Comprehensive Study Guide on the Modern Periodic Table and Periodic Properties

Early Classifications and Periodic Laws

• Döbereiner's Law of Triads:

  • Elements are organized into groups of three (triads) in which the atomic mass of the middle element is approximately the arithmetic average of the atomic masses of the other two elements.

  • Observed Triad Examples:

  • Lithium ($Li$, $A = 7$), Sodium ($Na$, $A = 23$), Potassium ($K$, $A = 39$), where $\frac{7 + 39}{2} = 23$.

  • Calcium ($Ca$, $A = 40$), Strontium ($Sr$, $A = 88$), Barium ($Ba$, $A = 137$), where $\frac{40 + 137}{2} = 88.5 \to 88$.

  • Chlorine ($Cl$, $A = 35.5$), Bromine ($Br$, $A = 80$), Iodine ($I$, $A = 127$), where $\frac{35.5 + 127}{2} = 81.25 \to 80$.

  • Phosphorus ($P$, $A = 31$), Arsenic ($As$, $A = 75$), Antimony ($Sb$, $A = 120$), where $\frac{31 + 120}{2} = 75.5 \to 75$.

  • Sulfur ($S$, $A = 32$), Selenium ($Se$, $A = 79$), Tellurium ($Te$, $A = 127$), where $\frac{32 + 127}{2} = 79.5 \to 79$.

  • Condition for Triads using Atomic Number ($Z$):

  • Triads can be identified without atomic masses if elements $A$, $B$, and $C$ with atomic numbers $Z_A = x$, $Z_B = y$, and $Z_C = z$ satisfy the relationship:       $(y - x) = (z - y)$

• Lothar Meyer Curve:

  • Physical properties such as atomic volume, melting point (MP), and boiling point (BP) were plotted against atomic mass.

  • Position assignment on the Atomic Volume vs. Atomic Mass curve:

  • Curve Maxima (peaks): Occupied by Group 1 alkali metals ($Li$, $Na$, $K$, $Rb$, $Cs$).

  • Descending Slopes: Occupied by Group 2 alkaline earth metals ($Be$, $Mg$, $Ca$, $Sr$, $Ba$).

  • Ascending Slopes: Occupied by halogens ($F$, $Cl$, $Br$, $I$).

  • Curve Minima (troughs): Occupied by transition metals and heavy metals.

• Moseley's Experiment and the Modern Periodic Law:

  • Proposed by Henry Moseley, establishing atomic number ($Z$) rather than atomic mass as the fundamental property of elements.

  • Moseley bombarded various metal targets with high-speed electrons and analyzed the frequencies ($\nu$) of the resulting characteristic X-rays.

  • Mathematical relation discovered from X-ray spectra:     $\sqrt{\nu} = a(Z - b)$     $\sqrt{\nu} \propto Z$

  • Here, $\nu$ represents X-ray frequency, $Z$ represents atomic number, and $a$ and $b$ are constants.

  • Statement of Modern Periodic Law: The physical and chemical properties of elements are periodic functions of their atomic numbers.

Modern Periodic Table Architecture and Classifications

• Periods in the Modern Periodic Table:

  • The modern periodic table comprises seven horizontal rows termed periods.

  • Characteristics of the seven periods:

  • Period 1: Outermost shell $n = 1$; contains $1s$ subshell; capacity of 2 elements; designated as the shortest period.

  • Period 2: Outermost shell $n = 2$; contains $2s, 2p$ subshells; capacity of 8 elements; designated as a short period.

  • Period 3: Outermost shell $n = 3$; contains $3s, 3p$ subshells; capacity of 8 elements; designated as a short period.

  • Period 4: Outermost shell $n = 4$; contains $4s, 3d, 4p$ subshells; capacity of 18 elements; designated as a long period.

  • Period 5: Outermost shell $n = 5$; contains $5s, 4d, 5p$ subshells; capacity of 18 elements; designated as a long period.

  • Period 6: Outermost shell $n = 6$; contains $6s, 4f, 5d, 6p$ subshells; capacity of 32 elements; designated as the longest period.

  • Period 7: Outermost shell $n = 7$; contains $7s, 5f, 6d, 7p$ subshells; capacity of 32 elements; designated as the longest period.

