Comprehensive Study Notes on d- and f-Block Elements

Overview of the d-Block and f-Block Elements

• d-Block Elements: These elements occupy Groups 3 to 12 of the periodic table. They are characterized by the progressive filling of the d orbitals across four long periods. They are commonly referred to as transition metals.
• f-Block Elements: These consist of two series placed at the bottom of the periodic table where the $4f$ and $5f$ orbitals are progressively filled. They are known as inner transition metals.
• Transition Metal Definition: According to IUPAC, transition metals are defined as elements which have an incomplete d subshell either in their neutral atom state or in their common ions.
• Group 12 Elements ($Zn$, $Cd$, $Hg$): These elements have a full $d^{10}$ configuration in both their ground state and common oxidation states. While they are not technically transition metals by definition, their chemistry is studied alongside them as they are the end members of the 3d, 4d, and 5d series.
• 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 ($Cn$).
• Inner Transition Series:
  • 4f series (Lanthanoids): Cerium ($Ce$) to Lutetium ($Lu$).
  • 5f series (Actinoids): Thorium ($Th$) to Lawrencium ($Lr$).

Position and Electronic Configurations of the d-Block

• Position: The d-block occupies the large middle section of the table, flanked by the s-block and p-block.
• General Electronic Configuration: The outer orbitals generally follow the formula $(n-1)d^{1-10} ns^{1-2}$.
• Inner d Orbitals: The $(n-1)$ represents the penultimate energy level.
• Exceptions to the Rule:
  • Palladium ($Pd$): Its electronic configuration is $4d^{10} 5s^0$.
  • Chromium ($Cr$): Has a configuration of $3d^5 4s^1$ instead of $3d^4 4s^2$ because half-filled sets of orbitals ($d^5$) are relatively more stable.
  • Copper ($Cu$): Has a configuration of $3d^{10} 4s^1$ instead of $3d^9 4s^2$ because completely filled sets of orbitals ($d^{10}$) are more stable.
• Energy Levels: The energy difference between $(n-1)d$ and $ns$ orbitals is very small, leading to these configuration variations.

General Physical Properties of Transition Metals

• Metallic Character: Nearly all transition elements display typical metallic properties: high tensile strength, ductility, malleability, high thermal and electrical conductivity, and metallic lustre.
• Lattice Structures:
  • Common structures include BCC (body-centred cubic), HCP (hexagonal close-packed), and CCP (cubic close-packed).
  • Exceptions include $Zn$, $Cd$, $Hg$, and $Mn$, which have unique or non-typical structures at normal temperatures.
• Melting and Boiling Points: They are very hard, have low volatility, and high melting/boiling points.
  • High melting points are due to the involvement of $(n-1)d$ electrons in addition to $ns$ electrons in interatomic metallic bonding.
  • Melting points rise to a maximum at approximately $d^5$ (middle of the series) and then fall regularly.
  • Anomalous low melting points are observed for Manganese ($Mn$) and Technetium ($Tc$).
• Enthalpy of Atomisation: Transition metals have high enthalpies of atomisation ($Δ_a H^∘$). Maxima occur at the middle of each series, indicating that one unpaired electron per d orbital favors strong interatomic interaction.
  • Metals of the 2nd and 3rd series have higher enthalpies of atomisation than those of the 1st series ($3d$), resulting in more frequent metal-metal bonding in heavy transition metal compounds.

Variation in Atomic and Ionic Sizes

• Trends within a Series: There is a progressive decrease in radius with increasing atomic number. This is due to the increasing nuclear charge while the new electron enters a d orbital.
• Shielding Effect: The shielding effect of a d electron is not very effective; hence, the net attraction between the nucleus and the outermost electrons increases, causing contraction.
• Comparison between Series:
  • Sizes increase from the 1st ($3d$) to the 2nd ($4d$) series.
  • Radii of the 3rd ($5d$) series are virtually the same as the 2nd ($4d$) series (e.g., $Zr = 160†pm$, $Hf = 159†pm$).
• Lanthanoid Contraction: This similarity in size is caused by the intervention of the $4f$ orbitals. Filling the $4f$ subshell before the $5d$ results in a regular decrease in atomic radii that compensates for the expected increase due to higher atomic numbers.
• Density: The decrease in metallic radius combined with the increase in atomic mass leads to a general increase in density. Density increases significantly from Titanium ($22$) to Copper ($29$).

