Comprehensive Study Notes on d- and f-Block Inorganic Chemistry

Definition and General Introduction to d- and f-Block Elements

• Definition of d-Block Elements: The elements in which the differentiating electron enters into the d-subshell of the penultimate shell, i.e., $(n - 1)d$ subshell, are called transition elements.

• Position: These elements belong to groups $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $11$, and $12$ of the Periodic Table.

• Constituency: They constitute a separate block called the d-block and are all metals.

• General Properties: They show several interesting properties and find a variety of applications in day-to-day life and industry.

• Definition of f-Block Elements: The elements in which the differentiating electron enters into the $(n - 2)f$ subshell are called inner-transition elements.

• Classification of f-Block: These elements are grouped into two series: the Lanthanoid series and the Actinoid series. They are placed separately at the bottom of the Periodic Table.

The Transition Elements or d-Block Elements

• Position in the Periodic Table:     - The d-block is situated in the middle of the Periodic Table between group $2$ and group $13$.     - It is flanked by the s-block (highly electropositive elements) and the p-block (weakly electropositive or electronegative elements).     - Transition Nomenclature: The name "transition" is given because these elements show a transitional behavior between the s-block elements (which form ionic compounds) and p-block elements (which have a tendency to form covalent compounds).

• Classification into Series:     - Transition elements are classified into four horizontal series based on the $(n - 1)d$ subshell being filled:         - First transition series (3d-series): Corresponds to the filling of the $3d$ subshell. It consists of ten elements from $Sc$ ($At. No. = 21$) to $Zn$ ($At. No. = 30$) in the $4^{th}$ period.         - Second transition series (4d-series): Corresponds to the filling of the $4d$ subshell. It consists of ten elements from $Y$ ($At. No. = 39$) to $Cd$ ($At. No. = 48$) in the $5^{th}$ period.         - Third transition series (5d-series): Corresponds to the filling of the $5d$ subshell. It consists of ten elements, starting with $La$ ($At. No. = 57$) followed by those from $Hf$ ($At. No. = 72$) to $Hg$ ($At. No. = 80$) in the $6^{th}$ period.         - Fourth transition series (6d-series): Corresponds to the filling of the $6d$ subshell. It consists of $Ac$ ($At. No. = 89$) and elements with atomic numbers $104$ and above, belonging to the $7^{th}$ period.

Electronic Configuration of Transition Elements

• General Formula: The general electronic configuration is $(n - 1)d^{1-10} ns^{1-2}$.

• First Transition Series (3d-series):     - Scandium ($Sc$, $21$): $[Ar] 3d^{1} 4s^{2}$     - Titanium ($Ti$, $22$): $[Ar] 3d^{2} 4s^{2}$     - Vanadium ($V$, $23$): $[Ar] 3d^{3} 4s^{2}$     - Chromium ($Cr$, $24$): $[Ar] 3d^{5} 4s^{1}$ (Exceptional due to half-filled stability)     - Manganese ($Mn$, $25$): $[Ar] 3d^{5} 4s^{2}$     - Iron ($Fe$, $26$): $[Ar] 3d^{6} 4s^{2}$     - Cobalt ($Co$, $27$): $[Ar] 3d^{7} 4s^{2}$     - Nickel ($Ni$, $28$): $[Ar] 3d^{8} 4s^{2}$     - Copper ($Cu$, $29$): $[Ar] 3d^{10} 4s^{1}$ (Exceptional due to completely filled stability)     - Zinc ($Zn$, $30$): $[Ar] 3d^{10} 4s^{2}$

• Second Transition Series (4d-series):     - Yttrium ($Y$, $39$): $[Kr] 4d^{1} 5s^{2}$     - Zirconium ($Zr$, $40$): $[Kr] 4d^{2} 5s^{2}$     - Niobium ($Nb$, $41$): $[Kr] 4d^{4} 5s^{1}$     - Molybdenum ($Mo$, $42$): $[Kr] 4d^{5} 5s^{1}$     - Technetium ($Tc$, $43$): $[Kr] 4d^{5} 5s^{2}$     - Ruthenium ($Ru$, $44$): $[Kr] 4d^{7} 5s^{1}$     - Rhodium ($Rh$, $45$): $[Kr] 4d^{8} 5s^{1}$     - Palladium ($Pd$, $46$): $[Kr] 4d^{10} 5s^{0}$     - Silver ($Ag$, $47$): $[Kr] 4d^{10} 5s^{1}$     - Cadmium ($Cd$, $48$): $[Kr] 4d^{10} 5s^{2}$

• Third Transition Series (5d-series):     - Lanthanum ($La$, $57$): $[Xe] 5d^{1} 6s^{2}$     - Hafnium ($Hf$, $72$): $[Xe] 4f^{14} 5d^{2} 6s^{2}$     - Tantalum ($Ta$, $73$): $[Xe] 4f^{14} 5d^{3} 6s^{2}$     - Tungsten ($W$, $74$): $[Xe] 4f^{14} 5d^{4} 6s^{2}$     - Rhenium ($Re$, $75$): $[Xe] 4f^{14} 5d^{5} 6s^{2}$     - Osmium ($Os$, $76$): $[Xe] 4f^{14} 5d^{6} 6s^{2}$     - Iridium ($Ir$, $77$): $[Xe] 4f^{14} 5d^{7} 6s^{2}$     - Platinum ($Pt$, $78$): $[Xe] 4f^{14} 5d^{9} 6s^{1}$     - Gold ($Au$, $79$): $[Xe] 4f^{14} 5d^{10} 6s^{1}$     - Mercury ($Hg$, $80$): $[Xe] 4f^{14} 5d^{10} 6s^{2}$

