Inorganic ChemistryHigh Yield (2 Qs in JEE)

Periodic Table & Periodic Properties Formulas

Ionization enthalpy, electron gain enthalpy, electronegativity (Pauling & Mulliken scales), screening effect, and atomic radii trends.

7 Formulas•367+ Questions in Bank

Core Formulas & Mathematical Identities

Effective Nuclear Charge (Slater's Rules)

Z_{\text{eff}} = Z - \sigma, \quad \text{Shielding Power: } s > p > d > f

Net positive nuclear attraction felt by valence electrons after screening.

Examiner Tip: Poor shielding of 3d and 4f electrons causes scandide and lanthanide contractions.

Electronegativity Scales (Pauling & Mulliken)

\chi_A - \chi_B = 0.208 \sqrt{\Delta} \; (\text{in kcal}), \quad \chi_{\text{Mulliken}} = \frac{\text{IE} + \text{EA}}{2 \text{ (in eV)}} \approx 2.8 \chi_{\text{Pauling}}

Tendency of bonded atom to attract shared electron pair.

Examiner Tip: Fluorine has maximum electronegativity = 4.0 on Pauling scale.

Ionization Enthalpy & Anomalies

\text{IE}_1(\text{Be}) > \text{IE}_1(\text{B}), \quad \text{IE}_1(\text{N}) > \text{IE}_1(\text{O}), \quad \text{IE}_1(\text{P}) > \text{IE}_1(\text{S})

Penetration effect (2s² > 2p¹) and extra stability of half-filled subshells (2p³ > 2p⁴).

Examiner Tip: Successive ionization energies strictly increase: IE₁ < IE₂ < IE₃ < IE₄.

Electron Gain Enthalpy (\Delta_{eg}H) Anomalies

|\Delta_{eg}H|: \; \text{Cl} > \text{F} > \text{Br} > \text{I}, \quad \text{S} > \text{Se} > \text{Te} > \text{Po} > \text{O}

Compact 2p orbital in F and O creates strong electron-electron repulsion, making 3p elements (Cl, S) have more negative electron gain enthalpy.

Examiner Tip: Noble gases have positive Δ_eg H. Nitrogen, Be, and Mg have Δ_eg H close to zero or slightly positive.

Allred-Rochow Scale of Electronegativity

\chi_{\text{AR}} = 0.359 \frac{Z_{\text{eff}}}{r^2} + 0.744 \quad (r \text{ in \AA})

Electrostatic force exerted by effective nuclear charge on an electron at the covalent radius distance.

Examiner Tip: Pauling scale connection: χ_Pauling ≈ χ_AR ≈ χ_Mulliken / 2.8.

Lanthanide Contraction & Pairs with Identical Radii

r(\text{Zr}^{4+}) \approx r(\text{Hf}^{4+}) \approx 0.80\,\text{\AA}, \quad r(\text{Nb}^{5+}) \approx r(\text{Ta}^{5+}), \quad r(\text{Mo}^{6+}) \approx r(\text{W}^{6+})

Poor shielding of 14 inner 4f electrons causes atomic/ionic radii of 4d and 5d transition series to be almost identical.

Examiner Tip: Explains why separation of Zr and Hf is extremely difficult chemically.

Hydration Enthalpy & Aqueous Ionic Mobility

\Delta H_{\text{hyd}} \propto \frac{z}{r} \implies \text{Hydrated Radius: } \text{Li}^+_{\text{aq}} > \text{Na}^+_{\text{aq}} > \text{K}^+_{\text{aq}} > \text{Cs}^+_{\text{aq}}, \quad \text{Mobility: } \text{Cs}^+ > \text{Rb}^+ > \text{K}^+ > \text{Na}^+ > \text{Li}^+

Smaller gaseous cations have higher charge density, attract more water molecules, and become bulkier with slower electrical conductivity in aqueous solution.

Examiner Tip: Li⁺ has smallest gaseous ionic radius but largest hydrated radius in water.

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Periodic Table & Periodic Properties

•Electron gain enthalpy of Chlorine (Cl) is MORE NEGATIVE than Fluorine (F) due to compact 2p interelectronic repulsion in F.
•Ionization energy of Nitrogen (N: half-filled 2p³) is GREATER than Oxygen (O: 2p⁴).

Previous Chapter

Solid State Chemistry

7 Formulas•Physical Chemistry

Next Chapter

p-Block Elements

Inorganic Chemistry•9 Formulas