Ionisation Enthalpies of Transition Elements

• General Trend: Ionisation enthalpy increases along each series from left to right due to increased nuclear charge.
• Rate of Increase: The successive enthalpies do not increase as steeply as in non-transition elements because $3d$ electrons shield the $4s$ electrons from the increasing nuclear charge.
• First Ionisation Enthalpy ($Δ_i H^∘$): The trend is irregular. When ions form, $ns$ electrons are lost before $(n-1)d$ electrons.
• Second Ionisation Enthalpy: Unusually high values are found for $Cr$ and $Cu$ because their $M^+$ ions have stable $d^5$ and $d^{10}$ configurations.
• Third Ionisation Enthalpy: Very high for Manganese ($Mn^{2+}$ to $Mn^{3+}$, $d^5 \rightarrow d^4$) and Zinc ($Zn^{2+}$ to $Zn^{3+}$, $d^{10} \rightarrow d^9$) due to the removal of an electron from stable configurations.
• Exchange Energy: Stability is often imparted by exchange energy, which is proportional to the number of pairs of parallel spins in degenerate orbitals. This explains why $Fe^{3+}$ ($d^5$) is more stable than $Fe^{2+}$ ($d^6$).

Oxidation States

• Variability: A defining characteristic is the variety of oxidation states, which usually differ by units of one (e.g., $V^{II}$, $V^{III}$, $V^{IV}$, $V^V$). This is due to the participation of both $(n-1)d$ and $ns$ electrons.
• Middle of the Series: Elements near the middle exhibit the most states. Manganese ($Mn$) shows all states from $+2$ to $+7$.
• Extreme Ends: Scandium rarely shows states other than $+3$. Zinc only shows $+2$ because d electrons are not involved.
• Stability Trends:
  • Early in the series, high oxidation states are more stable ($Ti^{IV}$, $V^V$).
  • In later groups, lower states are more common ($Fe^{II,III}$, $Cu^{I,II}$, $Zn^{II}$).
  • In the d-block, heavier members ($Mo$, $W$) favour higher oxidation states (e.g., $W^{VI}$ is more stable than $Cr^{VI}$). This is opposite to the p-block's "inert pair effect."
• Zero Oxidation State: Possible in complexes with $π$-acceptor ligands like $Ni(CO)_4$ and $Fe(CO)_5$.

Standard Electrode Potentials ($E^∘$ )

• $M^{2+}/M$ Couple: Values generally become less negative across the series.
  • Copper ($Cu$) is unique with a positive $E^∘$ of $+0.34†V$, meaning it cannot liberate $H_2$ from acids. The high energy required for sublimation and ionisation is not compensated by its hydration enthalpy.
  • $Mn$, $Ni$, and $Zn$ have more negative values than expected due to stable half-filled ($Mn^{2+}$), fully-filled ($Zn^{2+}$), or high hydration enthalpy ($Ni^{2+}$).
• $M^{3+}/M^{2+}$ Couple:
  • $Sc^{3+}$ is very stable (noble gas configuration).
  • $Mn^{2+}$ is very stable ($d^5$); hence the $E^∘$ for $Mn^{3+}/Mn^{2+}$ is highly positive ($+1.57†V$).
  • $Fe^{3+}$ is stable ($d^5$); hence the $E^∘$ for $Fe^{3+}/Fe^{2+}$ is relatively low ($+0.77†V$).
  • $Cr^{2+}$ is a strong reducing agent ($E^∘ = -0.41†V$) because it changes from $d^4$ to the stable $d^3$ ($t_{2g}^3$) configuration.

Chemical Reactivity and Compounds

• Reactivity: Many transition metals are electropositive enough to dissolve in mineral acids. Titanium and Vanadium are passive to dilute non-oxidising acids at room temperature.
• Oxides: Transition metals form oxides reacting with oxygen at high temperatures.
  • Oxides are generally ionic in low oxidation states (e.g., $MnO$, $CoO$) and covalent/acidic in high states (e.g., $Mn_2O_7$, $CrO_3$).
  • $V_2O_5$ is amphoteric.
  • Oxocations like $VO_2^+$, $VO^{2+}$, and $TiO^{2+}$ are common.
• Halides: Fluorine is best at stabilising high oxidation states (e.g., $CrF_6$, $VF_5$) due to high lattice energy or bond enthalpy.

Magnetic and Coloured Properties

• Magnetic Properties: Observed types are diamagnetism (repelled by field) and paramagnetism (attracted).
  • Paramagnetism arises from unpaired electrons.
  • Spin-only formula: $μ = ∘∘n(n+2)∘∘$ where $n$ is the number of unpaired electrons and $μ$ is magnetic moment in Bohr magnetons (BM).
  • Example: $Mn^{2+}$ ($3d^5$) has $n = 5$, so $μ = −−5(5+2)−−−−−−−−−−−−−− ≈ 5.92†BM$.
• Colour: Ions with partly filled d orbitals ($d^1$ to $d^9$) are typically coloured.
  • Colour results from d-d transitions: excitation of an electron from a lower energy d orbital to a higher one.
  • The absorbed frequency of light aligns with the complementary colour observed.
  • Examples: $Cu^{2+}$ (blue), $Fe^{2+}$ (green), $Fe^{3+}$ (yellow), $Mn^{2+}$ (pink).

