Comprehensive Study Notes on d- and f-Block Elements

Position and Classification 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 across four long periods. These elements are commonly referred to as transition metals.

• The f-Block Elements: These consist of elements where the $4f$ and $5f$ orbitals are progressively filled. They are placed in two separate rows at the bottom of the periodic table. These are known as inner transition metals.

• Transition Metal 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 ($Cn$).

• Inner Transition Metal Series:

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

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

• IUPAC Definition of Transition Metals: Metals which have an incomplete d subshell either in their neutral atom or in any of their common ions.

• The Group 12 Exception: Zinc ($Zn$), Cadmium ($Cd$), and Mercury ($Hg$) are not technically regarded as transition metals because they have a completely filled $d^{10}$ configuration in both their ground state and common oxidation states. However, their chemistry is studied alongside transition metals as they are the end members of the series.

Electronic Configurations of the d-Block Elements

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

  • Exception - Palladium ($Pd$): Electronic configuration is $4d^{10} 5s^0$.

  • $(n-1)$ refers to the penultimate shell d orbitals.

• Stability of Filled and Half-filled Orbitals: There is small energy difference between $(n-1)d$ and $ns$ orbitals. Half-filled ($d^5$) and completely filled ($d^{10}$) shells possess extra stability.

• Specific Configurations in the 3d Series ($z=21-30$):

  • Chromium ($Cr$, $Z=24$): Configuration is $3d^5 4s^1$ (instead of $3d^4 4s^2$) to achieve a stable half-filled d-subshell.

  • Copper ($Cu$, $Z=29$): Configuration is $3d^{10} 4s^1$ (instead of $3d^9 4s^2$) to achieve a stable completely filled d-subshell.

• Physical Influence of d Orbitals: The d orbitals protrude to the periphery of the atom more than s and p orbitals, making transition metal ions more susceptible to surroundings and determining properties like complex formation and magnetism.

Physical Properties of Transition Elements

• Metallic Nature: Nearly all display typical metallic properties: high tensile strength, ductility, malleability, high thermal and electrical conductivity, and metallic lustre.

• Lattice Structures:

  • $hcp$, $bcc$, and $ccp$ are the most common.

  • Exceptions: $Zn$, $Cd$, $Hg$, and $Mn$ have more complex or typical metal structures ($X$) at normal temperatures.

• Hardness and Volatility: Transition metals (except Group 12) are very hard and have low volatility.

• Melting and Boiling Points: These are exceptionally high due to strong interatomic metallic bonding involving both $ns$ and $(n-1)d$ electrons.

  • Melting points rise to a maximum at roughly $d^5$ (middle of the series) because one unpaired electron per d orbital is ideal for interatomic interaction.

  • Anomalous low melting points occur for Manganese ($Mn$) and Technetium ($Tc$).

• Enthalpy of Atomisation:

  • Transition metals have high enthalpies of atomisation ($\Delta_a H^∘$). Maxima occur at the middle of each series.

  • Metals of the second (4d) and third (5d) series have higher enthalpies of atomisation than the first (3d) series, which facilitates more frequent metal–metal bonding in heavy transition metal compounds.

Trends in Atomic and Ionic Sizes

• General Trend: In a given series, there is a progressive decrease in radius with increasing atomic number due to increasing nuclear charge while the shielding effect of d electrons is poor.

• Specific Variation: The variation within a series is small because the d electrons shield the outer $ns$ electrons from the nucleus slightly more effectively as the series progresses.

• Lanthanoid Contraction:

  • There is an expected increase in size from 3d to 4d series.

  • However, the radii of the 5d series elements are nearly identical to those of the corresponding 4d series (e.g., $Zr = 160 pm$ and $Hf = 159 pm$).

  • Cause: Filling of the $4f$ orbitals before the $5f$ orbitals. Since $4f$ shielding is even poorer than d shielding, the increasing nuclear charge draws the electrons closer, compensating for the increase in size due to higher shells.

• Density: As radii decrease and atomic mass increases across a period, density increases significantly (e.g., $Ti = 4.1 g cm^{-3}$ to $Cu = 8.9 g cm^{-3}$, while $Sc = 3.43 g cm^{-3}$).

