The d- and f-Block Elements: Comprehensive Study Notes

Position and General Definitions of d- and f-Block Elements

• The d-Block Elements: These occupy groups 3 to 12 in the periodic table. They are characterized by the progressive filling of the $d$ orbitals in the four long periods.

• The f-Block Elements: These consist of the elements where the $4f$ and $5f$ orbitals are progressively filled. They are located in two separate rows in a panel at the bottom of the periodic table.

• Terminology:

  • Transition Metals: Often used for $d$-block elements.

  • Inner Transition Metals: Used for $f$-block elements.

• The Four Transition Series:

  1. 3d series: Scandium ($Sc$) to Zinc ($Zn$).

  2. 4d series: Yttrium ($Y$) to Cadmium ($Cd$).

  3. 5d series: Lanthanum ($La$) and Hafnium ($Hf$) to Mercury ($Hg$).

  4. 6d series: Actinium ($Ac$) and elements from Rutherfordium ($Rf$) to Copernicium ($Cn$).

• The Two Inner Transition Series:

  1. Lanthanoids (4f series): Cerium ($Ce$) to Lutetium ($Lu$).

  2. Actinoids (5f series): Thorium ($Th$) to Lawrencium ($Lr$).

• IUPAC Definition of Transition Metals: A metal which has an incomplete $d$ subshell either in its neutral atom state or in one of its common ions.

• Group 12 Exceptions: Zinc ($Zn$), Cadmium ($Cd$), and Mercury ($Hg$) possess a completely filled $d^{10}$ configuration in their ground state and common oxidation states. Technically, they are not regarded as transition metals by the IUPAC definition, but since they are the end members of the series, their chemistry is studied alongside transition metals.

Electronic Configurations of d-Block Elements

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

• Exceptions and Stability: Several exceptions to the general rule exist because the energy difference between $(n-1)d$ and $ns$ orbitals is very small. Half-filled ($d^5$) and completely filled ($d^{10}$) sets of orbitals are relatively more stable.

• Chromium (Z=24): Its configuration is $3d^5 4s^1$ instead of $3d^4 4s^2$.

• Copper (Z=29): Its configuration is $3d^{10} 4s^1$ instead of $3d^9 4s^2$.

• Palladium (Pd): A unique case where the configuration is $4d^{10} 5s^0$.

• Group 12 Configurations: Represented by $(n-1)d^{10} ns^2$.

• Chemical Properties Influenced by Orbitals: Because $d$ orbitals protrude more to the periphery of the atom than $s$ and $p$ orbitals, they are more influenced by the surrounding environment and affect the surrounding ligands.

Physical Properties of Transition Metals

• Metallic Nature: Transition metals exhibit high tensile strength, ductility, malleability, metallic lustre, and high thermal and electrical conductivity.

• Crystal Structures:

  • Sc: hcp

  • Ti, Zr, Hf: hcp (bcc at high temperatures)

  • V, Nb, Ta, Cr, Mo, W: bcc

  • Mn: Typical metal structure (X)

  • Fe: bcc (hcp, ccp at high temperatures)

  • Co, Ni, Rh, Pd, Ir, Pt, Cu, Ag, Au: ccp (hcp for Co and others)

  • Zn, Cd, Hg: Typical metal structures (X).

• Hardness and Volatility: Except for $Zn, Cd, Hg$, transition metals are very hard and have low volatility.

• Melting Points: Transition metals have high melting and boiling points. These rise to a maximum at about the middle of each series (at the $d^5$ configuration). Notably, $Mn$ and $Tc$ show anomalous lower melting points.

• Enthalpies of Atomisation: These metals have high enthalpies of atomisation, peaking at the middle of the series where the number of unpaired electrons is highest, resulting in strong interatomic bonding.

• Density: There is a general increase in density from left to right across a series (e.g., from $Ti$ at $4.10,g\,cm^{-3}$ to $Cu$ at $8.90,g\,cm^{-3}$) due to decreasing atomic radius and increasing atomic mass.

Variation in Atomic and Ionic Sizes

• Trends within a Series: There is a progressive decrease in the radius of ions of the same charge with increasing atomic number. This is because every new electron enters a $d$ orbital while the nuclear charge increases.

• Shielding: The shielding effect of a $d$ electron is ineffective, so the net electrostatic attraction between the nucleus and the outermost electrons increases, shrinking the radius.

