d- and f-Block Elements revision notes

Key Concepts & Definitions

d-Block Elements:

Elements in groups 3-12 where the inner d orbitals are progressively filled in each of the four long periods. Consists of four series: 3d (Sc-Zn), 4d (Y-Cd), 5d (La and Hf-Hg), and 6d (Ac and Rf-Cn).

Transition Metals (IUPAC Definition):

Metals which have an incomplete d subshell either in the neutral atom or in their ions.

f-Block Elements (Inner Transition Metals):

Elements placed in a separate panel where the 4f and 5f orbitals are progressively filled. Consists of Lanthanoids (Ce to Lu) and Actinoids (Th to Lr).

Lanthanoid Contraction:

The regular decrease in atomic and ionic radii along the lanthanoid series (from La to Lu) due to the imperfect shielding of one 4f electron by another, which is less effective than d electron shielding, leading to an increased effective nuclear charge.

Actinoid Contraction:

The gradual decrease in the size of atoms or M3+M^{3+}M3+ ions across the actinoid series. This contraction is greater from element to element than the lanthanoid contraction because 5f electrons provide even poorer shielding from the nuclear charge than 4f electrons.

Disproportionation:

A reaction where a particular oxidation state becomes less stable relative to other oxidation states and simultaneously undergoes self-oxidation and self-reduction. Example: Manganese(VI) in acidic solution converts to Mn(VII) and Mn(IV).

Important Rules, Laws & Principles

• Electronic Configuration Rule: The outer orbital configuration is generally $(n-1)d^{1-10}ns^{1-2}$. When d-block elements form ions, $ns$ electrons are lost before $(n-1)d$ electrons.
• Ionization Enthalpy Trends: Successive ionization enthalpies do not increase as steeply as in non-transition elements. The relatively small energy difference allows for the loss of a variable number of electrons and the display of variable oxidation states.
• Stability of Half-Filled / Completely Filled Orbitals: Configurations like $d^5$, $d^{10}$, $f^7$, and $f^{14}$ provide extra stability due to high exchange energy and maximum parallel spins (Hund's Rule). This directly affects melting points, ionization enthalpies, and electrode potentials.
• Variable Oxidation States rule: Transition metals exhibit variable oxidation states differing by units of ONE (e.g., $V^{2+}, V^{3+}, V^{4+}, V^{5+}$). This directly contrasts with p-block elements where oxidation states differ by units of TWO due to the inert pair effect.
• Stabilization of High Oxidation States: Only fluorine and oxygen can stabilize the highest oxidation states of transition metals. Fluorine does this via high lattice energy (e.g., $CoF_3$) or high bond enthalpy (e.g., $VF_5$). Oxygen is even superior to fluorine because of its ability to form multiple bonds (e.g., $Mn_2O_7$, $MnO_4^-$).
• Low Oxidation State Stabilization: Found in complex compounds where ligands have $\pi$-acceptor character in addition to $\sigma$-bonding (e.g., $Ni(CO)_4$ and $Fe(CO)_5$ where metals have an oxidation state of zero).
• Magnetic Behavior: Determined by unpaired electrons. Paramagnetism increases with the number of unpaired electrons. Ferromagnetism is an extreme form of paramagnetism. $KMnO_4$ is diamagnetic due to an absence of unpaired electrons, but shows temperature-dependent weak paramagnetism.

