d and f Block Elements

The d-block elements are those in which the differentiating valence electrons progressively enter the penultimate $(n-1)d$ subshell. They occupy Groups 3 through 12 across Periods 4, 5, 6, and 7 of the periodic table.
IUPAC Definition of Transition Elements: A transition element is defined as an element that has an incompletely filled (partially filled) $d$-subshell in its atomic ground state or in any of its common chemically stable oxidation states.
General Valence Shell Electronic Configuration:
$$\mathbf{(n-1)d^{1-10} \, ns^{1-2}}$$ (Where $n = 4, 5, 6, 7$ corresponds to the principal quantum number of the outermost valence shell).

The Group 12 elements—Zinc ($ ext{Zn}$), Cadmium ($ ext{Cd}$), and Mercury ($ ext{Hg}$)—possess a completely filled $(n-1)d^{10}$ electronic configuration both in their ground state ($[\text{noble gas}](n-1)d^{10}ns^2$) and in their standard divalent oxidation state ($M^{2+} = [\text{noble gas}](n-1)d^{10}$). Because their $d$-subshell remains completely filled under all normal conditions:

• They do not participate in $d\text{-}d$ electronic transitions and therefore form colorless compounds and diamagnetic species.
• They exhibit only a single fixed oxidation state of $+2$ (except $\text{Hg}_2^{2+}$ with mercurous ion).
• Because no unpaired $d$-electrons participate in metallic bonding, their metallic bonding is weak, resulting in low enthalpies of atomization, low melting points, and soft mechanical character (mercury is liquid at room temperature).
• Consequently, they are classified as d-block elements but NOT typical transition elements.

Across the first transition series ($3d$) from Scandium ($ ext{Sc}$) to Zinc ($ ext{Zn}$), atomic and ionic radii exhibit a unique three-stage profile:

• Initial Decrease ($ ext{Sc} o ext{Cr}$): As nuclear charge $Z$ increases by one unit per element, the added $3d$ electron provides only imperfect shielding to the outer $4s$ electrons. Hence, the effective nuclear charge ($Z_{ ext{eff}}$) increases and pulls the valence cloud inward, contracting the atomic radius.
• Mid-Series Plateau ($ ext{Mn} o ext{Ni}$): As the number of $3d$ electrons accumulates, the increasing screening/shielding effect of the $(n-1)d$ electrons progressively counterbalances the rising nuclear charge. The two opposing forces virtually balance, keeping radii nearly constant ($pprox 125 ext{ pm}$).
• Slight Expansion at the Terminus ($ ext{Cu} o ext{Zn}$): In $ ext{Cu}$ ($3d^{10}4s^1$) and $ ext{Zn}$ ($3d^{10}4s^2$), inter-electronic repulsions among the ten paired $3d$ electrons overcome the nuclear pull, causing a slight expansion in radius.

Unlike s-block elements which exhibit fixed oxidation states, transition metals display multiple variable oxidation states. This variability arises because the energy difference between the penultimate $(n-1)d$ subshell and the outermost $ns$ subshell is extremely small, enabling electrons from both subshells to participate in bond formation.

• Minimum Oxidation State: Generally $+2$, corresponding to the loss of the two outer $4s$ electrons (except $ ext{Sc}$ which displays exclusively $+3$, and $ ext{Cu}$ which exhibits $+1$ and $+2$).
• Maximum Oxidation State: Increases progressively from $ ext{Sc}$ ($+3$) to Manganese ($ ext{Mn}$), which reaches a maximum of $\mathbf{+7}$ in $ ext{KMnO}_4$ by involving all five $3d$ and two $4s$ electrons ($3d^5 4s^2$).
• Post-Manganese Decrease: After $ ext{Mn}$, electron pairing in the $3d$ subshell reduces the count of available unpaired electrons, decreasing the highest oxidation state ($ ext{Fe}$: $+6$, $ ext{Co}$: $+5$, $ ext{Ni}$: $+4$, $ ext{Cu}$: $+2$, $ ext{Zn}$: $+2$).
• Stabilization of High Oxidation States: Transition metals attain their highest oxidation states exclusively when bonded to the most electronegative elements, Fluorine and Oxygen (e.g., $ ext{CrO}_4^{2-}$, $ ext{Cr}_2 ext{O}_7^{2-}$, $ ext{MnO}_4^-$, $ ext{VF}_5$), because oxygen can form multiple $p\pi ext{-}d\pi$ bonds and fluorine exhibits high electronegativity.

