Comprehensive Study Guide to the d- and f-Block Elements

Overview of the d- and f-Block Elements

• The d-block consists of the elements from groups 3 to 12. In these elements, the d orbitals are progressively filled across four long periods.
• The f-block consists of elements in which the $4f$ and $5f$ orbitals are progressively filled. They occupy a separate panel at the bottom of the periodic table.
• Definitions:
  • Transition Metals: Historically, the name refers to elements whose properties were transitional between s- and p-block elements. According to IUPAC, transition metals are elements that have an incomplete d subshell either in their neutral atom state or in their common ions.
  • Inner Transition Metals: Refers to the f-block elements.
• The Four Transition Series:
  • 3d series: Scandium ($Sc$) to Zinc ($Zn$).
  • 4d series: Yttrium ($Y$) to Cadmium ($Cd$).
  • 5d series: Lanthanum ($La$) and Hafnium ($Hf$) to Mercury ($Hg$).
  • 6d series: Actinium ($Ac$) and elements from Rutherfordium ($Rf$) to Copernicium ($Cn$).
• Group 12 Elements: Zinc ($Zn$), Cadmium ($Cd$), and Mercury ($Hg$) are not technically regarded as transition metals because they have a full $d^{10}$ configuration in their ground state and common oxidation states. However, their chemistry is studied alongside transition metals as they are end-members of the series.
• Inner Transition Series:
  • Lanthanoids: $4f$ series from Cerium ($Ce$) to Lutetium ($Lu$).
  • Actinoids: $5f$ series from Thorium ($Th$) to Lawrencium ($Lr$).

Electronic Configurations of d-Block Elements

• General Electronic Configuration: The outer orbitals follow the formula $(n-1)d^{1-10} ns^{1-2}$.
  • The $(n-1)$ represents the inner d orbitals (penultimate energy level).
  • Exception: Palladium ($Pd$) has the configuration $4d^{10} 5s^0$.
• Stability Factors: Half-filled ($d^5$) and completely filled ($d^{10}$) sets of orbitals are relatively more stable.
  • Chromium ($Cr$, Z=24): Configuration is $3d^5 4s^1$ instead of $3d^4 4s^2$ because the energy gap between $3d$ and $4s$ is small enough that shifting an electron to achieve a half-filled d-subshell provides extra stability.
  • Copper ($Cu$, Z=29): Configuration is $3d^{10} 4s^1$ instead of $3d^9 4s^2$ to achieve a completely filled d-subshell.
• Protrusion of d-Orbitals: The d-orbitals of transition elements protrude to the periphery of the atom more than s and p orbitals. Consequently, they are more influenced by surroundings and significantly affect neighboring atoms or molecules.

Physical Properties of Transition Metals

• Metallic Nature: Nearly all transition elements exhibit high tensile strength, ductility, malleability, high thermal/electrical conductivity, and metallic lustre.
• Lattice Structures:
  • Most exhibit typical structures: bcc (body-centred cubic), hcp (hexagonal close-packed), or ccp (cubic close-packed).
  • Exceptions: $Zn$, $Cd$, $Hg$, and $Mn$ do not have typical metallic structures at normal temperatures.
• Hardness and Volatility: They are generally very hard and have low volatility (except for $Zn$, $Cd$, and $Hg$).
• Melting Points:
  • Attributed to strong interatomic metallic bonding involving both $(n-1)d$ and $ns$ electrons.
  • In any row, melting points rise to a maximum at approximately $d^5$ (one unpaired electron per d orbital is ideal for interaction).
  • Anomalies: Manganese ($Mn$) and Technetium ($Tc$) show anomalously low melting points compared to their neighbors.

Enthalpies of Atomisation and Atomic Sizes

• Enthalpies of Atomisation (\\Delta_a H^\\circ):
  • High enthalpies are due to strong interatomic interactions resulting from many unpaired electrons.
  • Zinc has the lowest enthalpy ($126 \, kJ \, mol^{-1}$) in the 3d series because no d-electrons are involved in its metallic bonding.
  • Second and third series metals have higher enthalpies of atomisation than the first series, facilitating more frequent metal-metal bonding in heavy transition metal compounds.
• Trends in Atomic and Ionic Radii:
  • Generally, radius decreases with increasing atomic number in a series due to increased nuclear charge and poor shielding by d electrons.
  • Lanthanoid Contraction: Filling of the $4f$ orbitals before the $5d$ series leads to a regular decrease in atomic radii. This compensates for the expected size increase due to higher atomic numbers.
  • Result of Contraction: Post-lanthanoid elements like Zirconium ($Zr$, $160 \, pm$) and Hafnium ($Hf$, $159 \, pm$) have nearly identical radii, making them difficult to separate and giving them similar properties.