General Characteristics & Trends

• Melting Points: Transition metals have high melting points due to strong interatomic metallic bonding from large numbers of unpaired (n-1)d electrons. In any row, the melting point rises to a maximum at $d^5$ and then falls regularly as atomic number increases.
• Enthalpies of Atomization ($\Delta_aH^o$): Maxima occur around the middle of each series. Metals of the 2nd and 3rd series have greater enthalpies of atomization than the 1st series, leading to frequent metal-metal bonding in heavy transition metals.
• Oxidizing/Reducing Power: $Mn^{3+}$ and $Co^{3+}$ are the strongest oxidizing agents in aqueous solution. $Ti^{2+}, V^{2+}, \text{ and } Cr^{2+}$ are strong reducing agents and liberate $H_2$ from dilute acids. $Cr^{2+}$ is a stronger reducing agent than $Fe^{2+}$ because the resulting $Cr^{3+}$ has a stable half-filled $t_{2g}$ configuration ($d^3$) in aqueous medium.
• Oxide Acidity: As the oxidation number of a metal increases, ionic character decreases and acidic character increases. $Mn_2O_7$ (gives $HMnO_4$), $CrO_3$ (gives $H_2CrO_4$), and $V_2O_5$ are predominantly acidic. $V_2O_3$ is basic, $V_2O_4$ is less basic, and $V_2O_5$ is amphoteric (though mainly acidic).
• Interstitial Compounds: Non-stoichiometric compounds formed when small atoms (H, C, N) are trapped inside the crystal lattices of transition metals (e.g., $TiC$, $Mn_4N$, $Fe_3H$, $VH_{0.56}$, $TiH_{1.7}$). They have higher melting points than the pure metals, are extremely hard, retain metallic conductivity, and are chemically inert.JEE TIPThey are neither typically ionic nor covalent, and formulas do not correspond to normal oxidation states.
• Alloys: Homogeneous solid solutions formed readily by transition metals because their metallic radii are within about 15% of each other. Examples include ferrous alloys with Cr, V, W, Mo, and Mn, or non-transition mixtures like Brass (Cu-Zn) and Bronze (Cu-Sn).
• Catalytic Activity: Transition metals act as catalysts because they can adopt multiple oxidation states and form complexes. They utilize their 3d and 4s electrons to form bonds on their solid surface, increasing reactant concentration and lowering activation energy. Examples: $V_2O_5$ for Contact Process, finely divided iron for Haber’s Process, $PdCl_2$ for Wacker process, and Ziegler catalyst ($TiCl_4$ + $Al(CH_3)_3$).
• Color of Hydrated Ions: Color arises from d-d transitions in the visible region. $Sc^{3+}$ ($3d^0$), $Ti^{4+}$ ($3d^0$), and $Zn^{2+}$ ($3d^{10}$) are colorless. $Cu^{2+}$ ($3d^9$) is blue, $Fe^{2+}$ ($3d^6$) is green, and $Mn^{2+}$ ($3d^5$) is pink.

Chemical Equilibrium & Reaction Extent (pH Dependency)

• Chromate-Dichromate Equilibrium: The yellow chromate ion ($CrO_4^{2-}$) and orange dichromate ion ($Cr_2O_7^{2-}$) are interconvertible depending on the pH of the aqueous solution. The oxidation state of Cr (+6) remains the same in both.
  • $2 CrO_4^{2-} \text{ (yellow)} + 2H^+ \rightarrow Cr_2O_7^{2-} \text{ (orange)} + H_2O$
  • $Cr_2O_7^{2-} \text{ (orange)} + 2 OH^- \rightarrow 2 CrO_4^{2-} \text{ (yellow)} + H_2O$

Reactions & Mechanisms

1. Potassium Dichromate ($K_2Cr_2O_7$)

• Preparation: Fusion of chromite ore ($FeCr_2O_4$) with sodium or potassium carbonate in free access of air.
  1. $4 FeCr_2O_4 + 8 Na_2CO_3 + 7 O_2 \rightarrow 8 Na_2CrO_4 + 2 Fe_2O_3 + 8 CO_2$ (Yellow $Na_2CrO_4$ is filtered)
  2. $2 Na_2CrO_4 + 2 H^+ \rightarrow Na_2Cr_2O_7 + 2 Na^+ + H_2O$ (Acidification to more soluble orange $Na_2Cr_2O_7$)
  3. $Na_2Cr_2O_7 + 2 KCl \rightarrow K_2Cr_2O_7 + 2 NaCl$ (Displacement; $K_2Cr_2O_7$ crystallizes out)
• Oxidizing Action (Acidic Medium): $K_2Cr_2O_7$ is a strong oxidizer used as a primary standard in volumetric analysis.
  • $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O \quad (E^o = 1.33V)$
  • Oxidizes $I^-$ to $I_2$, $S^{2-}$ to $S$, $Sn^{2+}$ to $Sn^{4+}$, $Fe^{2+}$ to $Fe^{3+}$.