The standard electrode potential $E^\circ(M^{2+}/M)$ represents the thermodynamic measure of the overall process $M(s) ightarrow M^{2+}(aq) + 2e^-$, which is governed by three sequential thermodynamic enthalpy parameters (Born-Haber cycle):
$$\Delta H_{ ext{total}} = \Delta_{ ext{sub}}H^\circ + \Delta_i H_1^\circ + \Delta_i H_2^\circ + \Delta_{ ext{hyd}}H^\circ$$

• Why $E^\circ( ext{Cu}^{2+}/ ext{Cu})$ is Positive ($+0.34 ext{ V}$): Copper is the only $3d$ metal with a positive $E^\circ(M^{2+}/M)$ value. The exceptionally high enthalpy of atomization ($\Delta_{ ext{sub}}H^\circ = +339 ext{ kJ mol}^{-1}$) combined with high first and second ionization enthalpies is not compensated by the hydration enthalpy of the small $ ext{Cu}^{2+}$ ion ($\Delta_{ ext{hyd}}H^\circ = -2121 ext{ kJ mol}^{-1}$). Hence, copper cannot liberate hydrogen gas from dilute non-oxidizing acids.
• Why $E^\circ( ext{Mn}^{3+}/ ext{Mn}^{2+})$ is Highly Positive ($+1.57 ext{ V}$): $ ext{Mn}^{2+}$ has a half-filled, extra-stable $3d^5$ configuration, whereas $ ext{Mn}^{3+}$ is $3d^4$. Removing an electron from $3d^5$ requires enormous ionization enthalpy ($\Delta_i H_3^\circ$). Consequently, $ ext{Mn}^{3+}$ acts as a powerful oxidizing agent, readily gaining an electron to form stable $ ext{Mn}^{2+}$.
• Why $ ext{Cr}^{2+}$ is Reducing while $ ext{Mn}^{3+}$ is Oxidizing ($d^4$ Congeners): In aqueous solution, $ ext{Cr}^{2+}$ ($d^4$) readily oxidizes to $ ext{Cr}^{3+}$ ($d^3$), because the $d^3$ configuration corresponds to a half-filled, extra-stable $t_{2g}^3$ subshell in octahedral crystal fields ($E^\circ( ext{Cr}^{3+}/ ext{Cr}^{2+}) = -0.41 ext{ V}$). Conversely, $ ext{Mn}^{3+}$ ($d^4$) reduces to $3d^5$ ($ ext{Mn}^{2+}$).

Substances are classified according to their behavior in an external magnetic field:

• Paramagnetism: Exhibited by species possessing one or more unpaired electrons; weakly attracted into magnetic fields.
• Diamagnetism: Exhibited when all electrons are paired; weakly repelled by magnetic fields.
• Ferromagnetism: Spontaneous parallel domain alignment producing permanent macroscopic magnetization ($ ext{Fe}, ext{Co}, ext{Ni}$).

Key Values: $n=1 \implies \mu = 1.73 ext{ BM}$; $n=2 \implies \mu = 2.83 ext{ BM}$; $n=3 \implies \mu = 3.87 ext{ BM}$; $n=4 \implies \mu = 4.90 ext{ BM}$; $n=5 \implies \mu = 5.92 ext{ BM}$.

The vibrant colors exhibited by transition metal compounds originate through two fundamentally distinct physical mechanisms:

• 1. $d\text{-}d$ Electronic Transitions (Crystal Field Splitting): In an isolated gaseous transition metal ion, all five $d$-orbitals are degenerate. When surrounding ligands approach (e.g., water molecules in hydrated ions), electrostatic field splitting breaks this degeneracy. In an octahedral field, orbitals split into lower energy $t_{2g}$ ($d_{xy}, d_{yz}, d_{zx}$) and higher energy $e_g$ ($d_{x^2-y^2}, d_{z^2}$) sets separated by crystal field splitting energy $\Delta_o$. Absorption of photons in the visible spectrum promotes an electron from $t_{2g}$ to $e_g$, transmitting the complementary color.
  Examples: $[ ext{Cu}( ext{H}_2 ext{O})_6]^{2+}$ is blue, $[ ext{Ti}( ext{H}_2 ext{O})_6]^{3+}$ ($d^1$) is violet, $[ ext{Fe}( ext{H}_2 ext{O})_6]^{2+}$ ($d^6$) is pale green.
  Colorless Ions: Ions with $d^0$ ($ ext{Sc}^{3+}, ext{Ti}^{4+}$) or $d^{10}$ ($ ext{Zn}^{2+}, ext{Cu}^+, ext{Cd}^{2+}$) configurations cannot undergo $d\text{-}d$ transitions and are completely colorless.
• 2. Ligand-to-Metal Charge Transfer (LMCT - High-Yield Trap): Compounds such as $ ext{KMnO}_4$ (deep purple) and $ ext{K}_2 ext{Cr}_2 ext{O}_7$ (intense orange) contain transition metals in their highest oxidation states: $ ext{Mn}^{7+}$ ($3d^0$) and $ ext{Cr}^{6+}$ ($3d^0$). Because they possess ZERO $d$-electrons, $d\text{-}d$ transitions are physically impossible! Their intense color arises from Charge Transfer Spectra: momentary electron excitation from the filled $2p$ orbitals of oxo-ligands ($ ext{O}^{2-}$) into the vacant $3d$ orbitals of the central metal ion ($ ext{Mn}^{7+}$ or $ ext{Cr}^{6+}$).

