Exhaustive Study Notes on the d- and f-Block Elements

Position and Classification of d- and f-Block Elements

• The d-Block Elements: These reside in Groups 3–12 of the periodic table. They are characterized by the progressive filling of d orbitals in each of the four long periods.

• The f-Block Elements: These consist of elements where the $4f$ and $5f$ orbitals are progressively filled. They are typically displayed in a separate panel at the bottom of the periodic table.

• Terminology:     * Transition Metals: Often used interchangeably with d-block elements.     * Inner Transition Metals: Often used to refer to f-block elements.

• Transition Series:     * 3d series: Sc (Z = 21) to Zn (Z = 30).     * 4d series: Y (Z = 39) to Cd (Z = 48).     * 5d series: La (Z = 57) and Hf (Z = 72) to Hg (Z = 80).     * 6d series: Ac (Z = 89) and Rf (Z = 104) to Cn (Z = 112).

• Inner Transition Series:     * 4f series (Lanthanoids): Ce (Z = 58) to Lu (Z = 71).     * 5f series (Actinoids): Th (Z = 90) to Lr (Z = 103).

• IUPAC Definition of Transition Metals: Metals that possess an incomplete d subshell in their neutral atom state or in any of their common ions.

• Exclusion of Group 12 Elements: Zinc ($Zn$), Cadmium ($Cd$), and Mercury ($Hg$) have a full $d^{10}$ configuration in their ground state and common oxidation states. Technically, they are not regarded as transition metals, but their chemistry is studied alongside them as end members of the series.

General Electronic Configurations of d-Block Elements

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

• Components: $(n-1)$ represents the inner d orbitals (penultimate energy level); $ns$ represents the outermost s orbital.

• Exceptions to the Rule:     * Palladium ($Pd$): Electronic configuration is $4d^{10} 5s^0$.     * Chromium ($Cr$): Exhibits $3d^5 4s^1$ instead of $3d^4 4s^2$. This is due to the relative stability of half-filled subshells and the small energy gap between $3d$ and $4s$ orbitals.     * Copper ($Cu$): Exhibits $3d^{10} 4s^1$ instead of $3d^9 4s^2$ due to the stability of a completely filled d subshell.

• Shielding Effects: The d electrons in the transition series do not shield the outer s electrons effectively. As nuclear charge increases, the net electrostatic attraction on outermost electrons increases, causing a decrease in ionic/atomic radii.

Physical and Metallic Properties

• Metallic Character: Transition elements display typical metallic traits: high tensile strength, ductility, malleability, high thermal/electrical conductivity, and metallic lustre.

• Lattice Structures:     * Sc: hcp.     * Ti, V, Cr: hcp/bcc.     * Mn: X (typical metal structure).     * Fe, Co, Ni, Cu: bcc/ccp.     * Zn, Cd, Hg: X structures (non-typical for transition metals).

• Melting and Boiling Points: They are exceptionally high (except for Zn, Cd, and Hg). High melting points are caused by the involvement of $(n-1)d$ electrons alongside $ns$ electrons in interatomic metallic bonding.

• Melting Point Trends: Rise to a maximum at approximately $d^5$ (middle of the series), with Mn and Tc showing anomalous lower values, then fall regularly as atomic number increases.

• Enthalpies of Atomisation: These are very high for transition metals. Maxima occur at the middle of each series, indicating that one unpaired electron per d orbital is favorable for strong interatomic interaction. Metals with very high enthalpies of atomisation (and high boiling points) tend to be noble in their chemical reactions.

Variation in Atomic and Ionic Sizes

• General Trend: There is a progressive decrease in radius across a series with increasing atomic number due to increased nuclear charge and poor shielding by d electrons.

• Lanthanoid Contraction: The radii of the third (5d) series are virtually identical to those of the corresponding members of the second (4d) series. This is caused by the filling of $4f$ orbitals before the $5d$ series.     * Cause: Imperfect shielding of one $4f$ electron by another is even less than that of d electrons. This leads to a regular decrease in size across the lanthanoid series.     * Consequence: Elements like Zirconium ($Zr$, $160\,pm$) and Hafnium ($Hf$, $159\,pm$) have nearly identical radii, making them difficult to separate chemically.

• Density: There is a general increase in density from left to right in a period (e.g., Titanium to Copper) due to the decrease in metallic radius accompanied by an increase in atomic mass.