2. Potassium Permanganate ($KMnO_4$)

• Preparation:
  1. Fusion: $2MnO_2 + 4KOH + O_2 \rightarrow 2K_2MnO_4 + 2H_2O$ (Produces dark green manganate)
  2. Oxidation: Commercially by electrolytic oxidation of manganate in alkaline solution: $MnO_4^{2-} \rightarrow MnO_4^- + e^-$
  3. Laboratory Prep: $Mn^{2+}$ oxidized by peroxodisulphate: $2Mn^{2+} + 5S_2O_8^{2-} + 8H_2O \rightarrow 2MnO_4^- + 10SO_4^{2-} + 16H^+$
• Disproportionation of Manganate: In neutral or acidic solution, green manganate undergoes disproportionation.
  • $3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- \text{ (purple)} + MnO_2 \text{ (solid)} + 2H_2O$
• Oxidizing Action in Acidic Solutions:
  • $MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O \quad (E^o = +1.52 V)$
  • $10I^- + 2MnO_4^- + 16H^+ \rightarrow 2Mn^{2+} + 8H_2O + 5I_2$
  • $5Fe^{2+} + MnO_4^- + 8H^+ \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+}$
  • $5C_2O_4^{2-} (\text{oxalate}) + 2MnO_4^- + 16H^+ \xrightarrow{333 K} 2Mn^{2+} + 8H_2O + 10CO_2$
  • $5S^{2-} + 2MnO_4^- + 16H^+ \rightarrow 2Mn^{2+} + 8H_2O + 5S$ (from $H_2S$)
  • $5SO_3^{2-} + 2MnO_4^- + 6H^+ \rightarrow 2Mn^{2+} + 3H_2O + 5SO_4^{2-}$
  • $5NO_2^- + 2MnO_4^- + 6H^+ \rightarrow 2Mn^{2+} + 5NO_3^- + 3H_2O$
• Oxidizing Action in Neutral or Faintly Alkaline Solutions:
  • $2MnO_4^- + H_2O + I^- \rightarrow 2MnO_2 + 2OH^- + IO_3^-$ (Iodide is oxidized to Iodate!)
  • $8MnO_4^- + 3S_2O_3^{2-} + H_2O \rightarrow 8MnO_2 + 6SO_4^{2-} + 2OH^-$ (Thiosulphate to Sulphate)
  • $2MnO_4^- + 3Mn^{2+} + 2H_2O \rightarrow 5MnO_2 + 4H^+$ (Catalyzed by $ZnSO_4$ or $ZnO$)

f-Block Elements: Lanthanoids & Actinoids

• Lanthanoids (Ln): Tarnish rapidly in air and behave similarly to calcium in early members and aluminum in later members.
  • Reactions: Burns in halogens to form $LnX_3$. Reacts with water to give $Ln(OH)_3$ + $H_2$. Liberates $H_2$ from dilute acids. When heated with carbon at 2773 K, forms carbides ($Ln_3C$, $Ln_2C_3$, $LnC_2$). Heating with N forms nitrides ($LnN$), with S forms sulphides ($Ln_2S_3$), and burning in air forms oxides ($Ln_2O_3$).
  • Mischmetall: An alloy of ~95% lanthanoid metal, ~5% iron, and traces of S, C, Ca, and Al. Used in Mg-based alloys for bullets, shells, and lighter flints.
• Actinoids: Elements from Ac (89) to Lr (103) progressively fill 5f orbitals. All are radioactive; later members have half-lives of minutes and are made in nanogram quantities.
  • Oxidation States: Exhibit a much wider range of oxidation states than lanthanoids (up to +7 for Np and Pu) because 5f, 6d, and 7s levels are of comparable energies.
  • Reactivity: Highly reactive, especially finely divided. Boiling water gives a mixture of oxide and hydride. HCl attacks all actinoids, but most are only slightly affected by nitric acid due to a protective oxide layer.
• Lanthanoids vs Actinoids: The actinoid contraction is greater than the lanthanoid contraction from element to element because 5f electrons provide even poorer shielding than 4f electrons. The 5f electrons penetrate less into the inner core and are more available for bonding than 4f electrons.