Ionisation Enthalpies

• General Trend: Ionisation enthalpy increases along each series from left to right due to increased nuclear charge.
• 3d Series Dynamics: When d-block elements form ions, $ns$ electrons are lost before $(n-1)d$ electrons.
• Irregularities: Trends are influenced by shielding and exchange energy.
  • Exchange Energy: Proportional to the number of pairs of parallel spins in degenerate orbitals. Higher stability is associated with half-filled and full-filled configurations.
  • Mn and Fe: The second ionisation enthalpy break occurs at Manganese ($d^5$) and the third at Iron ($d^6 \rightarrow d^5$). Iron's third ionisation enthalpy is lower than Manganese's because removing an electron from Iron ($3d^6$) results in a stable $3d^5$ configuration.
  • Cu and Cr: Show unusually high second ionisation enthalpies because the $M^+$ ions have stable $d^{10}$ and $d^5$ configurations respectively.

Oxidation States of Transition Metals

• Uniqueness: Transition metals show a wide variety of oxidation states differing by units of one (e.g., $V^{II}, V^{III}, V^{IV}, V^V$), unlike non-transition elements which usually differ by two.
• Middle of the Series: Elements like Manganese show the maximum number of states (from $+2$ to $+7$). Scandium exhibits only $+3$, and Zinc exhibits only $+2$.
• Stability Patterns:
  • Early series: Scandium(II) is unknown; Titanium(IV) is more stable than Titanium(III).
  • Late series: Only lower oxidation states are stable ($Cu^{I}, Cu^{II}, Zn^{II}$).
• Group Trends: In d-blocks, higher oxidation states are more stable in heavier members. For example, in Group 6, $Mo(VI)$ and $W(VI)$ are more stable than $Cr(VI)$. Consequently, $Cr(VI)$ (as dichromate) is a strong oxidant, while $MoO_3$ and $WO_3$ are not.
• Low Oxidation States: Found in complexes with $\\pi$-acceptor ligands (e.g., $Ni(CO)_4$ and $Fe(CO)_5$ have oxidation states of zero).

Standard Electrode Potentials (E^\\circ)

• $M^{2+}/M$ System:
  • The general trend across the series is toward less negative E^\\circ values.
  • Copper ($+0.34 \, V$): Unique positive value. Copper cannot liberate $H_2$ from acids. The high energy required to transform solid $Cu$ to $Cu^{2+}(aq)$ (atomisation + ionisation) is not compensated by its hydration enthalpy.
  • Mn, Ni, and Zn: Have more negative values than expected. For $Mn$ and $Zn$, this is due to stable $d^5$ and $d^{10}$ subshells. For $Ni$, it is due to a very high negative enthalpy of hydration.
• $M^{3+}/M^{2+}$ System:
  • Low value for Scandium reflects the stability of $Sc^{3+}$ (noble gas configuration).
  • High value for Manganese shows the stability of $Mn^{2+}$ ($d^5$).
  • Low value for Iron shows the stability of $Fe^{3+}$ ($d^5$).

Magnetic and Colour Properties

• Magnetic Behaviour:
  • Paramagnetism: Arises from unpaired electrons. Each electron acts as a tiny magnet due to spin and orbital angular momentum.
  • Spin-only Formula: For the first series, orbital momentum is quenched. Magnetic moment ($\mu$) is calculated by: $\mu = \sqrt{n(n+2)}$ where $n$ is the number of unpaired electrons. Units: Bohr magneton (BM).
  • Examples: $Sc^{3+} (3d^0, n=0, \mu=0)$, $Mn^{2+} (3d^5, n=5, \mu=5.92 \, BM)$.
• Colour:
  • Colours arise from d-d transitions. Energy of excitation corresponds to visible light frequency.
  • Examples:
    • $Ti^{3+}$: Purple ($3d^1$)
    • $V^{4+}/Cu^{2+}$: Blue
    • $Fe^{3+}$: Yellow
    • $Mn^{2+}$: Pink
    • $Sc^{3+}/Ti^{4+}/Zn^{2+}$: Colourless ($d^0$ or $d^{10}$)

Complex Formation and Catalytic Properties

• Complex Compounds: Transition metals form complexes (e.g., $[Fe(CN)_6]^{3-}, [Cu(NH_3)_4]^{2+}$) due to small ion size, high ionic charge, and available d orbitals.
• Catalytic Activity: Attributed to multiple oxidation states and complex formation.
  • Examples:
    • $V_2O_5$ in the Contact Process.
    • Finely divided Iron in the Haber Process.
    • Nickel in Catalytic Hydrogenation.
  • Surface Action: Reactants are concentrated on the catalyst surface and bonds are weakened, lowering activation energy.

Interstitial Compounds and Alloys

• Interstitial Compounds: Formed when small atoms ($H, C, N$) are trapped in metal crystal lattices (e.g., $TiC, Mn_4N, Fe_3H$).
  • Characteristics: High melting points, extremely hard (borides approach diamond hardness), retain metallic conductivity, and are chemically inert.
• Alloys: Blends of metals. Transition metals readily form alloys because their metallic radii are within $15\%$ of each other.
  • Ferrous Alloys: Steels are produced using $Cr, V, W, Mo, Mn$.
  • Non-ferrous Alloys: Brass ($Cu-Zn$) and Bronze ($Cu-Sn$).