Ionisation Enthalpies

• Trends: Ionisation enthalpy increases along each series from left to right due to increased nuclear charge.

• Comparison to Non-Transition Elements: Successive enthalpies ($\Delta_i H_1$, $\Delta_i H_2$, $\Delta_i H_3$) do not increase as steeply as in p-block elements.

• Order of Electron Loss: When d-block elements form ions, $ns$ electrons are always lost before $(n-1)d$ electrons.

• Exchange Energy: This contributes to the stability of certain configurations. For example, the third ionisation enthalpy of Fe is lower than Mn because Fe loses an electron to reach a stable $d^5$ configuration, whereas Mn would lose the stability of $d^5$.

• High Third Enthalpies: Ions like $Cu^{3+}$, $Ni^{3+}$, and $Zn^{3+}$ are difficult to obtain due to exceptionally high third ionisation enthalpies.

Oxidation States

• Variability: Unique to transition elements, oxidation states often differ by units of one (e.g., $V^{II}$, $V^{III}$, $V^{IV}$, $V^V$). This is due to the proximity of $(n-1)d$ and $ns$ energy levels.

• Mid-Series Maxima: Elements in the middle of the series ($Mn$) show the greatest number of oxidation states ($+2$ to $+7$). Ends of the series show fewer states (e.g., $Sc$ only $+3$, $Zn$ only $+2$).

• Stability Trends:     * Groups 4-10: In the d-block, higher oxidation states are more stable for heavier members (opposite of the p-block). Example: $Mo(VI)$ and $W(VI)$ are more stable than $Cr(VI)$.     * $Cr(VI)$ in acidic medium is a strong oxidising agent (dichromate).

• Low Oxidation States: Can be achieved with specialized ligands like $CO$ which have $\pi$-acceptor character (e.g., $[Ni(CO)_4]$ and $[Fe(CO)_5]$ where oxidation state is zero).

Chemical Reactivity and Electrode Potentials ($E^\circ$)

• Standard Electrode Potential ($M^{2+}/M$): Generally becomes less negative across the series, indicating a decreasing tendency to form divalent cations.

• The Copper Anomaly: $E^\circ(Cu^{2+}/Cu)$ is $+0.34\,V$. Copper is the only first-row transition metal that does not liberate $H_2$ from acids because its high enthalpy of atomisation is not balanced by its hydration enthalpy.

• Mn, Ni, and Zn Values: These exhibit more negative values than expected due to:     * Mn: Stability of half-filled $d^5$ in $Mn^{2+}$.     * Zn: Stability of full $d^{10}$ in $Zn^{2+}$.     * Ni: Extremely high negative enthalpy of hydration.

• Reducing Agents: $Ti^{2+}$, $V^{2+}$, and $Cr^{2+}$ are strong reducing agents and can liberate hydrogen from dilute acids.

• Oxidising Agents: $Mn^{3+}$ and $Co^{3+}$ are strong oxidising agents in aqueous solutions.

Magnetic and Colored Properties

• Paramagnetism: Results from unpaired electrons. Most transition metal ions are paramagnetic.

• Spin-Only Formula: The magnetic moment ($\mu$) is calculated as:     * $\mu = \sqrt{n(n+2)}\,BM$     * Where $n$ is the number of unpaired electrons and $BM$ is Bohr Magnetons.     * Example: An ion with $n=1$ has $\mu = 1.73\,BM$. An ion with $n=5$ ($Mn^{2+}$) has $\mu = 5.92\,BM$.

• Diamagnetism: Substances repelled by magnetic fields (no unpaired electrons).

• Ferromagnetism: Extreme form of paramagnetism (e.g., Fe).

• Colour: Caused by d-d transitions. When light is absorbed, an electron is excited from a lower energy d orbital to a higher one. The observed colour is complementary to the frequency absorbed.     * $Sc^{3+}$ ($3d^0$) and $Zn^{2+}$ ($3d^{10}$) are colourless.     * $V^{3+}$ is green; $Mn^{2+}$ is pink; $Cu^{2+}$ is blue.

Catalytic and Interstitial Properties

• Catalytic Activity: Attributed to the ability to adopt multiple oxidation states and form complexes. Transition metals lower the activation energy by providing a surface for reactants to bond.     * Contact Process: Uses $V_2O_5$.     * Haber’s Process: Uses finely divided $Fe$.     * Hydrogenation: Uses $Ni$.

