The d- and f-Block Elements

1. Position in Periodic Table & Electronic Configurations

• Definition: Transition elements are defined as elements having partially filled $d$-orbitals in their ground state or in any common oxidation state.
• Non-typical Elements: Group 12 elements ($\text{Zn}, \text{Cd}, \text{Hg}$) have completely filled $d^{10}$ configurations in their ground state ($d^{10} s^2$) and common +2 state ($d^{10}$). They are not regarded as true transition elements, but are studied alongside them.
• General Valence Configuration: $(n-1)d^{1-10} ns^{1-2}$.
  • Chromium ($Z=24$): $[\text{Ar}]3d^5 4s^1$ (stability of half-filled subshell).
  • Copper ($Z=29$): $[\text{Ar}]3d^{10} 4s^1$ (stability of completely filled subshell).

2. Physical Trends: Atomic Radii, Melting Points & Atomisation

• Atomic & Ionic Radii: Across the 3d series, atomic radii decrease from $\text{Sc}$ to $\text{Cr}$, remain nearly constant from $\text{Fe}$ to $\text{Ni}$ (nuclear charge balanced by $d-d$ shielding), and increase slightly at $\text{Cu}$ and $\text{Zn}$ due to inter-electronic repulsion.
• Melting Points & Enthalpy of Atomisation: Transition metals exhibit high melting points and enthalpies of atomisation due to metallic bonding involving both $ns$ and $(n-1)d$ unpaired electrons. Maxima occur near the middle of each series ($d^5$), with an anomaly at Manganese ($3d^5 4s^2$, tightly held electrons reduce delocalisation).

3. Variable Oxidation States & Standard Electrode Potentials ($E^\circ$)

• Variable Oxidation States: Due to small energy differences between $(n-1)d$ and $ns$ orbitals, transition metals exhibit multiple oxidation states differing by units of one (e.g., $\text{V}^{2+}, \text{V}^{3+}, \text{V}^{4+}, \text{V}^{5+}$).
  • Minimum oxidation state: number of $s$-electrons.
  • Maximum oxidation state: sum of $s$- and $d$-electrons up to Manganese ($\text{Mn}$ shows +2 to +7).
  • Heavy transition elements stabilise higher oxidation states (e.g., $\text{Mo(VI)}$ and $\text{W(VI)}$ are stable, while $\text{Cr(VI)}$ is a strong oxidant).
• Thermochemical Breakdown of $E^\circ(\text{M}^{2+}/\text{M})$:

  $$\Delta H = \Delta_a H^\circ + \Delta_i H_1^\circ + \Delta_i H_2^\circ + \Delta_{\text{hyd}} H^\circ$$

  • $\text{Mn}, \text{Zn}$ have more negative $E^\circ$ values due to stable $d^5$ and $d^{10}$ configurations.
  • $\text{Ni}$ has a more negative $E^\circ$ value due to its high negative hydration enthalpy.
  • $\text{Cu}$ has a positive $E^\circ$ (+0.34 V) because hydration enthalpy cannot offset high atomisation and ionisation energies.

4. Magnetic Properties, Colour Formation & Catalysis

• Spin-Only Magnetic Moment:

  $$\mu = \sqrt{n(n+2)}\text{ BM}$$

  Where $n$ is the number of unpaired electrons ($1\text{ BM} = 9.27 \times 10^{-24}\text{ A m}^2$).
  • $n = 1 \implies \mu = 1.73\text{ BM}$ ($\text{Ti}^{3+}, \text{Cu}^{2+}$)
  • $n = 2 \implies \mu = 2.84\text{ BM}$ ($\text{Ti}^{2+}, \text{Ni}^{2+}$)
  • $n = 3 \implies \mu = 3.87\text{ BM}$ ($\text{V}^{2+}, \text{Cr}^{3+}$)
  • $n = 4 \implies \mu = 4.90\text{ BM}$ ($\text{Cr}^{2+}, \text{Fe}^{2+}$)
  • $n = 5 \implies \mu = 5.92\text{ BM}$ ($\text{Mn}^{2+}, \text{Fe}^{3+}$)
• Origin of Colour: In aquated transition ions, the presence of ligands splits degenerate $d$-orbitals. Promoting an electron between split $d$-orbitals absorbs specific wavelengths of visible light, displaying the complementary colour.
• Catalytic Activity: Transition metals act as catalysts because they can adopt variable oxidation states, form unstable intermediates, and provide solid surfaces for chemisorption (e.g., $\text{V}_2\text{O}_5$ in Contact Process, finely divided $\text{Fe}$ in Haber process, $\text{Ni}$ in hydrogenation).