Formulae & Equations

• Spin-Only Magnetic Moment: $\mu = \sqrt{n(n + 2)} \text{ B.M.}$ Where $n$ = number of unpaired electrons. 1 B.M. = Bohr Magneton.

⚠️ EXCEPTIONS & ANOMALIES (EXHAUSTIVE LIST)

• Group 12 Exclusion: Zn, Cd, and Hg are NOT considered transition metals because they have full $d^{10}$ configurations in their ground state and in their common oxidation states.
• Electronic Configuration Anomalies:
  • Cr: $3d^5 4s^1$ (not $3d^4 4s^2$) due to extra stability of half-filled subshell.
  • Cu: $3d^{10} 4s^1$ (not $3d^9 4s^2$) due to extra stability of fully-filled subshell.
  • Pd: $4d^{10} 5s^0$.
• Melting Point Anomalies: While melting points generally rise to a maximum at $d^5$, Mn and Tc show an anomalous dip in their melting points.
• Enthalpy of Atomization Minimum: Zn has the lowest enthalpy of atomization ($126 \text{ kJ mol}^{-1}$) in the 3d series because it has zero unpaired electrons, meaning no d-electrons participate in metallic bonding.
• Atomic Size Anomaly (Lanthanoid Contraction): The atomic radii of the 5d series (3rd series) are practically identical to the 4d series (2nd series) elements (e.g., Zr = 160 pm; Hf = 159 pm) due to poor shielding by 4f electrons, overriding the expected size increase.
• Ionization Enthalpy Breaks: The steady increase expected in the 2nd and 3rd ionization enthalpies breaks for $Mn^{2+}$ (stable $d^5$ opposes 3rd IE) and $Fe^{3+}$ (stable $d^5$ opposes 4th IE). The third ionization enthalpies of La, Gd, and Lu are abnormally low due to the stability attained by leaving an empty ($f^0$), half-filled ($f^7$), or fully-filled ($f^{14}$) f-subshell.
• JEE TIPUnlike the p-block where heavier members favor lower oxidation states (inert pair effect), in the d-block, heavier members favor higher oxidation states. Example: Mo(VI) and W(VI) are highly stable, but Cr(VI) is unstable and a strong oxidizing agent.
• Anomalous Standard Electrode Potential ($E^\circ$):
  • Copper's Positive $E^\circ$: Cu is the ONLY 3d element with a positive $E^\circ_{M^{2+}/M}$ (+0.34V), meaning it cannot liberate $H_2$ from non-oxidizing acids. Its high atomization and ionization enthalpies are not compensated by its hydration enthalpy.
  • Mn, Ni, and Zn Deviations: Their $E^\circ$ values are more negative than expected from the general trend. Mn and Zn are stabilized by $d^5$ and $d^{10}$ configurations, respectively, while Ni's deviation is due to its exceptionally high negative hydration enthalpy.
• Instability of Low Oxidation State Fluorides: While F stabilizes high oxidation states, low oxidation state fluorides are unstable. Example: $VX_2$ exists for X = Cl, Br, I, but $VF_2$ is not known.
• Non-existence of $CuI_2$: All Cu(II) halides exist EXCEPT the iodide. $Cu^{2+}$ oxidizes $I^-$ to $I_2$, forcing the formation of Cu(I).
• Instability of Cu(I) in Water: Many Cu(I) compounds undergo disproportionation in aqueous solution to $Cu^{2+}$ and $Cu(s)$. Cu(II) is stable due to its highly negative hydration enthalpy.
• Physical State Anomaly of Metal Oxides: Metal oxides are typically solid, but $Mn_2O_7$ is a covalent green oil because higher oxidation states cause decreased ionic character.
• Lanthanoid Color Exceptions: Trivalent lanthanoids generally form colored ions due to f-f transitions, EXCEPT $La^{3+}$ ($4f^0$) and $Lu^{3+}$ ($4f^{14}$) which are colorless due to lacking transitionable f-electrons.
• Lanthanoid Oxidation State Anomalies: While +3 is the rule, $Ce^{4+}$ is stable due to a noble gas ($f^0$) configuration. $Eu^{2+}$ and $Yb^{2+}$ are unusually stable due to $f^7$ and $f^{14}$ configurations, respectively.
• Reactivity with Nitric Acid Exception: While HCl attacks all actinoids, most actinoids are only slightly affected by nitric acid due to the formation of a protective, passive oxide layer.