• Interstitial Compounds: Formed when small atoms (H, C, N) are trapped in metal crystal lattices (e.g., $TiC$, $Mn_4N$, $Fe_3H$).     * Properties: High melting points, extreme hardness (some borides near diamond), metallic conductivity, and chemical inertness.

• Alloys: Homogeneous solid solutions of metals. Readiness to form alloys is due to similar metallic radii (within 15%).     * Examples: Brass ($Cu-Zn$), Bronze ($Cu-Sn$), Stainless Steel (Cr, Ni added to Fe).

Important Compounds: $K_2Cr_2O_7$ and $KMnO_4$

• Potassium Dichromate ($K_2Cr_2O_7$):     * Preparation: From chromite ore ($FeCr_2O_4$).         1. Fusion with sodium carbonate: $4FeCr_2O_4 + 8Na_2CO_3 + 7O_2 \rightarrow 8Na2CrO_4 + 2Fe_2O_3 + 8CO_2$         2. Acidification to dichromate: $2Na_2CrO_4 + 2H^+ \rightarrow Na_2Cr_2O_7 + 2Na^+ + H_2O$         3. Addition of $KCl$ to crystallize $K_2Cr_2O_7$.     * pH Stability: Chromate ($CrO_4^{2-}$) and dichromate ($Cr_2O_7^{2-}$) are interconvertible. Chromate (yellow) is stable in alkaline pH; dichromate (orange) is stable in acidic pH.     * Oxidising Action: $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O$ ($E^\circ = 1.33\,V$).

• Potassium Permanganate ($KMnO_4$):     * Preparation: Fusion of $MnO_2$ with $KOH$ and an oxidant like $KNO_3$ to form green $K_2MnO_4$, followed by electrolytic oxidation or disproportionation.     * Disproportionation: $3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- + MnO_2 + 2H_2O$.     * Physical Properties: Dark purple crystals, isostructural with $KClO4$. It is diamagnetic (weakly paramagnetic with temperature).     * Oxidising Action in Acid: $MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$ ($E^\circ = 1.52\,V$).

The f-Block: Lanthanoids and Actinoids

• Lanthanoids:     * Oxidation State: Most stable is $+3$. $Ce$ exhibits $+4$ (noble gas config). $Eu^{2+}$ and $Yb^{2+}$ are strong reducing agents.     * Contraction: Lanthanoid contraction causes regular decrease in atomic/ionic radii.     * Mischmetall: Alloy of lanthanoid metal ($\sim 95\%$) and iron ($\sim 5\%$) used in bullets and lighter flints.

• Actinoids:     * Radioactivity: All are radioactive. Earlier members have long half-lives; later members (like Lr) have half-lives of minutes.     * Oxidation States: More varied than lanthanoids ($+3$ to $+7$) because $5f$, $6d$, and $7s$ levels are comparable in energy.     * Comparison: Actinoid contraction is greater than lanthanoid contraction due to even poorer shielding by $5f$ electrons than $4f$.

Questions & Discussion

• Example 4.1: Why is Sc (Z=21) a transition element but Zn (Z=30) is not?     * Response: Scandium has an incompletely filled $3d$ orbital ($3d^1$) in its ground state. Zinc has completely filled $d$ orbitals ($3d^{10}$) in both ground and oxidized states.

• Intext Question 4.1: Is Silver (Z=47) a transition element if its ground state is $4d^{10}$?     * Response: Yes, because silver can exhibit a $+2$ oxidation state where it has an incompletely filled $d$ shell ($4d^9$).

• Example 4.4: Why is $Cr^{2+}$ reducing and $Mn^{3+}$ oxidising despite both having $d^4$ configurations?     * Response: $Cr^{2+}$ reduces to $Cr^{3+}$ ($d^3$), achieving a stable half-filled $t_{2g}$ level. $Mn^{3+}$ oxidises to $Mn^{2+}$ ($d^5$), achieving the extra stability of a half-filled d subshell.

• Example 4.9: What is disproportionation?     * Response: It occurs when an oxidation state becomes unstable and changes into one higher and one lower state. Example: $3Mn^{VI}O_4^{2-} + 4H^+ \rightarrow 2Mn^{VII}O_4^- + Mn^{IV}O_2 + 2H_2O$.