Chemistry Basics – MIT‑Level Study Notes
Subject: General Awareness & Current Affairs
Exam: Puducherry PSC (Program) – Chemistry Basics
These notes are written for an advanced audience (undergraduate/graduate level).
Each section starts from first principles, develops the full theory, points out subtle edge cases, and ends with a challenging problem that integrates multiple concepts.
1. Atomic Structure
| Concept | First Principle | Key Equations | Deeper Theory |
|---|---|---|---|
| Protons & Neutrons | Conservation of baryon number | ( A = Z + N ) | Isotopic mass defect, binding energy per nucleon |
| Electrons | Pauli Exclusion Principle | ( n, l, m_l, m_s ) | Spin‑orbit coupling, fine structure |
| Quantum Numbers | Solutions to Schrödinger equation in central potential | ( \psi_{n,l,m_l}(r,\theta,\phi) ) | Radial nodes, quantum defect |
| Electron Density | Born–Oppenheimer approximation | ( \rho(\mathbf{r}) = \sum_i | \psi_i(\mathbf{r}) |
Edge Cases
- Hydrogenic vs Multi‑electron atoms:
- Hydrogen – exact solution.
- Multi‑electron – require electron–electron repulsion; correlation effects.
- Superheavy elements (Z > 118):
- Relativistic effects on s‑orbitals (contracted), d‑ and f‑orbitals (expanded).
- Theoretical predictions of a “periodic table beyond 118” rely on relativistic Dirac–Fock calculations.
2. Periodic Table & Trends
| Trend | Observation | Underlying Explanation |
|---|---|---|
| Atomic radius | Decreases across a period, increases down a group | Effective nuclear charge ( Z_{\text{eff}} ) and penetration |
| Ionization energy | Increases across a period, decreases down a group | Same reasons as radius, plus shielding |
| Electron affinity | Varies irregularly (s‑block > p‑block) | Energy released during addition of an electron |
| Electronegativity (Pauling) | Similar trend to ionization energy | Empirical scale derived from bond energies |
Theoretical Derivation (approximate)
( r_{\text{eff}} \approx a_0 \frac{n^2}{Z_{\text{eff}}} ) where ( a_0 ) is Bohr radius.
( E_{\text{ion}} \approx \frac{Z_{\text{eff}}^2}{n^2} ) (Rydberg formula).
Edge Cases
- Transition metals – d‑electron shielding is less effective → larger radii than expected.
- Lanthanides – 4f orbitals poorly shield → lanthanide contraction.
- Group 13 (B, Al, Ga, In, Tl) – anomalously low ionization energies due to filled p‑orbitals.
3. Chemical Bonding
| Bond Type | First Principles | Key Equations | Deeper Theory |
|---|---|---|---|
| Covalent | Overlap of atomic orbitals | ( \text{Covalent bond energy} = -\frac{1}{2}\sum_{\text{occupied}} \langle \psi_i | \hat{H} |
| Ionic | Electrostatic attraction between ( \text{Na}^+ ) & ( \text{Cl}^- ) | ( \Delta H_{\text{ion}} = \Delta H_{\text{vap}} + \Delta H_{\text{ionization}} + \Delta H_{\text{electron affinity}} + \Delta H_{\text{lattice}} ) | Born‑Haber cycle |
| Metallic | Electron “sea” | ( E(k) = E_0 - 2t \cos(ka) ) | Band theory, Fermi‑Dirac statistics |
| Hydrogen Bond | Partial covalent + electrostatic | ( E_{\text{HB}} \approx 5-30,\text{kJ mol}^{-1} ) | Quantum tunneling, O‑H…O potential surface |
Edge Cases
- π‑bonding in conjugated systems – delocalization leads to aromaticity (Hückel’s rule).
- Spin‑dependent bonds – In transition metal complexes, ligand field theory predicts high‑spin vs low‑spin.
- Hypervalent molecules – ( \text{XeF}_6 ), ( \text{SF}_6 ) – involve d‑orbitals, 3c‑4e bonds, or expanded octet arguments.
4. Stoichiometry & Law of Mass Conservation
First Principles
- Conservation of mass: the total mass of reactants equals that of products.
- Avogadro’s Law: equal volumes at same T, P contain equal numbers of molecules.
Key Equations
- ( m = nM ) (mass–moles)
- ( \frac{m_1}{M_1} : \frac{m_2}{