  • General Subshell Filling Order in a Period:

  • Subshell filling begins with $ns$ and terminates with $np$:       $ns \rightarrow (n - 2)f \rightarrow (n - 1)d \rightarrow np$

  • Structural Period Formulas:

  • Period Number = Outermost shell principal quantum number ($n$).

  • Number of elements in a period = Maximum number of electrons accommodated in the period subshells.

    • Example: Period 6 houses $6s^2 + 4f^{14} + 5d^{10} + 6p^6 = 32$ electrons, translating to 32 elements.

  • Number of elements in period $n$ based on parity:       $\text{Elements} = \frac{(n + 2)^2}{2} \quad (\text{when } n \text{ is even})$       $\text{Elements} = \frac{(n + 1)^2}{2} \quad (\text{when } n \text{ is odd})$

  • Number of period subshells:       $\text{Number of period subshells} = \frac{\text{Number of elements}}{2}$

• IUPAC Nomenclature for Elements with Atomic Number $Z > 100$:

  • Systematic names end with the suffix "-ium" and are synthesized from atomic digit word roots:

  • 0 = nil

  • 1 = un

  • 2 = bi

  • 3 = tri

  • 4 = quad

  • 5 = pent

  • 6 = hex

  • 7 = sept

  • 8 = oct

  • 9 = enn

  • Example: Element with $Z = 143$ is named Unquadtrium (symbol: Uqt).

• Bohr's Classification of Elements:

  • Inert Gases: Elements featuring a completely filled outermost shell; restricted to Group 18.

  • Normal / Representative Elements: Elements possessing a partially filled outermost shell; encompasses all s-block and p-block elements except Group 18.

  • Transition Elements: Elements with partially filled outermost $n$th and penultimate $(n - 1)$th shells in their atomic or ionic states; encompasses the entire d-block excluding $Zn$, $Cd$, $Hg$, and $Uub$.

  • Inner Transition Elements: Elements possessing incompletely filled $n$th, $(n - 1)$th, and antepenultimate $(n - 2)$th shells; encompasses the entire f-block totaling 28 elements.

• Key Definitions and Classifications:

  • Typical Elements: Elements of the 3rd period (excluding the noble gas Argon) that characterize the properties of their respective vertical groups ($Na$, $Mg$, $Al$, $Si$, $P$, $S$, $Cl$).

  • Diagonal Relationship: Diagonal pairs between 2nd and 3rd period elements of adjacent groups showing similar physical and chemical traits ($Li$ with $Mg$, $Be$ with $Al$, $B$ with $Si$).

  • Cause: Nearly identical ionic potential values ($\phi = \frac{\text{charge}}{\text{radius}}$).

  • Scope: Valid only up to Group 14.

  • Bridge Elements:

  • Mendeleev's Periodic Table classification: 3rd period elements ($Na$, $Mg$, $Al$) serve as bridge elements.

  • Modern Periodic Table classification: 2nd period elements ($Li$, $Be$, $B$) serve as bridge elements.

  • Unless specified, convention requires identifying bridge elements according to Mendeleev's Periodic Table.

  • Transuranium Elements: Elements possessing atomic numbers $Z > 92$. All transuranium elements are synthetic (man-made) and radioactive.

  • Periodicity: The regular recurrence of physical and chemical properties at uniform atomic intervals resulting from similar outer valence shell electronic configurations. Periodic properties include atomic radius, ionic potential, electronegativity, and electron affinity.

Electronic Configurations of the Blocks

• General Electronic Configurations of Groups:

  • Group IA (Alkali Metals): $ns^1$ (where $n \ge 2$; Hydrogen is excluded as an alkali metal).

  • Group IIA (Alkaline Earth Metals): $ns^2$.

  • Group IIIA (Boron Family): $ns^2\,np^1$.

  • Group IVA (Carbon Family): $ns^2\,np^2$.

  • Group VA (Pnictogens): $ns^2\,np^3$.

  • Group VIA (Chalcogens): $ns^2\,np^4$.

  • Group VIIA (Halogens): $ns^2\,np^5$.

  • Group 0 / Inert Gases: $ns^2\,np^6$ (Helium possesses the exception $1s^2$).

  • Group Anomalies: Outer shell configurations are generally identical across a group, except in Groups 5, 6, 8, 9, 10, and 18.