• Catalytic Proficiency: Transition metals and their oxides act as catalysts due to: (i) ability to adopt multiple oxidation states to form reactive intermediates, (ii) vacant $d$-orbitals providing active coordination sites on surfaces, and (iii) adsorption capacity that increases reactant local concentration and weakens substrate bonds. Examples: Finely divided $ ext{Fe}$ in Haber process, $ ext{V}_2 ext{O}_5$ in Contact process, finely divided $ ext{Ni}$ in vegetable oil hydrogenation.
• Interstitial Compounds: Formed when tiny non-metallic atoms ($ ext{H}, ext{C}, ext{N}, ext{B}$) become trapped inside interstitial lattice voids of transition metals. Characteristics: Very high melting points (higher than pure metals), extreme hardness (titanium carbide $ ext{TiC}$ approaches diamond hardness), chemically inert, yet retain metallic electrical and thermal conductivity.
• Alloy Formation: Transition metals form extensive alloys because their atomic radii are very similar (differ by $< 15\%$, conforming to the Hume-Rothery rule). In the molten state, atoms of one metal readily substitute into the crystal lattice of another (e.g., Brass $[ ext{Cu-Zn}]$, Bronze $[ ext{Cu-Sn}]$, Stainless Steel $[ ext{Fe-Cr-Ni}]$).

Potassium dichromate is industrially manufactured from Chromite Ore ($ ext{FeCr}_2 ext{O}_4$ or $ ext{FeO} \cdot ext{Cr}_2 ext{O}_3$) in three sequential stages:

• Stage 1: Alkaline Oxidative Roasting: Finely powdered chromite ore is fused with sodium carbonate ($ ext{Na}_2 ext{CO}_3$) and quicklime ($ ext{CaO}$) in a reverberatory furnace in excess air:
  $$4 ext{FeCr}_2 ext{O}_4 + 8 ext{Na}_2 ext{CO}_3 + 7 ext{O}_2 \longrightarrow 8 ext{Na}_2 ext{CrO}_4 ( ext{yellow sol.}) + 2 ext{Fe}_2 ext{O}_3(s) + 8 ext{CO}_2(g)$$
• Stage 2: Acidification of Sodium Chromate: The filtered yellow solution of $ ext{Na}_2 ext{CrO}_4$ is acidified with concentrated sulfuric acid to yield orange sodium dichromate:
  $$2 ext{Na}_2 ext{CrO}_4 + ext{H}_2 ext{SO}_4 \longrightarrow ext{Na}_2 ext{Cr}_2 ext{O}_7 ( ext{orange sol.}) + ext{Na}_2 ext{SO}_4(s) + ext{H}_2 ext{O}$$
• Stage 3: Metathesis with Potassium Chloride: Because $ ext{Na}_2 ext{Cr}_2 ext{O}_7$ is highly deliquescent, it is treated with $ ext{KCl}$ to crystallize less soluble orange potassium dichromate:
  $$ ext{Na}_2 ext{Cr}_2 ext{O}_7 + 2 ext{KCl} \longrightarrow ext{K}_2 ext{Cr}_2 ext{O}_7(s) + 2 ext{NaCl}$$