Important Compounds: Potassium Dichromate ($K_2Cr_2O_7$)

• Preparation: From chromite ore ($FeCr_2O_4$).
  1. Fusion: $4 FeCr_2O_4 + 8 Na_2CO_3 + 7 O_2 \rightarrow 8 Na_2Cr_2O_4 + 2 Fe_2O_3 + 8 CO_2$
  2. Acidification: $2 Na_2CrO_4 + 2 H^+ \rightarrow Na_2Cr_2O_7 + 2 Na^+ + H_2O$
  3. Conversion: $Na_2Cr_2O_7 + 2 KCl \rightarrow K_2Cr_2O_7 + 2 NaCl$
• Structures:
  • Chromate ($CrO_4^{2-}$): Yellow, tetrahedral.
  • Dichromate ($Cr_2O_7^{2-}$): Orange, two tetrahedra sharing a corner. $Cr-O-Cr$ bond angle is $126^\circ$.
• pH Dependence: Chromate and dichromate are interconvertible. Chromate is stable in alkaline solutions; dichromate is stable in acidic solutions.
• Oxidising Action: In acidic solution: $Cr_2O_7^{2-} + 14 H^+ + 6 e^- \rightarrow 2 Cr^{3+} + 7 H_2O$ (E^\\circ = 1.33 \, V).

Important Compounds: Potassium Permanganate ($KMnO_4$)

• Preparation: From $MnO_2$ (Pyrolusite).
  1. Alkaline oxidative fusion: $2 MnO_2 + 4 KOH + O_2 \rightarrow 2 K_2MnO_4 + 2 H_2O$ (Dark green manganate).
  2. Disproportionation in acidic/neutral solution: $3 MnO_4^{2-} + 4 H^+ \rightarrow 2 MnO_4^- + MnO_2 + 2 H_2O$.
• Properties: Dark purple crystals, isostructural with $KClO_4$. Diamagnetic with weak temperature-dependent paramagnetism.
• Oxidising Action:
  • In acid: $MnO_4^- + 8 H^+ + 5 e^- \rightarrow Mn^{2+} + 4 H_2O$ (E^\\circ = 1.52 \, V).
  • In neutral/faintly alkaline: Iodide is converted to iodate ($I^- \rightarrow IO_3^-$) and Thiosulphate to sulphate.

The Lanthanoids (f-Block)

• Electronic Configuration: Common $6s^2$ configuration; tripositive ions ($Ln^{3+}$) are most stable with $4f^n$ configuration.
• Lanthanoid Contraction: Gradual decrease in atomic and ionic radii leading to nearly identical sizes of elements in corresponding rows of 4d and 5d series.
• Oxidation States: Predominantly $+3$. $Ce(IV)$ is a strong oxidant; $Eu(II)$ and $Yb(II)$ are strong reductants.
• General Characteristics: Silvery white soft metals. Tarnish in air. Hardness increases with atomic number. All other than $f^0$ and $f^{14}$ types are paramagnetic.
• Mischmetall: An alloy consisting of lanthanoid metals ($\sim 95\%$) and iron ($\sim 5\%$) with traces of $S, C, Ca, Al$. Used in lighters, bullets, and shells.

The Actinoids (f-Block)

• Radioactivity: All actinoids are radioactive. Early members have long half-lives; later members like Lawrencium ($Z=103$) have half-lives of minutes.
• Electronic Configuration: Formally adds 14 electrons to the $5f$ orbitals. electrons in $5f$ can participate in bonding more than $4f$ electrons because they are less effectively shielded.
• Oxidation States: Shows a wider range than lanthanoids due to comparable energies of $5f, 6d, 7s$ levels. Maximum oxidation state increases from Thorium ($+4$) to Neptunium ($+7$), then decreases.
• Actinoid Contraction: Greater than lanthanoid contraction due to poorer shielding by $5f$ compared to $4f$ electrons.

Questions & Discussion

• Q: Why is Scandium (Z=21) a transition element but Zinc (Z=30) is not?
  • A: Scandium has an incompletely filled $3d^1$ subshell in its ground state. Zinc has a completely filled $3d^{10}$ subshell in its ground state and its common oxidation state ($Zn^{2+}$).
• Q: Why is silver (Z=47) considered a transition element despite having a filled $4d^{10}$ configuration?
  • A: Silver can exhibit a $+2$ oxidation state ($Ag^{2+}$) where it has an incompletely filled d-subshell ($4d^9$).
• Q: Why is $Cr^{2+}$ reducing and $Mn^{3+}$ oxidising despite both having $d^4$ configurations?
  • A: $Cr^{2+} \rightarrow Cr^{3+}$ results in a stable half-filled $t_{2g}$ level ($d^3$). $Mn^{3+} \rightarrow Mn^{2+}$ results in the extra stability of a half-filled $d^5$ configuration.
• Q: What is the cause of Lanthanoid Contraction?
  • A: It is caused by the imperfect shielding of one $4f$ electron by another as nuclear charge increases along the series, leading to a regular decrease in volume.
• Q: Why do transition metals exhibit high enthalpies of atomisation?
  • A: Because of many unpaired electrons, they have strong interatomic interactions and metallic bonding.