  • Group 10 configuration divergence:

    • Nickel ($Ni$, $Z = 28$): $3d^8\,4s^2$

    • Palladium ($Pd$, $Z = 46$): $4d^{10}\,5s^0$

    • Platinum ($Pt$, $Z = 78$): $5d^9\,6s^1$

• d-Block Electron Configurations and Non-Existent States:

  • Forbidden Electron States:

  • In the $3d$ series: Configurations $3d^4$ and $3d^9$ never occur.

  • In the $4d$ series: Configurations $4d^3$, $4d^6$, and $4d^9$ never occur.

  • In the $5d$ series: Configuration $5d^8$ never occurs.

  • Specific Configuration Examples and Justifications:

  • Chromium ($_{24}Cr$): $3d^5\,4s^1$ (avoids $3d^4$; extra stability of half-filled subshell).

  • Copper ($_{29}Cu$): $3d^{10}\,4s^1$ (avoids $3d^9$; extra stability of fully-filled subshell).

  • Niobium ($_{41}Nb$): $4d^4\,5s^1$ (avoids forbidden $4d^3$).

  • Molybdenum ($_{42}Mo$): $4d^5\,5s^1$ ($4d^5$ is more stable).

  • Technetium ($_{43}Tc$): Recorded as $4d^5\,5s^2$ (NCERT XII) and $4d^6\,5s^1$ (NCERT XI).

  • Ruthenium ($_{44}Ru$): $4d^7\,5s^1$ (avoids forbidden $4d^6$).

  • Rhodium ($_{45}Rh$): $4d^8\,5s^1$ (stabilized by $t_{2g}^6\,e_g^2$ subshell distribution).

  • Palladium ($_{46}Pd$): $4d^{10}\,5s^0$ (avoids forbidden $4d^9$; fully-filled $4d^{10}$ is stable).

  • Silver ($_{47}Ag$): $4d^{10}\,5s^1$ (avoids forbidden $4d^9$).

  • Platinum ($_{78}Pt$): $5d^9\,6s^1$ (avoids forbidden $5d^8$).

  • Gold ($_{79}Au$): $5d^{10}\,6s^1$.

  • Roentgenium ($_{111}Rg$): Displays $6d^{10}\,7s^1$ (note notation cites $7d^{10}\,5s^1$ / $d^9$ instability).

• f-Block Configurations: Lanthanoids and Actinoids:

  • Lanthanoids ($4f$ Series):

  • Baseline Reference: Core of $[Xe] + 6s^2 = 56\,e^-$.

  • Presence of $5d^1$: Only Cerium ($_{58}Ce$), Gadolinium ($_{64}Gd$), and Lutetium ($_{71}Lu$) contain an electron in $5d$ ($5d^1$). All other 11 lanthanoids possess $5d^0$, with successive filling occurring directly in $4f$.

  • Complete Series Configurations:

    • $_{58}Ce = [Xe]\,4f^1\,5d^1\,6s^2$

    • $_{59}Pr = [Xe]\,4f^3\,5d^0\,6s^2$

    • $_{60}Nd = [Xe]\,4f^4\,5d^0\,6s^2$

    • $_{61}Pm = [Xe]\,4f^5\,5d^0\,6s^2$

    • $_{62}Sm = [Xe]\,4f^6\,5d^0\,6s^2$

    • $_{63}Eu = [Xe]\,4f^7\,5d^0\,6s^2$

    • $_{64}Gd = [Xe]\,4f^7\,5d^1\,6s^2$

    • $_{65}Tb = [Xe]\,4f^9\,5d^0\,6s^2$

    • $_{66}Dy = [Xe]\,4f^{10}\,5d^0\,6s^2$

    • $_{67}Ho = [Xe]\,4f^{11}\,5d^0\,6s^2$

    • $_{68}Er = [Xe]\,4f^{12}\,5d^0\,6s^2$

    • $_{69}Tm = [Xe]\,4f^{13}\,5d^0\,6s^2$

    • $_{70}Yb = [Xe]\,4f^{14}\,5d^0\,6s^2$

    • $_{71}Lu = [Xe]\,4f^{14}\,5d^1\,6s^2$

  • Mnemonic for Lanthanoid Element Names:

    • "Ce (Sir) Pr (Pe) Nd (Nandu) Pm (Prasad) Sm (Singh), Eu (English) Gd (Guide) Tb (Tution) Dy (dete) Ho (ho), Er (Engineer) Tm (Tumhare) Yb (Yaha) Lu (Lally)"

  • Actinoids ($5f$ Series):

  • Baseline Reference: Core of $[Rn] + 7s^2 = 88\,e^-$.

