \, (70)$: $4f^{14} 6s^2 \rightarrow \text{Yb}^{3+} \, (4f^{13})$, radius $86 \, \text{pm}$

  • $\text{Lu} \, (71)$: $4f^{14} 5d^1 6s^2 \rightarrow \text{Lu}^{3+} \, (4f^{14})$      

    

• Oxidation States and Reactivity:

  • Common oxidation state: $+3$.

  • Anomalous states $+2$ and $+4$ occur due to stable $f^0, f^7, f^{14}$ states:

  • $\text{Ce}^{4+} \, (4f^0)$: Strong oxidizing agent.

  • $\text{Eu}^{2+} \, (4f^7)$: Strong reducing agent.

  • $\text{Tb}^{4+} \, (4f^7)$: Oxidizing agent.

  • $\text{Yb}^{2+} \, (4f^{14})$: Reducing agent.

• Consequences along $\text{Ce}^{3+} \rightarrow \text{Gd}^{3+} \rightarrow \text{Lu}^{3+}$:

  • Ionic size decreases, ionization energy increases, basic character of oxides/hydroxides decreases ($\text{Ce}(\text{OH})_3$ most basic, $\text{Lu}(\text{OH})_3$ least basic).

  • Covalent character, halide hydrolysis, and complexation tendency increase.      

    

• Chemical Reactions of Lanthanoids ($\text{Ln}$):

  • $\text{Ln} + \text{O}_2 \xrightarrow{\Delta} \text{Ln}_2\text{O}_3$

  • $\text{Ln} + \text{S} \xrightarrow{\Delta} \text{Ln}_2\text{S}_3$

  • $\text{Ln} + \text{N}_2 \xrightarrow{\Delta} \text{LnN}$

  • $\text{Ln} + \text{C} \xrightarrow{2773 \, \text{K}} \text{LnC}_2$

  • $\text{Ln} + \text{H}_2\text{O} \rightarrow \text{Ln}(\text{OH})_3 + \text{H}_2\uparrow$

  • $\text{Ln} + \text{Acid} \rightarrow \text{H}_2\uparrow$

  • $\text{Ln} + \text{Halogen} \rightarrow \text{LnX}_3$      

    

• Lanthanoid Applications:

  1. Misch Metal: $\sim 95\%$ Lanthanoids ($\text{Ce}$ rich) + $\sim 5\%$ Iron + traces of $\text{S}, \text{C}, \text{Ca}, \text{Al}$. Used for cigarette lighter flints.

  2. Crookes Glass: Contains $\text{CeO}_2$ to absorb harmful UV rays.

  3. Lanthanoid Oxides ($\text{Ln}_2\text{O}_3$): Used in TV screens and petroleum cracking catalysts.

Inner Transition Elements: Actinoids (5f Series)

• General Configuration: $[\text{Rn}] 5f^{1-14} 6d^{0-1} 7s^2$

• Elements: Thorium ($\text{Th}, Z=90$) to Lawrencium ($\text{Lr}, Z=103$).

• Natural vs. Synthetic Elements:

  • Natural actinides: Thorium ($\text{Th}$), Protactinium ($\text{Pa}$), Uranium ($\text{U}$).

  • Transuranic elements ($Z > 92$): Synthesized artificially.

• Configurations & Ionic Radii Table:

  • $\text{Ac} \, (89)$: $6d^1 7s^2 \rightarrow \text{Ac}^{3+} \, (5f^0)$, radius $111 \, \text{pm}$

  • $\text{Th} \, (90)$: $6d^2 7s^2 \rightarrow \text{Th}^{4+} \, (5f^0)$, radius $99 \, \text{pm}$

  • $\text{Pa} \, (91)$: $5f^2 6d^1 7s^2 \rightarrow \text{Pa}^{4+} \, (5f^1)$, radius $96 \, \text{pm}$

  • $\text{U} \, (92)$: $5f^3 6d^1 7s^2 \rightarrow \text{U}^{4+} \, (5f^2)$, radius $93 \, \text{pm}$

  • $\text{Np} \, (93)$: $5f^4 6d^1 7s^2 \rightarrow \text{Np}^{4+} \, (5f^3)$, radius $92 \, \text{pm}$

  • $\text{Pu} \, (94)$: $5f^6 7s^2 \rightarrow \text{Pu}^{4+} \, (5f^4)$, radius $90 \, \text{pm}$

  • $\text{Am} \, (95)$: $5f^7 7s^2 \rightarrow \text{Am}^{4+} \, (5f^5)$, radius $89 \, \text{pm}$

  • $\text{Cm} \, (96)$: $5f^7 6d^1 7s^2 \rightarrow \text{Cm}^{4+} \, (5f^6)$, radius $88 \, \text{pm}$

  • $\text{Bk} \, (97)$: $5f^9 7s^2 \rightarrow \text{Bk}^{4+} \, (5f^7)$, radius $87 \, \text{pm}$

  • $\text{Cf} \, (98)$: $5f^{10} 7s^2 \rightarrow \text{Cf}^{4+} \, (5f^8)$, radius $86 \, \text{pm}$

  • $\text{Es} \, (99)$: $5f^{11} 7s^2$

  • $\text{Fm} \, (100)$: $5f^{12} 7s^2$

  • $\text{Md} \, (101)$: $5f^{13} 7s^2$

  • $\text{No} \, (102)$: $5f^{14} 7s^2$

  • $\text{Lr} \, (103)$: $5f^{14} 6d^1 7s^2$

• Oxidation States & Actinoid Contraction:

  • Actinoids show a wide range of oxidation states ($+3, +4, +5, +6, +7$) because $5f, 6d,$ and $7s$ subshells are close in energy.

  • Maximum oxidation state increases from $\text{Th} \, (+4)$ up to $\text{Np} \, (+7)$, then drops in later elements.      

    

  • Actinoid contraction is greater than lanthanoid contraction due to poorer shielding by $5f$ electrons.

• Comparison Table: Lanthanides vs. Actinides:

  • Oxidation States: Lanthanides show predominantly $+3$ (rarely $+2, +4$); Actinides show $+3, +4, +5, +6, +7$.

  • Complex Formation: Lanthanides have weak tendency; Actinides have strong tendency.

  • Oxo Cations: Lanthanides do not form oxo cations; Actinides form oxo cations like $\text{UO}_2^{2+}, \text{PuO}_2^{2+}, \text{NpO}_2^+$.

  • Basicity: Lanthanide compounds are less basic; Actinide compounds are more basic.

  • Radioactivity: Lanthanides non-radioactive (except Promethium); All Actinides are radioactive.