Ionisation Enthalpies

• Trend: There is a general increase in ionisation enthalpy ($\Delta_i H^∘$) across a series due to increasing nuclear charge.

• Successive Enthalpies: Successive enthalpies (first, second, third) do not increase as steeply as in non-transition elements.

• Shielding Influence: In the 3d series, electrons added to the inner 3d orbitals shield the 4s electrons from the nucleus more effectively than outer electrons shield each other, leading to only a slight increase in first ionisation energy.

• The 4s Advantage: When d-block elements form ions, $ns$ electrons are lost before $(n-1)d$ electrons.

• Stability Effects:

  • Second ionisation enthalpies are unusually high for Chromium ($Cr^+$ to $Cr^{2+}$) and Copper ($Cu^+$ to $Cu^{2+}$) as these involve removing an electron from stable $d^5$ and $d^{10}$ configurations.

  • Third ionisation enthalpies are generally high and show breaks at $Mn^{2+}$ ($d^5$) and $Zn^{2+}$ ($d^{10}$), where removing another electron is extremely difficult.

• Exchange Energy: Stability is imparted by exchange energy, which is proportional to the number of possible pairs of parallel spins in degenerate orbitals. The highest exchange energy is associated with half-filled ($d^5$) states.

Oxidation States

• Variable Oxidation States: This is a hallmark of transition elements, caused by the incomplete filling of d orbitals such that oxidation states differ by unity (e.g., $V^{II}, V^{III}, V^{IV}, V^V$).

• Series Middle Peak: Elements in the middle of a series show the highest number of oxidation states. Manganese ($Mn$) exhibits states from $+2$ to $+7$.

• Series Ends:

  • Early elements ($Sc$, $Ti$) have too few electrons to lose/share.

  • Late elements ($Cu$, $Zn$) have too many d electrons (full/nearly full subshells) for high valency.

• Stability of Higher States:

  • For p-block elements, lower oxidation states are favored by heavier members (Inert Pair Effect).

  • For d-block elements, higher oxidation states are more stable in heavier members within a group. For example, in Group 6, $Mo(VI)$ and $W(VI)$ are more stable than $Cr(VI)$.

• Low Oxidation States: Specifically zero ($0$), occur in complexes with $π$-acceptor ligands like carbon monoxide (e.g., $[Ni(CO)_4]$ and $[Fe(CO)_5]$).

Standard Electrode Potentials ($E^∘$)

• M2+/M Couple:

  • General trend: Values become less negative across the series, reflecting an increasing sum of first and second ionisation enthalpies.

  • Copper Exception: $E^∘ = +0.34 V$. Copper is the only transition metal of the first series that does not liberate $H_2$ from acids. This is because high enthalpy of atomisation and high ionisation enthalpy are not balanced by hydration enthalpy.

  • Anomalies: $Mn$, $Ni$, and $Zn$ have more negative values than expected. For $Mn$ and $Zn$, this is due to stable $d^5$ and $d^{10}$ configurations in the ion; for $Ni$, it relates to its very high negative enthalpy of hydration.

• M3+/M2+ Couple:

  • Scandium: Low value reflects the stability of $Sc^{3+}$ (noble gas configuration).

  • Zinc: Highest value because removing an electron from stable $d^{10}$ of $Zn^{2+}$ is extremely difficult.

  • Manganese: High positive value means $Mn^{3+}$ is a strong oxidising agent (prefers stable $Mn^{2+}$ $d^5$).

  • Iron: Relatively low value means $Fe^{3+}$ is stable ($d^5$).

Chemical Reactivity and Stability

• Reactivity: Elements of the first series (except copper) are relatively reactive and oxidised by $1 M H^+$. Titanium and Vanadium are passive at room temperature toward dilute non-oxidising acids.

• Halides:

  • Highest oxidation states are found in fluorides: $VF_5$, $CrF_6$, and $TiX_4$.

  • Fluorine stabilizes high oxidation states due to high lattice energy or high bond enthalpy.

  • Copper ($II$) halides are all known except the iodide, because $Cu^{2+}$ oxidises $I^-$ to $I_2$: $2 Cu^{2+} + 4 I^- → Cu_2 I_2(s) + I_2$.