  • The initial four elements ($Th$, $Pa$, $U$, $Np$) and Curium ($_{96}Cm$) maintain exceptional $6d^1$ or $6d^2$ configurations.

  • Complete Series Configurations:

    • $_{90}Th = [Rn]\,5f^0\,6d^2\,7s^2$

    • $_{91}Pa = [Rn]\,5f^2\,6d^1\,7s^2$

    • $_{92}U = [Rn]\,5f^3\,6d^1\,7s^2$

    • $_{93}Np = [Rn]\,5f^4\,6d^1\,7s^2$

    • $_{94}Pu = [Rn]\,5f^6\,6d^0\,7s^2$

    • $_{95}Am = [Rn]\,5f^7\,6d^0\,7s^2$

    • $_{96}Cm = [Rn]\,5f^7\,6d^1\,7s^2$

    • $_{97}Bk = [Rn]\,5f^9\,6d^0\,7s^2$

    • $_{98}Cf = [Rn]\,5f^{10}\,6d^0\,7s^2$

    • $_{99}Es = [Rn]\,5f^{11}\,6d^0\,7s^2$

    • $_{100}Fm = [Rn]\,5f^{12}\,6d^0\,7s^2$

    • $_{101}Md = [Rn]\,5f^{13}\,6d^0\,7s^2$

    • $_{102}No = [Rn]\,5f^{14}\,6d^0\,7s^2$

    • $_{103}Lr = [Rn]\,5f^{14}\,6d^1\,7s^2$

  • Mnemonic for Actinoid Element Names:

    • "Th (Thapa) Pa (Pa) U (U), Np (Nepali), Pu (Pure) Am (aam) Cm (chakh) Bk (chat), Cf (Kyo) Es (isse) Fm (fit) Md (mOAn) No (na) Lr (Ladu?)"

• Rules for Identifying Group and Period:

  • Case 1: When Atomic Number ($Z$) is Given:

  • Step 1: Check f-block ranges:

    • If $58 \le Z \le 71$: Lanthanoids $\implies$ Period = 6, Group = IIIB (Group 3).

    • If $90 \le Z \le 103$: Actinoids $\implies$ Period = 7, Group = IIIB (Group 3).

  • Step 2: Correlate with Noble Gas Atomic Numbers (Magic Numbers: 2, 8, 8, 18, 18, 32, 32):

    • $He$: $Z = 2$ (Period 1)

    • $Ne$: $Z = 10$ (Period 2)

    • $Ar$: $Z = 18$ (Period 3)

    • $Kr$: $Z = 36$ (Period 4)

    • $Xe$: $Z = 54$ (Period 5)

    • $Rn$: $Z = 86$ (Period 6)

    • $Og$: $Z = 118$ (Period 7)

  • Step 3: For other atomic numbers, identify the next highest noble gas ($Z_{\text{inert}}$). The element shares the period of that noble gas.

    • Compute the group number:         $\text{Group} = 18 - [Z_{\text{inert}} - Z_{\text{given}}]$

    • If this yields a negative value, substitute 32 in place of 18:         $\text{Group} = 32 - [Z_{\text{inert}} - Z_{\text{given}}]$

    • Example: Determine location of $Z = 42$:

    • The succeeding noble gas is $Xe$ ($Z = 54$, Period 5).

    • Period = 5.

    • Group = $18 - (54 - 42) = 18 - 12 = 6$.

  • Case 2: When Electronic Configuration is Given:

  • Period Number = Outermost principal quantum shell ($n$) found in $ns$ or $np$.

  • Group Number Rules:

    • If $np$ electrons are present, the element belongs to the p-block:         $\text{Group} = 12 + (np \text{ electrons})$

    • If $np$ electrons are absent:

    • If only $ns^{1-2}$ electrons are present with $(n - 1)d$ and $(n - 2)f$ vacant, it is an s-block element:           $\text{Group} = ns \text{ electrons}$

    • If both $(n - 2)f^{1-14}$ and $(n - 1)d^{0-1}\,ns^2$ electrons are present, it is an f-block element:           $\text{Group} = 3 \text{ (IIIB)}$

    • If an incomplete d-subshell $(n - 1)d^{1-10}\,ns^{0-2}$ is present, it is a d-block element:           $\text{Group} = (n - 1)d \text{ electrons} + ns \text{ electrons}$

Effective Nuclear Charge and Slater's Rules

• Concepts of Shielding and Effective Nuclear Charge ($Z_{\text{eff}}$):

  • In multi-electron systems, the net positive nuclear charge experienced by a valence electron is reduced by intervening electrons through the screening or shielding effect.