• Lanthanoid Contraction: While radii increase from the 3d series to the 4d series, the radii of the 5d series elements are virtually the same as those of the 4d series (e.g., $Zr = 160\,pm$ and $Hf = 159\,pm$). This is due to the filling of the $4f$ orbitals before the $5d$ series, where shielding of one $4f$ electron by another is very poor.

• Consequences of Lanthanoid Contraction: Elements in the second and third transition series exhibit very similar physical and chemical properties, making them difficult to separate in nature.

Ionisation Enthalpies

• General Trend: There is a general increase in ionisation enthalpy across each series due to increased nuclear charge.

• Magnitude of Variation: The increase is less steep than in non-transition (main group) elements because the inner $d$ electrons shield the outer $ns$ electrons from the nucleus.

• Order of Removal: When forming ions, electrons are lost from the $ns$ orbital before the $(n-1)d$ orbital.

• Irregularities: The trend is broken by specific electronic configurations:

  • The second ionisation enthalpy is unusually high for $Cr$ and $Cu$ because removing an electron from stable $d^5$ or $d^{10}$ configurations requires more energy.

  • The third ionisation enthalpy of $Fe$ is lower than that of $Mn$ because $Fe^{2+}$ is $d^6$ (loss of one electron gives stable $d^5$) while $Mn^{2+}$ is already a stable $d^5$.

• Exchange Energy: This term accounts for the stabilization of energy states and is proportional to the number of parallel spins. Stability is highest for empty, half-filled, or completely filled $d$ subshells.

Oxidation States

• Variability: A defining characteristic of transition elements is the variety of oxidation states they exhibit, which typically differ by a unit of one (e.g., $V^{II}, V^{III}, V^{IV}, V^{V}$).

• Mid-Series Complexity: Elements in the middle of the series ($Mn$) show the maximum number of states ($+2$ to $+7$).

• End-Series Limitations:

  • $Sc$ only shows $+3$.

  • $Zn$ only shows $+2$.

• Stability Trends:

  • Early in the 3d series, high oxidation states are more stable (e.g., $Ti^{IV}$).

  • Late in the series, lower oxidation states are more stable ($Cu^{I}, Cu^{II}, Zn^{II}$).

• Group Trends: Unlike the $p$-block where lower oxidation states are favored by heavier elements (inert pair effect), in the $d$-block, heavier members favor higher oxidation states (e.g., $W^{VI}$ and $Mo^{VI}$ are more stable than $Cr^{VI}$).

• Zero Oxidation State: This can occur in complexes with $\text{π}$-acceptor ligands like carbon monoxide, e.g., $Ni(CO)_4$ and $Fe(CO)_5$.

Standard Electrode Potentials ($E^∘$)

• Transformation Process: The transformation of solid metal to $M^{2+}(aq)$ involves the enthalpy of atomisation, ionisation enthalpies, and hydration enthalpy.

• $M^{2+}/M$ Couple:

  • Most values are negative, indicating propensity to dissolve in acids.

  • Copper Exception: $E^∘ = +0.34\,V$. Copper cannot liberate $H_2$ from acids because its high energy of atomisation and ionisation is not compensated by its hydration enthalpy.

  • Anomalies: $Mn, Ni,$ and $Zn$ have more negative values than expected due to stable configurations ($Mn^{2+}$ is $d^5$, $Zn^{2+}$ is $d^{10}$) or high hydration energy ($Ni^{2+}$).

• $M^{3+}/M^{2+}$ Couple:

  • Low value for $Sc$ reflects the stability of $Sc^{3+}$ (noble gas config).

  • High value for $Mn$ shows $Mn^{2+}$ ($d^5$) is very stable, while a low value for $Fe$ shows $Fe^{3+}$ ($d^5$) is particularly stable.

  • $Mn^{3+}$ and $Co^{3+}$ are strong oxidising agents in aqueous solutions.

Magnetic Properties

• Types of Magnetism:

  • Diamagnetism: Repelled by magnetic fields (no unpaired electrons).

  • Paramagnetism: Attracted by magnetic fields (presence of unpaired electrons).

  • Ferromagnetism: Extreme form of paramagnetism (strong attraction).

• Spin-Only Formula: For 3d series, orbital angular momentum is quenched. Magnetic moment ($μ$) is calculated based on unpaired electrons ($n$):     $\mu = \sqrt{n(n + 2)}$     Units: Bohr magneton (BM).

