Exhaustive Study Guide on The d- and f-Block Elements

Definition and Scope of d-Block and f-Block Elements

• The d-block of the periodic table encompasses elements from groups $3$ to $12$. These elements are characterized by the progressive filling of d orbitals across four long periods.
• The f-block consists of elements where the $4f$ and $5f$ orbitals are progressively filled. These occupy a separate panel at the base of the periodic table.
• Terminology:
  • Transition metals: Generally refers to d-block elements.
  • Inner transition metals: Refers to f-block elements.

Classification into Series

• Transition Metals (d-block):
  • $3d$ 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 Metals (f-block):
  • $4f$ series ($Ce$ to $Lu$): Known as Lanthanoids.
  • $5f$ series ($Th$ to $Lr$): Known as Actinoids.

IUPAC Definition and Group 12 Elements

• Original name origin: Transition metals were named because their properties were transitional between s-block and p-block elements.
• IUPAC Definition: Transition metals are defined as metals having an incomplete d subshell either in the neutral atom or in their ions.
• Exclusion of Group 12 ($Zn, Cd, Hg, Cn$):
  • These have a full $d^{10}$ configuration in their ground state and common oxidation states.
  • Technically they are not transition metals, but their chemistry is studied alongside them as end-members of the series.

Electronic Configurations of d-Block Elements

• General electronic configuration: $(n-1)d^{1-10} ns^{1-2}$.
• The inner $(n-1)d$ orbitals can have $1$ to $10$ electrons, and the outermost $ns$ orbital can have $1$ or $2$ electrons.
• Exception: Palladium ($Pd$) has a configuration of $4d^{10} 5s^0$.
• Stability factors: Half-filled and completely filled sets of orbitals are relatively more stable.
  • Chromium ($Cr$): Configuration is $3d^5 4s^1$ instead of $3d^4 4s^2$.
  • Copper ($Cu$): Configuration is $3d^{10} 4s^1$ instead of $3d^9 4s^2$.
• Position: The d-block occupies the large middle section of the periodic table, flanked by s- and p-blocks.

Physical Properties of Transition Metals

• General Characteristics: High tensile strength, ductility, malleability, high thermal and electrical conductivity, and metallic lustre.
• Structures: Transition metals (except $Zn, Cd, Hg, Mn$) exhibit typical metallic structures like BCC (body-centred cubic), HCP (hexagonal close packed), and CCP (cubic close packed).
• Melting and Boiling Points: High values due to the involvement of $(n-1)d$ electrons in addition to $ns$ electrons in interatomic metallic bonding.
  • Trend: Rise to a maximum at $d^5$ (except for anomalous lows in $Mn$ and $Tc$) and kemudian fall regularly with increasing atomic number.
  • Volatility: Low volatility; silver, gold, and platinum are precious, while iron, copper, and titanium are industrially vital.

Variation in Atomic and Ionic Sizes

• Horizontal Trend: Progression across a series shows a regular decrease in atomic and ionic radii. This is due to the increase in nuclear charge; since d electrons shield poorly, total attraction on outer electrons increases.
• Vertical Trend: Size increases from the first ($3d$) series to the second ($4d$) series.
• Lanthanoid Contraction: Radii of the third ($5d$) series are virtually identical to the second ($4d$) series.
  • Example: $Zr = 160\,pm$ and $Hf = 159\,pm$.
  • Cause: Filling of $4f$ orbitals before $5d$; the imperfect shielding of $4f$ electrons results in a contraction that compensates for expected size increase.
• Density: General increase from left to right due to decreased metallic radius and increased atomic mass. Titanium ($Z=22$) to Copper ($Z=29$) shows significant density increases.

Enthalpies of Atomization

• Transition metals exhibit high enthalpies of atomization ($\Delta_{a}H^{\ominus}$).
• Trend: Maxima occur at the middle of each series, indicating that one unpaired electron per d orbital is ideal for strong interatomic interaction.
• Heavier elements: Metals of the $4d$ and $5d$ series have higher enthalpies of atomization than the $3d$ series, leading to more frequent metal-metal bonding.

Ionization Enthalpies

• General Trend: Increase in ionization enthalpy ($\Delta_{i}H^{\ominus}$) along each series due to increased nuclear charge.
• Successive Values: Magnitude of increase in second and third ionization enthalpies is higher than the first. In d-block elements, $ns$ electrons are lost before $(n-1)d$ electrons.
• Irregularities: Caused by electronic stability factors like d-subshell configuration.
  • $Cr^+$ to $Cr^{2+}$ and $Cu^+$ to $Cu^{2+}$ require high second ionization energy as they break stable $d^5$ and $d^{10}$ configurations.
  • $Mn^{2+}$ ($d^5$) and $Zn^{2+}$ ($d^{10}$) have unusually high third ionization enthalpies.