  • Fundamental Equation:     $Z_{\text{eff}} = Z - \sigma$

  • Here, $Z$ represents the nuclear charge (atomic number) and $\sigma$ represents the screening constant.

  • Screening Mechanism: Shielding is caused strictly by electrons in the same principal shell or inner shells. Electrons situated in outer shells (to the right of the reference electron) contribute zero shielding.

  • Penetration Effect: Electrons residing closer to the nucleus provide greater shielding. Subshell screening efficiency follows the sequence:     $s > p > d > f$

• Slater's Rules for Computing Screening Constant ($\sigma$):

  • Grouping the electron configuration from left to right:     $(1s)\,(2s, 2p)\,(3s, 3p)\,(3d)\,(4s, 4p)\,(4d)\,(4f)\,(5s, 5p)\dots$

  • Rules for a Test Electron in an $ns$ or $np$ Orbital:

  • Other electrons in the same $(ns, np)$ group contribute $0.35$ each toward $\sigma$.

  • Electrons in the penultimate $(n - 1)$ shell contribute $0.85$ each.

  • Electrons in the antepenultimate $(n - 2)$ and all deeper shells contribute $1.00$ each.

  • Rules for a Test Electron in an $nd$ or $nf$ Orbital:

  • Other electrons in the same $(nd)$ or $(nf)$ group contribute $0.35$ each toward $\sigma$.

  • All electrons residing in groups to the left (all inner shells) contribute $1.00$ each.

  • Electrons residing to the right of the test electron contribute $0.00$.

  • Two-Electron Species Exception ($He$, $Li^+$, $Be^{2+}$):

  • The screening of one electron on the other within a $1s^2$ configuration equals $0.30$ (not $0.35$).

  • Examples:       $(Z_{\text{eff}})_{He} = 2 - 0.30 = 1.7$       $(Z_{\text{eff}})_{Be^{2+}} = 4 - 0.30 = 3.7$

  • Shell Symmetry Rule: $Z_{\text{eff}}$ experienced by an $ns$ electron is identical to that experienced by an $np$ electron in the same shell ($Z^*$ on $3s$ of $Fe = Z^*$ on $3p$ of $Fe = 15.45$).

• Calculations of $Z_{\text{eff}}$:

  • Calculation for a $3d$ electron of Iron ($Fe$, $Z = 26$):

  • Grouping: $(1s^2)\,(2s^2, 2p^6)\,(3s^2, 3p^6)\,(3d^6)\,(4s^2)$

  • The two $4s$ electrons sit on the right and contribute $0$.

  • Remaining 5 electrons in $3d$ contribute: $5 \times 0.35 = 1.75$.

  • Inner 18 electrons contribute: $18 \times 1.00 = 18.00$.

  • Total $\sigma = 18.00 + 1.75 = 19.75$.

  • Effective nuclear charge:       $Z_{\text{eff}} = 26 - 19.75 = 6.25$

  • Calculation for the valence electron of Sodium ($Na$, $Z = 11$):

  • Grouping: $(1s^2)\,(2s^2, 2p^6)\,(3s^1)$

  • Zero other electrons in $3s$: $0 \times 0.35 = 0$.

  • 8 electrons in penultimate shell ($n = 2$): $8 \times 0.85 = 6.8$.

  • 2 electrons in inner shell ($n = 1$): $2 \times 1.00 = 2.0$.

  • Total $\sigma = 2.0 + 6.8 + 0 = 8.8$.