• Calculated Values:

  • $n=1 \rightarrow 1.73\,BM$

  • $n=2 \rightarrow 2.84\,BM$

  • $n=3 \rightarrow 3.87\,BM$

  • $n=4 \rightarrow 4.90\,BM$

  • $n=5 \rightarrow 5.92\,BM$

Coloured Ions and Complex Formation

• Colour: Arises from $d-d$ transitions. When white light falls on an ion, an electron from a lower energy $d$ orbital is excited to a higher one. The frequency absorbed corresponds to a specific color, and the observed color is the complementary one.

  • $Sc^{3+}, Ti^{4+}, Zn^{2+}$ are colourless (empty or full $d$ subshells).

  • $Ti^{3+}$: Purple; $V^{4+}$: Blue; $V^{3+}$: Green; $Mn^{2+}$: Pink; $Fe^{3+}$: Yellow; $Cu^{2+}$: Blue.

• Complex Formation: Transition metals form many complexes (e.g., $[Fe(CN)_6]^{3-}$) due to:

  1. Small size.

  2. High ionic charge.

  3. Availability of empty $d$ orbitals for bonding with ligands.

Catalytic, Interstitial, and Alloy Properties

• Catalytic Activity: Attributed to the ability to adopt multiple oxidation states and form complexes. Examples: $V_2O_5$ in Contact Process, Fe in Haber's Process, Ni in hydrogenation.

• Interstitial Compounds: Formed when small atoms ($H, C, N$) are trapped in metal lattices.

  • Examples: $TiC, Mn_4N, Fe_3H$.

  • Properties: High melting points, extreme hardness (some like diamond), metallic conductivity, chemically inert.

• Alloys: Solutions of metals. Formed by transition metals because their radii are within $15\%$ of each other.

  • Ferrous alloys: Steels containing $Cr, V, W, Mo, Mn$.

  • Non-ferrous: Brass ($Cu-Zn$), Bronze ($Cu-Sn$).

Important Compounds: Potassium Dichromate ($K_2Cr_2O_7$)

• Preparation:

  1. Fusion of chromite ore ($FeCr_2O_4$) with sodium carbonate in air:        $8 Na_2CO_3 + 4 FeCr_2O_4 + 7 O_2 \rightarrow 8 Na_2Cr_4 + 2 Fe_2O_3 + 8 CO_2$

  2. Acidification of sodium chromate:        $2 Na_2CrO_4 + 2 H^+ \rightarrow Na_2Cr_2O_7 + 2 Na^+ + H_2O$

  3. Conversion to potassium salt:        $Na_2Cr_2O_7 + 2 KCl \rightarrow K_2Cr_2O_7 + 2 NaCl$

• pH Dependency: Chromate ($CrO_4^{2-}$ - yellow) and dichromate ($Cr_2O_7^{2-}$ - orange) are interconvertible.

  • In acidic medium: Dichromate exists ($2 CrO_4^{2-} + 2 H^+ \rightarrow Cr_2O_7^{2-} + H_2O$).

  • In basic medium: Chromate exists ($Cr_2O_7^{2-} + 2 OH^- \rightarrow 2 CrO_4^{2-} + H_2O$).

• Structure: $CrO_4^{2-}$ is tetrahedral. $Cr_2O_7^{2-}$ consists of two tetrahedra sharing a corner ($Cr-O-Cr$ angle is $126^{\circ}$).

• Redox Action: Strong oxidant in acid.     $Cr_2O_7^{2-} + 14 H^+ + 6 e^- \rightarrow 2 Cr^{3+} + 7 H_2O$ ($E^∘ = 1.33\,V$).

  • Oxidises: $I^- \rightarrow I_2$; $Sn^{2+} \rightarrow Sn^{4+}$; $H_2S \rightarrow S$; $Fe^{2+} \rightarrow Fe^{3+}$.