Oxidation States of Transition Metals

• Variety: Transition elements show a great variety of oxidation states differing by units of one (e.g., $V^{II}, V^{III}, V^{IV}, V^{V}$).
• Maximum Stability:
  • Early series: Scandium ($Sc$) exhibits only $+3$. Titanium ($IV$) is more stable than $+3$ or $+2$.
  • Middle series: Manganese exhibits all states from $+2$ to $+7$.
  • Late series: Elements show fewer states. Zinc is exclusively $+2$.
• Group Differences: Unlike p-block (where lower states are stable in heavier atoms), d-block heavier elements favor higher states. Example: $Mo(VI)$ and $W(VI)$ are more stable than $Cr(VI)$.
• Low states: Occur in complexes with $\pi$-acceptor ligands like CO (e.g., $Ni(CO)_4$ and $Fe(CO)_5$, where oxidation state is zero).

Standard Electrode Potentials ($E^{\ominus}$)

• $M^{2+}/M$ Couple: Generally negative across the series, except for copper ($E^{\ominus} = +0.34\,V$).
  • Copper's positive value indicates it cannot liberate $H_2$ from non-oxidizing acids.
  • Irregularities in $Mn, Ni$, and $Zn$ values are linked to stable configurations ($d^5, d^{10}$) or high hydration enthalpy ($Ni$).
• $M^{3+}/M^{2+}$ Couple:
  • Stability of $Sc^{3+}$ (noble gas configuration).
  • $Mn^{3+}$ and $Co^{3+}$ are strong oxidizing agents.
  • $Ti^{2+}, V^{2+}, Cr^{2+}$ are strong reducing agents.
• Stability of $Cu^{2+}_{(aq)}$ vs $Cu^+_{(aq)}$: Even though second IE is high, $Cu^{2+}$ is more stable in water because of its very negative hydration enthalpy ($\Delta_{hyd}H^{\ominus}$).

Formation of Oxides and Halides

• High Oxidation States: Stabilized by fluorine and oxygen due to high electronegativity and small size.
• Halides: Highest states in $TiX_4, VF_5, CrF_6$. Manganese exhibits $+7$ in $MnO_3F$.
• Oxides: Highest state coincides with group number ($Sc_2O_3$ to $Mn_2O_7$).
  • Oxygen can form multiple bonds, allowing higher stabilization (e.g., $Mn_2O_7$ vs $MnF_4$).
  • Acidity: Higher oxides are more acidic ($Mn_2O_7$ gives $HMnO_4$, $CrO_3$ gives $H_2CrO_4$).

Magnetic and Optical Properties

• Magnetism: Most transition metal ions are paramagnetic due to unpaired electrons.
  • Spin-only formula: $\mu = \sqrt{n(n+2)}$, where $n$ is the number of unpaired electrons and $\mu$ is in Bohr magnetons (BM).
  • $n=1 \rightarrow 1.73\,BM$, $n=5 \rightarrow 5.92\,BM$.
• Color: Arises from excitation of electrons from lower energy d orbitals to higher energy d orbitals (d-d transitions). The complementary color of the absorbed frequency is observed.
  • $Sc^{3+}$ ($3d^0$) and $Zn^{2+}$ ($3d^{10}$) are colourless.
  • $Cu^{2+}$ is blue, $Fe^{3+}$ is yellow, $Mn^{2+}$ is pink.

Characteristics: Complexes, Catalysis, Interstitial Compounds

• Complex Formation: Form many complexes because of small ion size, high charge, and available d orbitals.
• Catalytic Activity: Due to multiple oxidation states and ability to form complexes. Examples:
  • $V_2O_5$ in Contact Process.
  • $Fe$ in Haber’s Process.
  • $Ni$ in Hydrogenation.
• Interstitial Compounds: Small atoms ($H, C, N$) trapped in metal lattices. Characteristics: High melting points, extremely hard, metallic conductivity, chemically inert (e.g., $TiC, Mn_4N$).
• Alloy Formation: Formed easily due to similar metallic radii (within $15\%$). Examples: Brass ($Cu/Zn$), Bronze ($Cu/Sn$), and Steels (alloyed with $Cr, V, W, Mo, Mn$).