  • Effective nuclear charge:       $Z_{\text{eff}} = 11 - 8.8 = 2.2$

• Empirical Trends of $Z^*$ ($Z_{\text{eff}}$):

  • Across Period 2 and Period 3: $Z^*$ increases by exactly $0.65$ for each step across both the 2nd and 3rd periods:

  • Period 2: $Li\,(1.30) \rightarrow Be\,(1.95) \rightarrow B\,(2.60) \rightarrow C\,(3.25) \rightarrow N\,(3.90) \rightarrow O\,(4.55) \rightarrow F\,(5.20) \rightarrow Ne\,(5.85)$

  • Period 3: $Na\,(2.20) \rightarrow Mg\,(2.85) \rightarrow Al\,(3.50) \rightarrow Si\,(4.15) \rightarrow P\,(4.80) \rightarrow S\,(5.45) \rightarrow Cl\,(6.10) \rightarrow Ar\,(6.75)$

  • Down a Group from Period 2 to Period 3: $Z^*$ increases by $0.90$ (e.g., from $Li$ to $Na$, or $Be$ to $Mg$).

  • Down a Group in the d-block: $Z_{\text{eff}}$ consistently increases moving down a group.

  • Across the Lanthanoid Series: $Z_{\text{eff}}$ continuously increases from $Ce$ to $Lu$ due to poor shielding by the diffuse $4f$ subshell.

  • Isoelectronic Species: $Z_{\text{eff}}$ scales with net positive charge:     $Z_{\text{eff}} \propto \text{positive charge} \propto \frac{1}{\text{negative charge}}$

  • $Z_{\text{eff}}$ order:       $O^{2-} < F^- < Ne < Na^+ < Mg^{2+} < Al^{3+}$

Atomic, Metallic, and Ionic Radii

• Types of Atomic Radii:

  • Covalent Radius: Half the internuclear distance between two identical, single-bonded non-metallic atoms.

  • Metallic Radius: Half the internuclear distance between two adjacent metal atoms in a metallic crystalline lattice.

  • van der Waals Radius: Half the internuclear distance between two non-bonded noble gas atoms in the solid state.

  • Hierarchy of Radii Magnitudes:     $\text{van der Waals Radius} > \text{Metallic Radius} > \text{Covalent Radius}$

  • Non-metallic elements demonstrate both covalent and van der Waals radii.

• Periodic Trends in Atomic Radii:

  • Variation Across a Period:

  • Atomic radius decreases across a period because $Z_{\text{eff}}$ increases:       $\text{Atomic Radius} \propto \frac{1}{Z_{\text{eff}}}$

  • Noble Gas Exception: In every period, the noble gas has the largest radius because it is defined by the van der Waals radius.

  • Irregularity in the $3d$ Series:       $Sc > Ti > V > Cr > Mn > Fe \approx Co \approx Ni < Cu < Zn$

    • Cause: Initial contraction driven by rising $Z_{\text{eff}}$, middle parity where shielding balances nuclear pull, and final expansion from $e^- - e^-$ repulsion in filled $d^{10}$ subshells.

  • Variation Down a Group:

  • Atomic radius increases down a group due to the addition of principal shells:       $\text{Atomic Radius} \propto \text{Number of shells}$

  • Iso-size Condition ($\Delta Z = 32$): When the difference in atomic number between consecutive elements down a group is 32, their radii remain nearly identical.

  • In the final two elements of a vertical column (up to Group 11, excluding Group 12), size remains almost constant.

  • Contractions in the d-Block:       $\text{Size: } 3d \text{ series} < 4d \text{ series} \approx 5d \text{ series} \approx 6d \text{ series}$

    • Lanthanoid Contraction: Inefficient screening by intervening $4f$ electrons holds $5d$ series radii equal to $4d$ series radii.

    • Actinoid Contraction: Inefficient screening by intervening $5f$ electrons similarly contracts the $6d$ series.

  • Exceptions to d-Block Radii Parity:

    • Group 3 (IIIB): Displays normal size expansion: $Sc < Y < La < Ac$.

    • Group 12 (IIB): Size increases down the column: $Zn < Cd < Hg$, attributable to enhanced metallic bonding.

  • Transition Contraction (Scandide Contraction):

  • Observed exclusively in Group 13.

  • Poor shielding of the $3d$ electrons causes Gallium ($Ga$) to contract, rendering it smaller than Aluminum ($Al$).

  • Group 13 Size Order:       $B < Ga < Al < In \approx Tl$

• Ionic Radii Trends:

  • For Isoelectronic Species:     $\text{Ionic Radius} \propto \frac{1}{Z_{\text{eff}}} \propto \frac{\text{negative charge}}{\text{positive charge}}$

  • Cations are smaller than their parent atoms; anions are larger than their parent atoms.