Important Compounds: Potassium Permanganate ($KMnO_4$)

• Preparation:

  1. Fusion of $MnO_2$ with $KOH$ and oxidant ($KNO_3$) produces green $K_2MnO_4$.

  2. Disproportionation of manganate in acid/neutral solution:        $3 MnO_4^{2-} + 4 H^+ \rightarrow 2 MnO_4^- + MnO_2 + 2 H_2O$

  3. Commercial/Lab: Oxidation of $Mn^{2+}$ with peroxodisulphate ($S_2O_8^{2-}$).

• Properties: Dark purple crystals, isostructural with $KClO_4$. Decomposes at $513\,K$:     $2 KMnO_4 \rightarrow K_2MnO_4 + MnO_2 + O_2$

• Oxidising Actions:

  • In Acid:

    • $Fe^{2+} \rightarrow Fe^{3+}$

    • $I^- \rightarrow I_2$

    • $C_2O_4^{2-} \rightarrow CO_2$ (at $333\,K$)

    • $H_2S \rightarrow S$

    • $SO_3^{2-} \rightarrow SO_4^{2-}$

    • $NO_2^- \rightarrow NO_3^-$

  • In Neutral/Alkaline:

    • $I^- \rightarrow IO_3^-$ (Iodate)

    • $S_2O_3^{2-} \rightarrow SO_4^{2-}$

    • $Mn^{2+} \rightarrow MnO_2$ (Zinc salts act as catalyst).

• Note: $HCl$ titrations are avoided as $KMnO_4$ oxidises $HCl$ to $Cl_2$.

The Lanthanoids (4f-Block)

• Electronic Configuration: Common $6s^2$ with variable $4f$ occupancy ($4f^n$ for $Ln^{3+}$).

• Lanthanoid Contraction: Cumulative decrease in atomic and ionic radii with increasing Z.

• Oxidation States:

  • Predominant: $+3$.

  • Others: $Ce^{IV}$ (stable empty $f$ shell), $Eu^{II}$ and $Yb^{II}$ (half-filled/filled $f$ shell).

  • $Ce^{IV}$ is a strong oxidant; $Eu^{II}$ is a strong reductant.

• Properties: Silvery-white, soft metals. Tarnish in air. Hardness increases with Z.

• Magnetism: All paramagnetic except $f^0$ ($La^{3+}, Ce^{4+}$) and $f^{14}$ ($Yb^{2+}, Lu^{3+}$).

• Common Use: Mischmetall (95% lanthanoid, 5% Iron) used in lighter flints and magnesium-based alloys.

The Actinoids (5f-Block)

• Characteristics: All are radioactive; earlier members have long half-lives but later members are very short-lived (Lawrencium is approx. 3 minutes).

• Configuration: Variable occupancy of $5f$ and $6d$ orbitals; all have $7s^2$.

• Oxidation States: Exhibit a greater range than lanthanoids because $5f, 6d, 7s$ shells are close in energy.

  • States range from $+3$ upto $+7$ for $Np$ and $Pu$.

• Actinoid Contraction: Similar to lanthanoid contraction but greater due to even poorer shielding by $5f$ electrons.

• Reactivity: Highly reactive; combine with most non-metals. Slightly affected by nitric acid due to protective oxide layer formation.

Questions and Discussion

• Q: Why is $Sc$ a transition metal but $Zn$ is not?

• A: $Sc$ has an incomplete $3d^1$ subshell in its ground state, fulfilling the definition. $Zn$ has a full $3d^{10}$ subshell in its ground state and in its ion ($Zn^{2+}$).

• Q: Is silver a transition element if $Ag$ is $4d^{10} 5s^1$?

• A: Yes, because it can exhibit the $+2$ oxidation state ($Ag^{2+}$) where it has an incomplete $4d^9$ configuration.

• Q: Why is the enthalpy of atomisation for $Zn$ the lowest ($126,kJ\,mol^{-1}$)?

• A: Zinc involves no $d$-orbital electrons in metallic bonding, only $s$ electrons, resulting in weak interatomic interaction.

• Q: Why is $Cr^{2+}$ reducing and $Mn^{3+}$ oxidising despite both having $d^4$ configurations?

• A: $Cr^{2+}$ reduces to $Cr^{3+}$ which has a stable half-filled $t_{2g}$ level ($d^3$). $Mn^{3+}$ oxidises to $Mn^{2+}$ which has a stable half-filled $d^5$ configuration.

• Q: What is disproportionation?

• A: When a specific oxidation state becomes unstable and converts into a higher and a lower oxidation state simultaneously. Example: $3 MnO_4^{2-} + 4 H^+ \rightarrow 2 MnO_4^- + MnO_2 + 2 H_2O$.