Catalytic and Interstitial Properties

• Complex Formation: Transition metals form complexes (e.g., $[Fe(CN)_6]^{3-}$) because of small ion size, high charge, and available d orbitals.
• Catalytic Activity: Attributed to the ability to adopt multiple oxidation states and form complexes.
  • $V_2O_5$ in the Contact Process.
  • $Fe$ in the Haber Process.
  • $Ni$ in hydrogenation.
• Interstitial Compounds: Formed when small atoms ($H$, $C$, $N$) are trapped in metal lattices (e.g., $TiC$, $Mn_4N$).
  • They are non-stoichiometric, very hard, and have higher melting points than pure metals but retain metallic conductivity.
• Alloys: Homogeneous solid solutions formed by metals with radii within $15†$ of each other.
  • Examples: Steel ($Fe/C/Cr/V$), Brass ($Cu/Zn$), Bronze ($Cu/Sn$).

Important Oxoanions: Dichromates and Permanganates

• Potassium Dichromate ($K_2Cr_2O_7$):
  • Preparation: Obtained from chromite ore ($FeCr_2O_4$) by fusion with sodium carbonate in air to form yellow sodium chromate, which is then acidified to form orange sodium dichromate. Finally, it is reacted with $KCl$.
  • Structure: Chromate ion ($CrO_4^{2-}$) is tetrahedral. Dichromate ion ($Cr_2O_7^{2-}$) consists of two tetrahedra sharing one corner ($Cr-O-Cr$ angle is $126^∘$).
  • Oxidising Action: In acidic medium: $Cr_2O_7^{2-} + 14H^+ + 6e^- → 2Cr^{3+} + 7H_2O$ ($E^∘ = 1.33†V$).
• Potassium Permanganate ($KMnO_4$):
  • Preparation: Produced by fusion of pyrolusite ($MnO_2$) with $KOH$ and an oxidant ($KNO_3$) to form green $K_2MnO_4$. This is then acidified or electrolytically oxidised to purple $KMnO_4$.
  • Properties: Dark purple crystals, diamagnetic. It decomposes at $513†K$ into $K_2MnO_4$, $MnO_2$, and $O_2$.
  • Oxidising Action: Strong oxidant in neutral, alkaline, or acidic media. In acidic solution: $MnO_4^- + 8H^+ + 5e^- → Mn^{2+} + 4H_2O$ ($E^∘ = 1.52†V$).

The f-Block Elements: Lanthanoids and Actinoids

• Lanthanoids ($Ce$ to $Lu$):
  • Common Oxidation State: Primarily $+3$.
  • Electronic Configuration: General form is $4f^n 5d^0 6s^2$ or $4f^n 5d^1 6s^2$.
  • Atomic/Ionic Radii: Decrease across the series due to Lanthanoid Contraction (poor shielding by $4f$ electrons).
  • Physical state: Silvery white soft metals. Color is displayed by many trivalent ions ($f-f$ transitions).
  • Uses: Mischmetall ($95†$ lanthanoid, $5†$ iron) used in Mg-alloys for bullets and flints.
• Actinoids ($Th$ to $Lr$):
  • Radioactivity: All are radioactive; later members have very short half-lives.
  • Oxidation States: Exhibit a greater range than lanthanoids ($+3$ to $+7$) because $5f$, $6d$, and $7s$ levels have comparable energies.
  • Contraction: Actinoid Contraction is greater than lanthanoid contraction because $5f$ electrons provide even poorer shielding than $4f$.
  • Reactivity: Highly reactive, especially when finely divided.

Questions & Discussion

• Question: Why is Scandium ($Z=21$) a transition element but Zinc ($Z=30$) is not?
• Answer: Scandium has an incompletely filled $3d^1$ orbital in its ground state. Zinc has a completely filled $3d^{10}$ orbital in both its ground state and common oxidation state ($Zn^{2+}$).
• Question: Why does Copper have a positive $E^∘$ ($+0.34†V$)?
• Answer: The high energy required to transform solid Copper to aqueous $Cu^{2+}$ (atomisation + ionisation) is not compensated by its relatively low hydration enthalpy.
• Question: Why is $Cr^{2+}$ reducing and $Mn^{3+}$ oxidising despite both being $d^4$?
• Answer: $Cr^{2+}$ loses an electron to reach the stable $d^3$ ($t_{2g}^3$) level. $Mn^{3+}$ gains an electron to reach the stable half-filled $d^5$ configuration.
• Question: What is Mischmetall?
• Answer: An alloy consisting of approximately $95†$ lanthanoid metals and $5†$ iron, with traces of $S$, $C$, $Ca$, and $Al$.
• Question: Why are $Zr$ and $Hf$ similar in size?
• Answer: Due to Lanthanoid Contraction, which results in the radii of the third transition series ($5d$) being almost identical to the second series ($4d$).