Ionisation Enthalpy and Applications

• Definitions and Principles:

  • Ionisation Enthalpy (IE): The minimum energy required to detach the most loosely bound valence electron from an isolated neutral gaseous atom in its ground state.

  • Energy delivered through heat is termed Ionisation Enthalpy.

  • Energy delivered through an accelerating electric field is termed Ionisation Potential.

  • Thermochemistry: IE is always an endothermic quantity ($\Delta H > 0$) for neutral species.

  • Successive Ionisation Enthalpies: Successive values rise monotonically as electrons are removed from species of increasing positive charge:     $Al(g) \xrightarrow{IE_1} Al^+(g) \xrightarrow{IE_2} Al^{2+}(g) \xrightarrow{IE_3} Al^{3+}(g)$     $IE_1 < IE_2 < IE_3$

• Factors Influencing Ionisation Enthalpy:

  • Isoelectronic Species:     $IE \propto Z_{\text{eff}} \propto \frac{\text{positive charge}}{\text{negative charge}}$

  • Group Trends:     $IE \propto \frac{1}{\text{Size}}$

  • Contraction Exception: When size remains fixed down a group due to Lanthanoid, Actinoid, or Transition contractions, IE increases because $Z$ and $Z_{\text{eff}}$ increase.

  • Group 13 IE Hierarchy:       $B > Tl > Ga > Al > In$

  • d-Block IE Hierarchy:       $5d > 3d > 4d$

    • Exceptions: In Groups 4, 5, 6, and 10, IE follows: $3d < 4d < 5d$.

  • Period Trends:

  • Outermost shell and electron configuration dictate trends across a period.

  • Half-Filled Stability: $np^3 > np^4$ (valid up to the 4th period due to exchange stabilization).

  • Penetration Effect: $ns^2 > np^1$ (applicable when $\Delta Z = 1$).

  • If charge and valence shell are equal, noble gas configurations yield maximum IE.

  • Proportionality: $IE \propto Z_{\text{eff}}$.

  • Lanthanoids: IE increases from $Ce$ to $Lu$ as $Z_{\text{eff}}$ increases.

  • $3d$ Series: IE increases from left to right, showing irregular drops at intervals 2, 6, and 7:       $Sc < Ti > V < Cr < Mn < Fe > Co > Ni < Cu < Zn$

• Applications of Ionisation Enthalpy:

  • Determining Valence Electrons: Discontinuous spikes between consecutive IE values ($IE_n$ to $IE_{n+1}$) reflect the removal of an electron from an inner noble gas shell ($(n - 1)$). The number of valence electrons equals $n$.

  • Example: Given $IE_1 = 248\,kJ\,mol^{-1}$, $IE_2 = 377\,kJ\,mol^{-1}$, and $IE_3 = 1082\,kJ\,mol^{-1}$, the sharp increase from $IE_2$ to $IE_3$ establishes the presence of 2 valence electrons.

  • Determining Stable Oxidation States:

  • If the difference between two successive IE values is less than $11\,eV$:       $\Delta IE < 11\,eV \implies \text{Higher oxidation state is more stable}$

  • If the difference between two successive IE values is greater than $16\,eV$:       $\Delta IE > 16\,eV \implies \text{Lower oxidation state is more stable}$

  • Electropositive and Metallic Character:     $\text{Metallic Character} \propto \text{Electropositive Character} \propto \frac{1}{IE}$

Electron Affinity and Electron Gain Enthalpy

• Definitions and Thermochemical Relationships:

  • Electron Affinity (EA): Energy released when an electron is captured by the outermost shell of an isolated neutral gaseous atom.

  • Electron Gain Enthalpy ($\Delta H_{\text{eg}}$) Mathematical Definition:     $\Delta H_{\text{eg}} = -(\text{Electron Affinity})$     $|\Delta H_{\text{eg}}| = \text{Electron Affinity}$

  • First Electron Gain Enthalpy Sign:

  • $\Delta H_{\text{eg}}$ is negative (exothermic) for the majority of neutral atoms.

  • External energy is required (endothermic, $\Delta H_{\text{eg}} > 0$) for four species: $Be$, $Mg$, $N$, and inert gases.