Potassium Dichromate ($K_2Cr_2O_7$)

• Preparation: From chromite ore ($FeCr_2O_4$).
  • $4 FeCr_2O_4 + 8 Na_2CO_3 + 7 O_2 \rightarrow 8 Na_2CrO_4 + 2 Fe_2O_3 + 8 CO_2$.
  • $2 Na_2CrO_4 + 2 H^+ \rightarrow Na_2Cr_2O_7 + 2 Na^+ + H_2O$.
  • $Na_2Cr_2O_7 + 2 KCl \rightarrow K_2Cr_2O_7 + 2 NaCl$.
• Properties: Chromate ($CrO_4^{2-}$) and dichromate ($Cr_2O_7^{2-}$) are interconvertible depending on pH.
  • Acidic medium: $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O$ ($E^{\ominus} = 1.33\,V$).
  • Standard for volumetric analysis; oxidizes $I^-$ to $I_2, Fe^{2+}$ to $Fe^{3+}, Sn^{2+}$ to $Sn^{IV}$.

Potassium Permanganate ($KMnO_4$)

• Preparation: From pyrolusite ($MnO_2$).
  • Fusion: $2 MnO_2 + 4 KOH + O_2 \rightarrow 2 K_2MnO_4 + 2 H_2O$.
  • Disproportionation or Electrolytic oxidation transforms green manganate ($MnO_4^{2-}$) to purple permanganate ($MnO_4^-$).
• Properties: Intense purple color, diamagnetic (weakly paramagnetic at temp). Structure is tetrahedral.
• Oxidizing Actions (Acidic):
  • $MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$.
  • Oxidizes Oxalate ($C_2O_4^{2-}$) to $CO_2$, Nitrite ($NO_2^-$) to Nitrate ($NO_3^-$), and Iodide ($I^-$) to $I_2$.
• Neutral/Alkaline Medium: Oxidizes $I^-$ to $IO_3^-$ (iodate) and Thiosulphate ($S_2O_3^{2-}$) to Sulphate.

The Lanthanoids ($4f$ Series)

• General: Fourteen elements ($Ce$ to $Lu$) following Lanthanum ($La$).
• Electronic Configuration: Common $6s^2$ with variable $4f$ occupancy. Tripositive ions ($Ln^{3+}$) have $4f^n$ configuration ($n=1$ to $14$).
• Oxidation States: Principal state is $+3$. $Ce^{IV}$ is a strong oxidant (favored by $f^0$); $Eu^{II}$ and $Yb^{II}$ are reductants.
• Lanthanoid Contraction: Gradual decrease in atomic and ionic radii with increasing atomic number. Results in similarity between $4d$ and $5d$ series (e.g., $Zr/Hf$).
• Physical: Silvery white soft metals. Hardness increases with $Z$. $Sm$ is steel hard and melts at $1623\,K$.
• Uses: Production of alloy steels; Mischmetall ($95\%$ lanthanoid, $5\%$ iron) used for bullets and flints.

The Actinoids ($5f$ Series)

• General: Fourteen elements ($Th$ to $Lr$) following Actinium ($Ac$). All are radioactive.
• Electronic Configuration: Variable occupancy of $5f$ and $6d$ subshells. $5f$ electrons participate more in bonding than $4f$ because they are less "buried."
• Oxidation States: Greater range due to comparable energies of $5f, 6d$, and $7s$. Common is $+3$, but early members show up to $+7$ ($Np, Pu$).
• Contraction: Actinoid contraction is greater than lanthanoid contraction due to poorer shielding by $5f$ electrons.
• Chemical Reactivity: Highly reactive metals; form oxide/hydride with boiling water. Hydrochloric acid attacks them; nitric acid makes them passive (oxide layer).

Specific Examples and Questions from Transcript

• Scandium vs Zinc: Scandium ($Z=21$) is transition because ground state is $3d^1$. Zinc ($Z=30$) is not because $3d^{10}$ is full in ground and ion states.
• Silver ($Z=47$): Transition element because it can form $Ag^{2+}$ with incompletely filled $4d^9$ orbitals.
• Stable configurations: $d^0, d^5, d^{10}$ provide extra stability in ionization and redox potentials.
• Colorless Ions: $Sc^{3+}, Ti^{4+}, Zn^{2+}$ (either $d^0$ or $d^{10}$).
• Disproportionation: Example of $MnO_4^{2-}$ in acid and $Cu^+$ in water.
• Catalysts: Ziegler catalyst ($TiCl_4 + Al(CH_3)_3$), PdCl2 in Wacker process for ethyne to ethanal.