Previous Year JEE Topics

1. D-block Magnetic Moments: Direct calculation of unpaired electrons and $\mu$ using "spin-only" formula (e.g. comparing $Mn^{2+}$, $Fe^{2+}$, $Co^{2+}$, $Ni^{2+}$).
2. Disproportionation & Interconversion: The pH dependency of $CrO_4^{2-} / Cr_2O_7^{2-}$ and disproportionation of $MnO_4^{2-}$ to $MnO_4^-$ and $MnO_2$ in acid.
3. Equivalent weights in Redox: Specifically evaluating moles of electrons transferred by $KMnO_4$ in acidic ($n=5$), neutral/weakly alkaline ($n=3$).
4. Lanthanoid Contraction Consequences: Nearly identical radii of 4d and 5d metals (Zr/Hf, Nb/Ta, Mo/W) causing separation difficulties.
5. Anomalous Electrode Potentials: Why Cu has a positive reduction potential and why $Mn^{3+}/Mn^{2+}$ is exceptionally positive.

Memory Aids & Top 10 JEE MCQ Traps

• [JEE TIP] Trap 1 - Zinc Group Transition Status:

  • Misconception: Zinc, Cadmium, and Mercury are transition metals because they are located in the $d$-block.
  • Correct Understanding: According to IUPAC, they are not transition metals. They have completely filled $d^{10}$ configurations in both their ground state and all common oxidation states.

• [JEE TIP] Trap 2 - Isoelectronic Redox Asymmetry:

  • Misconception: Because $\text{Cr}^{2+}$ and $\text{Mn}^{3+}$ are both $d^4$ species, they share similar redox behavior.
  • Correct Understanding: $\text{Cr}^{2+}$ is a strong reducing agent because losing an electron yields a stable, half-filled $t_{2g}$ configuration ($d^3$) in water. Conversely, $\text{Mn}^{3+}$ is a strong oxidizing agent because gaining an electron yields the highly stable, half-filled $d^5$ configuration.

• [JEE TIP] Trap 3 - The Copper-Acid Exception:

  • Misconception: All $3d$ transition metals liberate $\text{H}_2$ gas when reacted with dilute non-oxidizing acids like $\text{HCl}$.
  • Correct Understanding: Copper ($\text{Cu}$) has a positive standard electrode potential ($E^\circ = +0.34\text{ V}$) and cannot liberate $\text{H}_2$ from acids. It only dissolves in oxidizing acids like $\text{HNO}_3$ or hot concentrated $\text{H}_2\text{SO}_4$, where the acid itself is reduced.

• [JEE TIP] Trap 4 - The Non-Existent Iodide:

  • Misconception: Copper forms stable dihalides ($\text{CuX}_2$) with all halogens.
  • Correct Understanding: Copper(II) Iodide ($\text{CuI}_2$) does not exist. The $\text{Cu}^{2+}$ ion is a sufficiently strong oxidizer to oxidize $\text{I}^-$ to $\text{I}_2$, which results in the spontaneous formation of Copper(I) Iodide ($\text{CuI}$) and free iodine instead.

• [JEE TIP] Trap 5 - High Oxidation Stability War:

  • Misconception: Fluorine stabilizes the highest oxidation states of transition metals better than oxygen because fluorine is the most electronegative element.
  • Correct Understanding: Oxygen is superior to fluorine in stabilizing the highest oxidation states (e.g., the highest manganese fluoride is $\text{MnF}_4$, whereas the highest oxide is $\text{Mn}_2\text{O}_7$). This is because oxygen can form stable multiple bonds ($p\pi-d\pi$) with the metal.

