d and f Block Elements: Properties, Trends, and Inorganic Chemistry Fundamentals

Definition of Transition Elements: Elements whose atoms or simple ions contain partially filled d-orbitals. Examples provided include $Ti$ and $Ti^{2+}$ , while $Zn$ and $Zn^{2+}$ are noted in the context of d-orbital occupancy.
Variable Oxidation States: Transition elements exhibit variable oxidation states due to the very similar energy levels of the $ns$ and $(n - 1)d$ orbitals. Electrons from both subshells can participate in chemical bonding.
Orbital Configuration: The d-block elements encompass the groups where the d-subshell is being filled. The transcript lists a sequence of elements including $Sc$ , $Ti$ , $V$ , $Cr$ , $Mn$ , $Fe$ , $Co$ , $Ni$ , $Cu$ , $Zn$ , as well as heavier series members like $Y$ , $Zr$ , $Nb$ , $Mo$ , $Tc$ , $Ru$ , $Rh$ , $Pd$ , $Ag$ , $Cd$ , and $La$ , $Hf$ , $Ta$ , $W$ , $Re$ , $Os$ , $Ir$ , $Pt$ , $Au$ , $Hg$ .

Common Oxidation States of the 3d Series:
- $Sc$ : +3 (Most common). It shows ONLY this oxidation state.
- $Ti$ : +2, +3, +4
- $V$ : +2, +3, +4, +5
- $Cr$ : +2, +3, +4, +5, +6
- $Mn$ : +2, +3, +4, +5, +6, +7
- $Fe$ : +2, +3, +4, +6
- $Co$ : +2, +3, +4
- $Ni$ : +2, +3, +4
- $Cu$ : +1, +2
- $Zn$ : +2 (Only)
Specific Observations:
- Scandium ( $Sc$ ): $Sc^{2+}$ is not known. It exists primarily as $Sc^{3+}$ because this ion achieves a stable inert gas configuration.
- Titanium ( $Ti$ ): $Ti^{4+}$ is more stable than $Ti^{2+}$ or $Ti^{3+}$ due to its inert gas configuration.
- Zinc ( $Zn$ ): Exhibits only the +2 oxidation state because the $Zn^{2+}$ ion has a stable $[Ar]3d^{10}$ configuration.
- Highest Oxidation States: In the 3d series, the maximum oxidation state is reached at Manganese ( $Mn$ ) with +7. For the d-block as a whole, the highest oxidation state is +8, exhibited by Ruthenium ( $Ru$ ) and Osmium ( $Os$ ).
- Calculation Rule: From $Sc$ to $Mn$ , the maximum oxidation state corresponds to the sum of the number of electrons in the 's' and 'd' subshells.

Oxidation State Increments: In transition elements, oxidation states typically differ by units of one (e.g., $V^{2+}, V^{3+}, V^{4+}, V^{5+}+$ ). In contrast, non-transition (p-block) elements often differ by units of two (e.g., $Pb^{2+}, Pb^{4+}$ ).
Stability in Heavy Elements:
- In the p-block, the "inert pair effect" makes lower oxidation states more stable for heavier elements ( $Tl, Pb, Bi$ ).
- In the d-block, the opposite is true: higher oxidation states are more stable in heavier elements. For example, $Mo(+6)$ and $W(+6)$ are more stable than $Cr(+6)$ .
Oxidizing Nature: $K_2Cr_2O_7$ in acidic medium ( $H^+$ ) is a strong oxidizing agent because $Cr(+6)$ readily reduces itself to $Cr(+3)$ . However, $MoO_3$ and $WO_3$ are not typical oxidizing agents.
Low Oxidation States: Metal atoms can exhibit zero or low oxidation states when bonded with ligands that are both $\sigma$ donors and $\pi$ acceptors, such as Carbon Monoxide ( $CO$ ). Examples include Nickel tetracarbonyl $Ni(CO)_4$ and Iron pentacarbonyl $Fe(CO)_5$ .