Chromate-Dichromate pH Equilibrium:
In aqueous solution, chromate ($ ext{CrO}_4^{2-}$, yellow) and dichromate ($ ext{Cr}_2 ext{O}_7^{2-}$, orange) exist in dynamic equilibrium governed strictly by solution pH:
$$2 ext{CrO}_4^{2-} ( ext{yellow}) + 2 ext{H}^+ ightleftharpoons ext{Cr}_2 ext{O}_7^{2-} ( ext{orange}) + ext{H}_2 ext{O}$$ *Adding acid ($ ext{pH} < 7$)* shifts equilibrium to the right (orange dichromate). *Adding alkali ($ ext{pH} > 7$)* removes $ ext{H}^+$ ions, shifting equilibrium left (yellow chromate). Note that the oxidation state of chromium remains $\mathbf{+6}$ in both ions.
Structure: $ ext{CrO}_4^{2-}$ is tetrahedral. $ ext{Cr}_2 ext{O}_7^{2-}$ consists of two tetrahedra sharing one oxygen corner with a $ ext{Cr-O-Cr}$ bridge angle of $126^\circ$ and bridge bond length of $179 ext{ pm}$ (terminal $ ext{Cr-O} = 163 ext{ pm}$).
Oxidizing Action in Acid Medium ($E^\circ = +1.33 ext{ V}$):
$$ ext{Cr}_2 ext{O}_7^{2-} + 14 ext{H}^+ + 6e^- \longrightarrow 2 ext{Cr}^{3+} ( ext{green}) + 7 ext{H}_2 ext{O}$$ * Oxidizes $ ext{Fe}^{2+} o ext{Fe}^{3+}$: $ ext{Cr}_2 ext{O}_7^{2-} + 14 ext{H}^+ + 6 ext{Fe}^{2+} ightarrow 2 ext{Cr}^{3+} + 6 ext{Fe}^{3+} + 7 ext{H}_2 ext{O}$
* Oxidizes $ ext{I}^- o ext{I}_2$: $ ext{Cr}_2 ext{O}_7^{2-} + 14 ext{H}^+ + 6 ext{I}^- ightarrow 2 ext{Cr}^{3+} + 3 ext{I}_2 + 7 ext{H}_2 ext{O}$
* Oxidizes $ ext{H}_2 ext{S} o ext{S}$: $ ext{Cr}_2 ext{O}_7^{2-} + 8 ext{H}^+ + 3 ext{H}_2 ext{S} ightarrow 2 ext{Cr}^{3+} + 3 ext{S}(s) + 7 ext{H}_2 ext{O}$

Potassium permanganate is prepared from the mineral Pyrolusite ($ ext{MnO}_2$):

• Step 1: Oxidative Alkaline Fusion: Pyrolusite ore is fused with $ ext{KOH}$ in the presence of air or $ ext{KNO}_3$ to yield dark green potassium manganate:
  $$2 ext{MnO}_2 + 4 ext{KOH} + ext{O}_2 \longrightarrow 2 ext{K}_2 ext{MnO}_4 ( ext{dark green}) + 2 ext{H}_2 ext{O}$$
• Step 2: Electrolytic Oxidation / Disproportionation: In commercial production, alkaline manganate is electrolytically oxidized at an iron anode. In laboratory, it is treated with dilute acid or carbon dioxide, disproportionating into purple permanganate:
  $$3 ext{MnO}_4^{2-} ( ext{green}) + 4 ext{H}^+ \longrightarrow 2 ext{MnO}_4^- ( ext{purple}) + ext{MnO}_2(s) + 2 ext{H}_2 ext{O}$$

Structures: Both manganate ($ ext{MnO}_4^{2-}$) and permanganate ($ ext{MnO}_4^-$) have tetrahedral geometry ($d^3s$ hybridization). Manganate is green and paramagnetic (one unpaired electron, $3d^1$). Permanganate is deep purple and diamagnetic (zero unpaired electrons, $3d^0$).
Oxidizing Actions Across Media:
1. Acidic Medium ($ ext{H}_2 ext{SO}_4$, $E^\circ = +1.52 ext{ V}$): $ ext{MnO}_4^- + 8 ext{H}^+ + 5e^- ightarrow ext{Mn}^{2+} + 4 ext{H}_2 ext{O}$
* Oxalate to carbon dioxide: $2 ext{MnO}_4^- + 16 ext{H}^+ + 5 ext{C}_2 ext{O}_4^{2-} ightarrow 2 ext{Mn}^{2+} + 10 ext{CO}_2 + 8 ext{H}_2 ext{O}$
* Ferrous to ferric: $ ext{MnO}_4^- + 8 ext{H}^+ + 5 ext{Fe}^{2+} ightarrow ext{Mn}^{2+} + 5 ext{Fe}^{3+} + 4 ext{H}_2 ext{O}$
* Iodide to iodine: $2 ext{MnO}_4^- + 16 ext{H}^+ + 10 ext{I}^- ightarrow 2 ext{Mn}^{2+} + 5 ext{I}_2 + 8 ext{H}_2 ext{O}$
2. Neutral or Faintly Alkaline Medium ($E^\circ = +1.23 ext{ V}$): $ ext{MnO}_4^- + 2 ext{H}_2 ext{O} + 3e^- ightarrow ext{MnO}_2(s) + 4 ext{OH}^-$
* Iodide to iodate: $2 ext{MnO}_4^- + ext{H}_2 ext{O} + ext{I}^- ightarrow 2 ext{MnO}_2 + 2 ext{OH}^- + ext{IO}_3^-$
* Thiosulfate to sulfate: $8 ext{MnO}_4^- + 3 ext{S}_2 ext{O}_3^{2-} + ext{H}_2 ext{O} ightarrow 8 ext{MnO}_2 + 6 ext{SO}_4^{2-} + 2 ext{OH}^-$