5. Potassium Dichromate ($\text{K}_2\text{Cr}_2\text{O}_7$)

• Industrial Preparation from Chromite Ore ($\text{FeCr}_2\text{O}_4$):
  1. Oxidative Roasting:

     $$4\text{FeCr}_2\text{O}_4 + 8\text{Na}_2\text{CO}_3 + 7\text{O}_2 \longrightarrow 8\text{Na}_2\text{CrO}_4\ (\text{yellow}) + 2\text{Fe}_2\text{O}_3 + 8\text{CO}_2$$

  2. Acidification to Dichromate:

     $$2\text{Na}_2\text{CrO}_4 + 2\text{H}^+ \longrightarrow \text{Na}_2\text{Cr}_2\text{O}_7\ (\text{orange}) + 2\text{Na}^+ + \text{H}_2\text{O}$$

  3. Potassium Metathesis:

     $$\text{Na}_2\text{Cr}_2\text{O}_7 + 2\text{KCl} \longrightarrow \text{K}_2\text{Cr}_2\text{O}_7\ (\text{orange crystals}) + 2\text{NaCl}$$

• Oxidising Reactions in Acidic Medium ($E^\circ = +1.33\text{ V}$):

  $$\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^- \longrightarrow 2\text{Cr}^{3+}\ (\text{green}) + 7\text{H}_2\text{O}$$

  • Oxidises $\text{Fe}^{2+}$ to $\text{Fe}^{3+}$: $\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O}$
  • Oxidises $\text{I}^-$ to $\text{I}_2$: $\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{I}^- \rightarrow 2\text{Cr}^{3+} + 3\text{I}_2 + 7\text{H}_2\text{O}$
  • Oxidises $\text{H}_2\text{S}$ to $\text{S}$: $\text{Cr}_2\text{O}_7^{2-} + 8\text{H}^+ + 3\text{H}_2\text{S} \rightarrow 2\text{Cr}^{3+} + 3\text{S} + 7\text{H}_2\text{O}$

6. Potassium Permanganate ($\text{KMnO}_4$)

• Synthesis from Pyrolusite ($\text{MnO}_2$):
  1. Alkaline Oxidative Fusion:

     $$2\text{MnO}_2 + 4\text{KOH} + \text{O}_2 \longrightarrow 2\text{K}_2\text{MnO}_4\ (\text{dark green}) + 2\text{H}_2\text{O}$$

  2. Disproportionation in Acid / Electrolytic Oxidation:

     $$3\text{MnO}_4^{2-} + 4\text{H}^+ \longrightarrow 2\text{MnO}_4^-\ (\text{purple}) + \text{MnO}_2 + 2\text{H}_2\text{O}$$

• Oxidising Half-Reactions Across Media:
  • Acidic Solution ($E^\circ = +1.52\text{ V}$):

    $$\text{MnO}_4^- + 8\text{H}^+ + 5e^- \longrightarrow \text{Mn}^{2+} + 4\text{H}_2\text{O}$$

    • Oxalate to $\text{CO}_2$: $2\text{MnO}_4^- + 16\text{H}^+ + 5\text{C}_2\text{O}_4^{2-} \rightarrow 2\text{Mn}^{2+} + 8\text{H}_2\text{O} + 10\text{CO}_2$
    • Nitrite to Nitrate: $2\text{MnO}_4^- + 6\text{H}^+ + 5\text{NO}_2^- \rightarrow 2\text{Mn}^{2+} + 3\text{H}_2\text{O} + 5\text{NO}_3^-$
  • Neutral / Faintly Alkaline Solution ($E^\circ = +1.69\text{ V}$):

    $$\text{MnO}_4^- + 2\text{H}_2\text{O} + 3e^- \longrightarrow \text{MnO}_2 + 4\text{OH}^-$$

    • Iodide to Iodate: $2\text{MnO}_4^- + \text{H}_2\text{O} + \text{I}^- \rightarrow 2\text{MnO}_2 + 2\text{OH}^- + \text{IO}_3^-$
    • Thiosulphate to Sulphate: $8\text{MnO}_4^- + 3\text{S}_2\text{O}_3^{2-} + \text{H}_2\text{O} \rightarrow 8\text{MnO}_2 + 6\text{SO}_4^{2-} + 2\text{OH}^-$

7. The f-Block: Lanthanoids vs Actinoids

Comparative Chemistry