3d Series Atomic Radius Trends:
- Sc to Cr: Radius decreases because the increase in nuclear charge dominates over other factors.
- Mn to Ni: Radius remains nearly constant. This occurs because the increasing Nuclear Charge ( $NC$ ) is balanced by increasing Inter-Electron Repulsion ( $IER$ ).
- Cu to Zn: Radius slightly increases because Inter-Electron Repulsion ( $IER$ ) dominates over the nuclear charge effect.
Lanthanoid Contraction:
- Definition: A fairly regular decrease in the sizes of atoms and ions with increasing atomic number throughout the Lanthanoid series ( $La$ to $Lu$ ).
- Cause: This is attributed to the imperfect shielding of one $4f$ electron by another in the same subshell. The shielding effect of $4f$ electrons is weaker than that of d electrons.
- Consequence: The radii of elements in the $5d$ series are very similar to the corresponding members of the $4d$ series. For example, $Zr$ and $Hf$ have nearly identical sizes.
- Practical Impact: Because of similar sizes, elements like $Zr$ and $Hf$ possess very similar physical and chemical properties, making their separation extremely difficult.

Trend: General increase in density across a period from left to right (from $Sc$ to $Cu$ ). This is due to the decrease in metallic radius coupled with an increase in atomic mass.
Density Values ( $g/cm^3$ ):
- $Sc$ : 3.43
- $Ti$ : 4.1
- $V$ : 6.07
- $Cr$ : 7.19
- $Mn$ : 7.21
- $Fe$ : 7.8
- $Co$ : 8.7
- $Ni$ : 8.9
- $Cu$ : 8.9
- $Zn$ : 7.1
Specific Density Facts:
- Density of $Cu$ (8.9) is higher than $Zn$ (7.1) because the metallic radius of $Zn$ is larger than that of $Cu$ .
- The highest densities in the periodic table are found in Osmium ( $Os = 22.51\,g/cm^3$ ) and Iridium ( $Ir = 22.61\,g/cm^3$ ).

Definition: A mixture of metals in a definite ratio in the solid state.
Formation Principle: d-block elements exhibit similar atomic sizes. For two metals to form an alloy, their sizes must differ by no more than approximately $15\%$ . This allows one metal atom to replace another within the metallic crystal lattice.
Examples of Alloys:
- Brass: $Cu + Zn$
- Bronze: $Cu + Sn$
- Gun metal / Bell metal: $Cu + Zn + Sn$
- Stainless Steel: $C + Fe + Cr + Ni$
Note on Currency: UK "copper" coins are copper-coated steel, while UK "silver" coins are a $Cu/Ni$ alloy.

Oxidation State Identification: Calculate OS for metals in Oxides/Oxo-ions: $Sc_2O_3$ , $TiO_2$ , $VO_{2}^{+}$ , $CrO_4^{2-}$ , $MnO_4^{-}$ .
Oxidizing Agents: Question regarding which among $CrO_3$ , $MoO_3$ , $WO_3$ , and $CrO_4^{2-}$ will NOT act as oxidizing agents. (Answer: $MoO_3$ and $WO_3$ ).
Variable Oxidation States: Which element does NOT usually show variable states? (Options: $Ti, V, Sc, Cu$ . Answer: $Sc$ ).
Color in Solid State: Transition elements usually form colored salts due to unpaired electrons. Which is colored: $Ag_2SO_4$ , $CuF_2$ , $ZnF_2$ , or $Cu_2Cl_2$ ? (Answer: $CuF_2$ possesses unpaired electrons).
Correct Statements (JEE 2023):
1. Manganese exhibits +7 in its oxide.
2. Ruthenium and Osmium exhibit +8 in oxides.
3. $Sc$ shows +4 (False, it shows +3).
4. $Cr$ is oxidizing in +6 state.
- Selected Correct: (i), (ii), and (iv).
Atomic Radius Comparison: Atomic radius of $Ag$ is closest to $Au$ . Pairs with similar radii include $Ti$ and $Hf$ (Incorrect match, it should be $Zr$ and $Hf$ based on $4d/5d$ series) and $Mo$ and $W$ .