The Lanthanoids comprise the series of fourteen elements following Lanthanum ($ ext{La}$, $Z=57$), spanning Cerium ($ ext{Ce}$, $Z=58$) to Lutetium ($ ext{Lu}$, $Z=71$). The valence electrons enter the deep antipenultimate $4f$ subshell.
General Valence Electronic Configuration:
$$\mathbf{[\text{Xe}] \, 4f^{1-14} \, 5d^{0-1} \, 6s^2}$$ Oxidation States: The predominant and most stable oxidation state across all lanthanoids is $\mathbf{+3}$. Certain elements display $+2$ or $+4$ oxidation states to achieve extra-stable empty ($4f^0$), half-filled ($4f^7$), or completely filled ($4f^{14}$) subshells:

• Cerium ($ ext{Ce}^{4+}$): Adopts $[\text{Xe}]4f^0$ noble gas configuration; behaves as a powerful analytical oxidizing agent, readily reduced to $ ext{Ce}^{3+}$ ($E^\circ = +1.74 ext{ V}$).
• Europium ($ ext{Eu}^{2+}$): Adopts $[\text{Xe}]4f^7$ half-filled configuration; behaves as a strong reducing agent, readily oxidized to $ ext{Eu}^{3+}$.
• Terbium ($ ext{Tb}^{4+}$): Attains $[\text{Xe}]4f^7$ half-filled configuration.
• Ytterbium ($ ext{Yb}^{2+}$): Attains $[\text{Xe}]4f^{14}$ completely filled configuration.

Definition: The steady, gradual decrease in atomic and ionic radii ($ ext{Ln}^{3+}$) with increasing atomic number across the lanthanoid series from $ ext{La}^{3+}$ ($103 ext{ pm}$) to $ ext{Lu}^{3+}$ ($86 ext{ pm}$) is called the Lanthanoid Contraction.
Underlying Physical Cause: As atomic number increases across the series, each added electron enters the inner $4f$ subshell while nuclear charge increments by $+1$. Due to their diffuse spatial geometry and poor radial distribution, $4f$ orbitals have an extremely imperfect and poor shielding effect on one another. The shielding power hierarchy is: $$s > p > d > f$$ Consequently, the progressive increase in nuclear charge is not sufficiently shielded by the $4f$ electrons. The effective nuclear charge ($Z_{ ext{eff}}$) experienced by outer $5d$ and $6s$ electrons increases steadily, pulling the entire electron cloud closer to the nucleus.

The Actinoids comprise fourteen elements from Thorium ($ ext{Th}$, $Z=90$) to Lawrencium ($ ext{Lr}$, $Z=103$) following Actinium ($ ext{Ac}$, $Z=89$). The differentiating electrons enter the $5f$ subshell.
General Valence Electronic Configuration:
$$\mathbf{[\text{Rn}] \, 5f^{1-14} \, 6d^{0-1} \, 7s^2}$$ Wider Range of Oxidation States: Unlike lanthanoids where $+3$ dominates almost exclusively, actinoids display a wider range of oxidation states ($+3, +4, +5, +6, +7$). For example, Uranium ($ ext{U}$) exhibits $+3, +4, +5, +6$, and Neptunium ($ ext{Np}$) and Plutonium ($ ext{Pu}$) reach $+7$. This occurs because the energy levels of $5f, 6d$, and $7s$ orbitals are of comparable magnitudes, allowing electrons from all three subshells to participate in chemical bonding.
Actinoid Contraction: There is a progressive decrease in the size of actinoid atoms and ions ($M^{3+}, M^{4+}$) with increasing atomic number. The actinoid contraction is greater from element to element than the lanthanoid contraction because $5f$ electrons exert even poorer shielding than $4f$ electrons.

Mischmetal: A pyrophoric alloy consisting of approximately $50\%$ Cerium, $40\%$ Lanthanum and Neodymium, with $\approx 5\%$ iron and traces of $\text{S, C, Ca, Al}$. Used in cigarette lighter flints, tracer bullets, and metallurgical deoxidizers.