• [JEE TIP] Trap 6 - The d-Block Valency Inversion:

  • Misconception: Just like in the $p$-block (due to the inert pair effect), lower oxidation states become more stable as you move down a group in the $d$-block.
  • Correct Understanding: The trend is exactly the opposite in the $d$-block. Higher oxidation states are more stable for heavier members. For example, in Group 6, $\text{Mo(VI)}$ and $\text{W(VI)}$ are highly stable, whereas $\text{Cr(VI)}$ is unstable and acts as a strong oxidizing agent.

• [JEE TIP] Trap 7 - Permanganate Ph-Dependent Target Switching:

  • Misconception: Potassium permanganate ($\text{KMnO}_4$) always oxidizes iodide ($\text{I}^-$) to free iodine ($\text{I}_2$).
  • Correct Understanding: The product depends strictly on the pH. In an acidic medium, $\text{I}^-$ is oxidized to $\text{I}_2$. However, in a neutral or faintly alkaline medium, $\text{I}^-$ is oxidized all the way to iodate ($\text{IO}_3^-$).

• [JEE TIP] Trap 8 - The Forbidden Titration Acid:

  • Misconception: $\text{KMnO}_4$ titrations in acidic medium can be performed using dilute $\text{HCl}$ to provide the required $\text{H}^+$ ions.
  • Correct Understanding: $\text{HCl}$ cannot be used because $\text{KMnO}_4$ will oxidize the $\text{Cl}^-$ in $\text{HCl}$ into $\text{Cl}_2$ gas, destroying the quantitative accuracy of the titration. Dilute $\text{H}_2\text{SO}_4$ must be used instead.

• [JEE TIP] Trap 9 - Contraction Magnitude Mismatch:

  • Misconception: The lanthanoid contraction is more severe than the actinoid contraction because $4f$ is a lower principal quantum number than $5f$.
  • Correct Understanding: The actinoid contraction is greater from element to element. This is because the $5f$ electrons of actinoids provide even poorer shielding from the increasing nuclear charge than the $4f$ electrons of lanthanoids.

• [JEE TIP] Trap 10 - The Chromate Redox Illusion:

  • Misconception: The conversion of yellow chromate ($\text{CrO}_4^{2-}$) to orange dichromate ($\text{Cr}_2\text{O}_7^{2-}$) in acidic medium is a redox reaction.
  • Correct Understanding: This is purely an acid-base equilibrium controlled by pH. The oxidation state of Chromium remains +6 in both the chromate and dichromate ions.

• [JEE TIP] Trap 11 - The Dichromate Angular Bridge:

  • Misconception: The dichromate ion ($\text{Cr}_2\text{O}_7^{2-}$) consists of two independent chromate units, or features a linear, symmetrical $\text{Cr}-\text{O}-\text{Cr}$ bridging arrangement.
  • Correct Understanding: While the individual chromate ion ($\text{CrO}_4^{2-}$) is a simple tetrahedron, the dichromate ion consists of two tetrahedral units sharing a single oxygen corner. Crucially, the bridging $\text{Cr}-\text{O}-\text{Cr}$ bond is bent, possessing a distinct bond angle of 126°.

• [JEE TIP] Trap 12 - The Lanthanide Colorless Bookends:

  • Misconception: All lanthanide series ions ($\text{Ln}^{3+}$) are intensely colored due to the presence of internal $f$-orbital transitions.
  • Correct Understanding: Color in lanthanides depends strictly on $f-f$ transitions. The series bookends—$\text{La}^{3+}$ ($f^0$) and $\text{Lu}^{3+}$ ($f^{14}$)—are completely colorless because they contain either empty or completely filled $f$-orbitals, making any $f-f$ electronic transitions impossible.

• [JEE TIP] Trap 13 - The Permanganate Overlap Illusion:

  • Misconception: The $\pi$-bonds in oxoanions like permanganate ($\text{MnO}_4^-$) are formed by typical $p\pi-p\pi$ orbital overlapping, similar to carbon-based organic molecules.
  • Correct Understanding: Because manganese is a transition metal, its high oxidation state ($\text{Mn}^{+7}$) heavily relies on its $d$-orbitals for stabilizing bonds. The strong $\pi$-bonding in $\text{MnO}_4^-$ occurs explicitly through the overlap of filled $p$-orbitals from oxygen with the empty $d$-orbitals of manganese ($d\pi-p\pi$ overlap).