• Fourth Transition Series (6d-series):     - Actinium ($Ac$, $89$): $[Rn] 6d^{1} 7s^{2}$     - Rutherfordium ($Rf$, $104$): $[Rn] 5f^{14} 6d^{2} 7s^{2}$     - Dubnium ($Db$, $105$): $[Rn] 5f^{14} 6d^{3} 7s^{2}$     - Seaborgium ($Sg$, $106$): $[Rn] 5f^{14} 6d^{4} 7s^{2}$     - Bohrium ($Bh$, $107$): $[Rn] 5f^{14} 6d^{5} 7s^{2}$     - Hassium ($Hs$, $108$): $[Rn] 5f^{14} 6d^{6} 7s^{2}$     - Meitnerium ($Mt$, $109$): $[Rn] 5f^{14} 6d^{7} 7s^{2}$     - Darmstadtium ($Ds$, $110$): $[Rn] 5f^{14} 6d^{8} 7s^{2}$     - Roentgenium ($Rg$, $111$): $[Rn] 5f^{14} 6d^{10} 7s^{1}$     - Copernicium ($Cn$, $112$): $[Rn] 5f^{14} 6d^{10} 7s^{2}$

Exceptional Configurations and Stability

• Stability of Half-filled and Completely Filled Subshells: Subshells of type $p^{6}, d^{10}$ (completely filled) or $p^{3}, d^{5}$ (half-filled) possess extra stability. This is explained by symmetrical distribution of electrons and maximum exchange energy.

• Chromium ($Cr$): Expected configuration is $3d^{4} 4s^{2}$. However, inter-electronic repulsion forces one $4s$ electron into the $3d$ subshell, resulting in $3d^{5} 4s^{1}$. Both are half-filled, imparting extra stability.

• Copper ($Cu$): Expected configuration is $3d^{9} 4s^{2}$. Inter-electronic repulsion forces one $4s$ electron into the $3d$ subshell, resulting in $3d^{10} 4s^{1}$. The $d$ subshell becomes completely filled.

Refined Definition of Transition Elements

• Incomplete d-orbitals: Transition elements are strictly defined as those which possess incompletely filled d-orbitals in their ground state or in any chemically significant oxidation state.

• Status of Copper ($Cu$): Although $Cu$ ($3d^{10} 4s^{1}$) and $Cu^{+}$ ($3d^{10}$) have filled d-subshells, the $Cu^{2+}$ ion has a partly filled configuration ($3d^{9}$). Thus, copper is regarded as a transition element in the $+2$ oxidation state.

• Status of Zinc, Cadmium, and Mercury:     - Zinc ($Zn$): Ground state is $3d^{10} 4s^{2}$; $Zn^{2+}$ is $3d^{10}$. It lacks partly filled d-orbitals.     - Cadmium ($Cd$): Ground state is $4d^{10} 5s^{2}$; $Cd^{2+}$ is $4d^{10}$.     - Mercury ($Hg$): Ground state is $5d^{10} 6s^{2}$; $Hg^{2+}$ is $5d^{10}$.     - Conclusion: $Zn, Cd,$ and $Hg$ are not transition elements in the true sense as they possess completely filled d-orbitals. However, they are studied with d-block elements to maintain a rational classification.

General Properties and Periodic Trends

• Atomic Radii:     - Radii of transition elements lie between those of s- and p-block elements.     - Trends Within a Series:         1. Initial Decrease: Radii decrease with increasing atomic number due to increased nuclear charge. Added electrons enter the $(n - 1)d$ subshell and shield the outermost electrons.         2. Mid-Series Constancy: From $Mn$ ($3d^{5}$) to $Ni$ ($3d^{8}$), the shielding effect of $(n - 1)d$ electrons counterbalances the increased nuclear charge, keeping radii almost constant.         3. End-Series Increase: At the end ($Cu$ and $Zn$), electron-electron repulsions between paired electrons in the same orbitals predominate over nuclear attraction, causing the electron cloud to expand and radii to increase.     - Trends Down a Group:         1. Radii increase from the first to the second transition series due to more electronic shells.         2. Radii of the second and third transition series are nearly identical (e.g., $Zr ≈ Hf$) due to Lanthanoid Contraction.

• Ionic Radii:     - Follow the same trends as atomic radii.     - Radii decrease as the oxidation state increases.     - For the same oxidation state, radii generally decrease with increasing nuclear charge across a series.     - Bivalent Ion Data ($M^{2+}$ in pm):         - $Ti^{2+}: 82$         - $V^{2+}: 79$         - $Cr^{2+}: 82$         - $Mn^{2+}: 82$         - $Fe^{2+}: 77$         - $Co^{2+}: 75$         - $Ni^{2+}: 70$         - $Cu^{2+}: 73$         - $Zn^{2+}: 75$

• Metallic Properties:     - Transition elements exhibit typical metallic properties: lustre, malleability, ductility, high tensile strength, and high thermal/electrical conductivity.     - Lattice Structure: Except for $Zn, Cd, Hg$, and $Mn$, they possess typical metallic structures at normal temperatures.