• Oxides:

  • Stabilized by oxygen's ability to form multiple bonds.

  • Highest oxide is $Mn_2 O_7$, where Mn is tetrahedrally surrounded by oxygen bridge.

  • As oxidation number of the metal increases, ionic character decreases and acidic character increases.

  • Vanadium oxides: $V_2 O_3$ (basic) → $V_2 O_4$ (less basic/amphoteric) → $V_2 O_5$ (amphoteric but primarily acidic).

Magnetic and Colored Properties

• Magnetic Properties:

  • Diamagnetism: Repelled by magnetic fields (all electrons paired).

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

  • Ferromagnetism: Extreme form of paramagnetism found in some solids.

  • Spin-Only Formula: For the first transition series, orbital angular momentum is quenched. Magnetic moment ($μ$) is calculated as: $\mu = √{n(n+2)}$ where $n$ is the number of unpaired electrons. Units are Bohr Magneton ($BM$).

• Formation of Coloured Ions:

  • Occurs due to d-d transitions. Excitation of an electron from a lower energy d orbital to a higher energy d orbital requires light energy in the visible region.

  • The color observed is the complementary color of the light absorbed.

  • $Sc^{3+}$ ($3d^0$), $Ti^{4+}$ ($3d^0$), and $Zn^{2+}$ ($3d^{10}$) are colorless.

  • Examples: $Ti^{3+}$ (purple), $Cu^{2+}$ (blue), $Mn^{2+}$ (pink).

Complex Formation, Catalysis, and Compounds

• Complex Compounds: Factors favoring complex formation include small metal ion size, high ionic charge, and available d orbitals for ligand bonding (e.g., $[Fe(CN)_6]^{3-}$, $[Cu(NH_3)_4]^{2+}$).

• Catalytic Activity: Enabled by multiple oxidation states and ability to form complexes.

  • Processes: Haber Process ($Fe$), Contact Process ($V_2 O_5$), Hydrogenation ($Ni$), Wacker Process ($PdCl_2$).

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

  • Characteristics: Non-stoichiometric, high melting points, extremely hard, retain metallic conductivity, chemically inert.

  • Examples: $TiC$, $Mn_4 N$, $Fe_3 H$.

• Alloy Formation: Transition metals readily form alloys because their metallic radii are often within 15 \text{%} of each other, allowing atoms to substitute easily in the lattice (e.g., Steel, Brass, Bronze).

Potassium Dichromate ($K_2 Cr_2 O_7$)

• Preparation:

  1. Fusion of chromite ore ($FeCr_2 O_4$) with sodium carbonate in air:         $4 FeCr_2 O_4 + 8 Na_2 CO_3 + 7 O_2 → 8 Na_2 CrO_4 + 2 Fe_2 O_3 + 8 CO_2$

  2. Acidification of the yellow sodium chromate solution:         $2 Na_2 CrO_4 + 2 H^+ → Na_2 Cr_2 O_7 + 2 Na^+ + H_2 O$

  3. Treatment with Potassium Chloride to get orange crystals:         $Na_2 Cr_2 O_7 + 2 KCl → K_2 Cr_2 O_7 + 2 NaCl$

• Properties:

  • Chromate ($CrO_4^{2-}$) and Dichromate ($Cr_2 O_7^{2-}$) are interconvertible based on pH. Low pH (acidic) favors dichromate; high pH (basic) favors chromate.

  • Structure: Chromate is tetrahedral. Dichromate is two tetrahedra sharing a corner with a bond angle of $126^∘$.

  • Oxidising Action in Acidic Solution: $Cr_2 O_7^{2-} + 14 H^+ + 6 e^- → 2 Cr^{3+} + 7 H_2 O (E^∘ = 1.33 V)$.

  • It oxidises $I^-$ to $I_2$, $Sn^{2+}$ to $Sn^{4+}$, and $Fe^{2+}$ to $Fe^{3+}$.

