📚 Chemistry Basics – MIT‑Level Study Notes
(Prepared for the Delhi Forest Guard – General Awareness & Current Affairs)
Goal: Build a solid, rigorous foundation in chemistry that can be applied to environmental and forestry contexts (e.g., understanding pollutants, soil chemistry, forest fire chemistry).
Scope: From first principles, through advanced theory, to edge‑case analysis and a challenging problem.
1. Atomic Structure – From Classical to Quantum
| Aspect | Classical View | Modern Quantum View |
|---|---|---|
| Electrons | Point particles orbiting nucleus | Wavefunctions (ψ) obey Schrödinger equation |
| Energy Levels | Discrete orbits | Quantized eigenvalues of Hamiltonian, ( H\psi = E\psi ) |
| Spin | Ignored | Two‑state system, Pauli spin matrices |
1.1 Schrödinger Equation (Time‑Independent)
[ \hat{H}\psi(\mathbf{r}) = E\psi(\mathbf{r}), \qquad \hat{H} = -\frac{\hbar^2}{2m}\nabla^2 - \frac{Ze^2}{4\pi\varepsilon_0 r} ]
- Solution: Hydrogenic orbitals ( \psi_{n\ell m} ).
- Radial part: ( R_{n\ell}(r) \propto r^\ell e^{-r/na_0} L^{2\ell+1}_{n-\ell-1}(2r/na_0) ).
- Angular part: Spherical harmonics ( Y_{\ell m}(\theta,\phi) ).
1.2 Quantum Numbers & Pauli Exclusion
| Quantum number | Physical meaning | Allowed values |
|---|---|---|
| ( n ) | Principal | 1,2,3,… |
| ( \ell ) | Orbital angular momentum | 0…( n-1 ) |
| ( m_\ell ) | Magnetic | (-\ell…+\ell) |
| ( s ) | Spin | (\pm \tfrac12) |
Edge case: Half‑filled d and f shells – lead to exchange energy and Hund’s rules, stabilising unique magnetic properties.
2. Periodic Table – Trends & Anomalies
| Trend | Explanation | Edge Cases |
|---|---|---|
| Atomic radius | Electron–nucleus attraction + shielding | In 4d/5d series, increased relativistic contraction |
| Ionization energy | Effective nuclear charge (Z_{\text{eff}}) | Inert gases have exceptionally high IE |
| Electron affinity | Energy change on gaining an electron | Pnictogens show negative EA (releasing energy) |
| Electronegativity (Pauling) | ( \chi = \frac{1}{2}(IE - EA) ) | Lanthanides exhibit nearly constant ( \chi ) due to shielding |
Advanced point: Periodic trends break down for 4d/5d metals because of relativistic effects increasing s‑orbital energy.
3. Chemical Bonding – From Electrostatics to Quantum
3.1 Ionic Bonding
- Model: Complete electron transfer.
- Energy balance: ( \Delta H_{\text{bond}} = -IE + EA - \Delta H_{\text{lattice}} ).
3.2 Covalent Bonding
- Molecular Orbital (MO) Theory
- Constructed from linear combinations of atomic orbitals (LCAO).
- Bonding orbitals lower energy, antibonding raise.
- Valence Bond (VB) Theory
- Overlap of hybrid orbitals; explains hybridization (sp, sp², sp³, sp³d, sp³d²).
- Edge case: π‑bonding in aromatic systems (delocalization, Hückel’s rule (4n+2)).
3.3 Coordinate (Dative) Bonds
- Definition: One atom donates both electrons.
- Example: (\text{[Fe(CN)}_6]^{4-}) – Fe(II) + 6 cyanide anions.
3.4 Hypervalent Molecules
- Valence‑Shell Electron‑Pair Repulsion (VSEPR) fails for (>8) valence electrons.
- Expanded Octet explained by d‑orbital participation or pseudocovalent interaction (e.g., SF6).
4. Stoichiometry & Reaction Balancing
4.1 Mole Concept
- (1,\text{mol} = 6.022\times10^{23}) entities.
- Avogadro’s law: (V_m = \frac{RT}{P}) for ideal gases.
4.2 Reaction Quotient (Q) & Equilibrium Constant (K)
[ Q = \frac{\prod_i [C_i]^{\nu_i}}{\prod_j [A_j]^{\mu_j}}, \quad K = Q_{\text{eq}} ]
- Le Chatelier’s principle: Predicts shift under