  • Quantitative Endothermic Examples:

    • $Ne(g) + e^- \rightarrow Ne^-(g) \quad (\Delta H_{\text{eg}} = +116\,kJ\,mol^{-1})$

    • $He(g) + e^- \rightarrow He^-(g) \quad (\Delta H_{\text{eg}} = +48\,kJ\,mol^{-1})$

  • Quantitative Exothermic Example:

    • $Cl(g) + e^- \rightarrow Cl^-(g) + 348\,kJ\,mol^{-1} \quad (\Delta H_{\text{eg}} = -348\,kJ\,mol^{-1})$

  • Successive Electron Gain Enthalpies: Subsequent additions (2nd $\Delta H_{\text{eg}}$ onward) are strictly positive/endothermic due to strong electrostatic repulsion between the anion and the incoming electron.

  • Poly-negative Anions: The overall formation of poly-negative ions (such as $O^{2-}$, $N^{3-}$) is endothermic ($EA = -\text{ve}$, $\Delta H_{\text{eg}} = +\text{ve}$).

• Trends in Electron Affinity:

  • Isoelectronic Species: $EA \propto Z_{\text{eff}} \propto \frac{\text{positive charge}}{\text{negative charge}}$.

  • Group Trends and the 2nd vs. 3rd Period Anomaly:

  • Electron affinity generally decreases with increasing size:       $EA \propto \frac{1}{\text{Size}}$

  • Group 14 to 17 Exception: Third-period elements exhibit higher electron affinity than corresponding second-period elements:       $EA(\text{2nd period}) < EA(\text{3rd period})$

    • Examples: $EA(F) < EA(Cl)$, $EA(O) < EA(S)$, $EA(C) < EA(Si)$, $EA(B) < EA(Al)$.

    • Cause: The small valence shells of 2nd period atoms create high electron charge density, producing severe electron-electron repulsion that destabilizes incoming electrons. The larger shells of 3rd period atoms experience less repulsion.

  • Period Trends:

  • $EA \propto Z_{\text{eff}}$.

  • Subshell Exceptions: $EA(ns^1) > EA(np^1)$ and $EA(np^2) > EA(np^3)$.

• Conjugate Relation Between IE and EA:

  • Thermodynamic cycles connect ionization enthalpies and electron affinities of conjugate pairs:

  • $X(g) \xrightarrow{IE} X^+(g) \quad \text{and} \quad X^+(g) \xrightarrow{EA} X(g)$       $IE \text{ of } X(g) = |EA \text{ of } X^+(g)|$

  • $X(g) \xrightarrow{EA} X^-(g) \quad \text{and} \quad X^-(g) \xrightarrow{IE} X(g)$       $EA \text{ of } X(g) = |IE \text{ of } X^-(g)|$

Electronegativity and Chemical Applications

• Fundamental Concepts of Electronegativity (EN):

  • Definition: The tendency of an atom to attract shared electron pairs toward itself within a covalent bond.

  • Properties: Electronegativity is a dimensionless, unitless property that does not depend on ground-state electron configurations.

• Trends and Influencing Factors:

  • Across a Period: Directly proportional to effective nuclear charge ($EN \propto Z_{\text{eff}}$).

  • Down a Group: Inversely proportional to atomic size ($EN \propto \frac{1}{\text{Size}}$).

  • Isoelectronic Species / Variable Oxidation States: Increases with positive oxidation state and decreases with negative oxidation state:     $EN \propto \text{positive oxidation state} \propto \frac{1}{\text{negative oxidation state}}$

  • Orbital Hybridization Effect: Electronegativity scales directly with the percentage of s-character in the bonding hybrid orbital:     $EN \propto \% s\text{-character}$     $EN: sp > sp^2 > sp^3$

• Chemical Applications of Electronegativity:

  • Non-Metallic Character: Directly proportional to electronegativity:     $\text{Non-Metallic Character} \propto EN$

  • Bond Polarity: Directly proportional to the difference in electronegativity:     $\text{Bond Polarity} \propto \Delta EN$

  • Bond Parameters:

  • An increase in $\Delta EN$ leads to an increase in ionic character.

  • An increase in $\Delta EN$ leads to a decrease in bond length.

  • An increase in $\Delta EN$ leads to an increase in bond strength.

  • Acidity of Oxides and Oxyacids: Acidic nature scales directly with the electronegativity of the central element:     $\text{Acidic nature of oxides / oxyacids} \propto EN \text{ of central atom}$