Potassium Permanganate ($KMnO_4$)

• Preparation:

  1. Fusion of $MnO_2$ with alkali ($KOH$) and oxidant ($KNO_3$) produces dark green Potassium Manganate ($K_2 MnO_4$).

  2. Disproportionation of manganate in neutral/acidic solution or electrolytic oxidation:         $3 MnO_4^{2-} + 4 H^+ → 2 MnO_4^- + MnO_2 + 2 H_2 O$

• Physical Properties: Dark purple, almost black crystals; isostructural with $KClO_4$. Diamagnetic (weakly temperature-dependent paramagnetic).

• Chemical Reactions (Acidic):

  • Oxidises Iodide: $10 I^- + 2 MnO_4^- + 16 H^+ → 2 Mn^{2+} + 8 H_2 O + 5 I_2$

  • Oxidises Iron(II): $5 Fe^{2+} + MnO_4^- + 8 H^+ → Mn^{2+} + 4 H_2 O + 5 Fe^{3+}$

  • Oxidises Oxalate: $5 C_2 O_4^{2-} + 2 MnO_4^- + 16 H^+ → 2 Mn^{2+} + 8 H_2 O + 10 CO_2$

• Chemical Reactions (Neutral/Alkaline):

  • Oxidises Iodide to Iodate ($IO_3^-$): $2 MnO_4^- + H_2 O + I^- → 2 MnO_2 + 2 OH^- + IO_3^-$

  • Oxidises Thiosulphate ($S_2 O_3^{2-}$) to Sulphate ($SO_4^{2-}$).

Inner Transition Elements - The Lanthanoids

• Electronic Configuration: Most stable state is $(+3)$, with a generic tripositive ion configuration of $4f^n$.

• Lanthanoid Contraction: The steady decrease in atomic and ionic radii from Lanthanum to Lutetium ($La^{3+} = 106 pm$ to $Lu^{3+} = 86 pm$). It is caused by poor shielding of 4f electrons.

• Oxidation States:

  • Predominantly $+3$.

  • $Ce^{IV}$ exists (noble gas configuration) but is a strong oxidant.

  • $Eu^{II}$ and $Yb^{II}$ are strong reductants (prefer stable $+3$ state).

• Physical Characteristics: Silvery white soft metals. Color/paramagnetism in many ions due to f electrons (except $f^0$ and $f^{14}$).

• Mischmetall: An alloy of lanthanoid metal (∼ 95 \text{%}) and iron (∼ 5 \text{%}) used in bullets, shells, and lighter flints.

Inner Transition Elements - The Actinoids

• Radioactivity: All are radioactive; later members have very short half-lives (e.g., Lawrencium has a 3-minute half-life).

• Electronic Configuration: Formally added to $5f$. Electrons in $5f$ can participate in bonding to a greater extent than $4f$ because they are less "buried."

• Ionic Sizes: Show constant decrease across the series (actinoid contraction). The contraction is greater than in lanthanoids due to even poorer shielding by 5f electrons.

• Oxidation States: Exhibit a wide range due to comparable energies of $5f$, $6d$, and $7s$ levels. States range from $+3$ up to $+7$ (specifically in $Pa$, $U$, and $Np$).

• Reactivity: Highly reactive metals. Attacked by $HCl$, but slightly affected by $HNO_3$ due to protective oxide layer formation.

Questions & Discussion

• Q: Why is Scandium a transition element but Zinc is not?

• A: Scandium (Z=21) has an incompletely filled 3d orbital ($3d^1$) in its ground state. Zinc (Z=30) has a completely filled 3d orbital ($3d^{10}$) in its ground state and its common oxidised state.

• Q: Why do heavy transition metals exhibit frequent metal-metal bonding?

• A: Metals of the second (4d) and third (5d) series have higher enthalpies of atomisation than those of the first (3d) series.

• Q: Is Silver (Z=47) a transition element?

• A: Yes, because although it is $4d^{10}$ in the ground state, it exhibits a $+2$ oxidation state where it has an incompletely filled 4d orbital.

• Q: Why is actinoid contraction greater than lanthanoid contraction?

• A: The 5f electrons provide even poorer shielding from the nuclear charge than 4f electrons do.

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

• A: $Cr^{2+}$ becomes $Cr^{3+}$ (stable $d^3$ with half-filled $t_{2g}$ level). $Mn^{3+}$ becomes $Mn^{2+}$ (stable $d^5$ half-filled level).