Comprehensive University Chemistry Study Notes

Planck’s Quantum Theory: Energy of a photon is given by $E = h\nu = \frac{hc}{\lambda}$ .
Photoelectric Effect: Einstein’s equation is $h\nu = h\nu_0 + \frac{1}{2}m_e v^2$ .
Bohr Model: Quantization of angular momentum mvr = \frac{nh}{2\times \text{\pi}}; Radius $r_n = \frac{0.529 \times n^2}{Z} \text{\,\AA}$ ; Energy $E_n = -13.6 \times \frac{Z^2}{n^2} \text{\,eV/atom}$ .
Wave Mechanics: De-Broglie wavelength $\lambda = \frac{h}{p}$ ; Heisenberg Uncertainty Principle \Delta x \cdot \Delta p \geq \frac{h}{4\times \text{\pi}}.
Quantum Numbers: Principal ( $n$ ), Azimuthal ( $l$ ) for subshells, Magnetic ( $m$ ) for orbitals, and Spin ( $s$ ). Orbital angular momentum L = \frac{h}{2\times \text{\pi}}\times \text{\sqrt{l(l+1)}}.

Concentration Terms: Molarity ( $M$ ), Molality ( $m$ ), Mole Fraction ( $x$ ), and Normality ( $N = M \times v.f.$ ).
Equivalent Weight: $E = \frac{\text{Molecular Weight}}{v.f.}$ . At equivalence point: $N_1V_1 = N_2V_2$ .
Water Hardness: Expressed in $ppm$ as $CaCO_3$ equivalent: $\text{Hardness (ppm)} = \frac{\text{mass of } CaCO_3}{\text{total mass of water}} \times 10^6$ .
Vapor Density: $V.D. = \frac{\text{Molar mass}}{2}$ .

Gas Laws: Ideal Gas Equation $PV = nRT$ ; Dalton’s Law of Partial Pressures P_{total} = \text{\sum} P_i.
Graham’s Law: Rate of diffusion r \propto \frac{1}{\text{\sqrt{M}}}.
Speeds: U_{rms} = \text{\sqrt{\frac{3RT}{M}}}, U_{avg} = \text{\sqrt{\frac{8RT}{\text{\pi}M}}}, and U_{mps} = \text{\sqrt{\frac{2RT}{M}}}.
Real Gases: van der Waals equation $(P + \frac{an^2}{V^2})(V - nb) = nRT$ . Critical constants: $V_c = 3b$ , $P_c = \frac{a}{27b^2}$ , $T_c = \frac{8a}{27Rb}$ .

First Law: $\Delta U = q + w$ . Work for reversible isothermal expansion: w = -nRT \text{\ln}(\frac{V_f}{V_i}).
Entropy ( $S$ ): Measures randomness; for spontaneous processes $\Delta S_{total} > 0$ .
Gibbs Free Energy ( $G$ ): $\Delta G = \Delta H - T\Delta S$ . Spontaneity: $\Delta G < 0$ (spontaneous), $\Delta G = 0$ (equilibrium).
Thermochemistry: Kirchhoff's Equation $\Delta H_2 = \Delta H_1 + \Delta C_p(T_2 - T_1)$ . Enthalpy of reaction \Delta H_r = \text{\sum} H_{products} - \text{\sum} H_{reactants}.

Equilibrium Constants: $K_p = K_c(RT)^{\Delta n}$ . Relationship with Gibbs energy: \Delta G^0 = -2.303RT \text{\log}(K).
Le Chatelier’s Principle: External stress shifts equilibrium to minimize the disturbance.
Ostwald Dilution Law: For weak acids, $K_a = C\alpha^2$ (if $\alpha << 1$ ).
Acidity: pH = -\text{\log}[H^+]. For water at $25\,^{\circ}\text{C}$ , $pK_w = pH + pOH = 14$ .
Salt Hydrolysis: Formulas for $pH$ depend on salt type (e.g., weak acid-strong base pH = 7 + \frac{1}{2}pK_a + \frac{1}{2}\text{\log}(C)).
Solubility Product ( $K_{sp}$ ): Equilibrium between a solid and its ions in solution: $K_{sp} = (xs)^x(ys)^y$ .

Nernst Equation: E_{cell} = E^0_{cell} - \frac{0.0591}{n} \text{\log}(Q) at $298\,K$ .
Electrolysis: Faraday’s First Law $w = Zit$ . Second Law $\frac{W_1}{E_1} = \frac{W_2}{E_2}$ .
Conductance: Molar conductivity \Lambda_m = \frac{1000\times \text{\kappa}}{M}. Kohlrausch’s Law: \Lambda^0_m = \text{\nu}_+ \text{\lambda}^0_+ + \text{\nu}_- \text{\lambda}^0_-.
Colligative Properties: Osmotic pressure $\pi = iCRT$ ; Relative lowering of vapor pressure $\frac{P^0 - P_s}{P^0} = iX_{solute}$ ; Boiling point elevation $\Delta T_b = iK_b m$ .

Rate Laws: $\text{Rate} = k[A]^n$ . Arrhenius Equation $k = Ae^{-E_a/RT}$ .
Integrated Rate Laws: Zero order $[A] = [A]_0 - kt$ ; First order kt = 2.303 \text{\log}(\frac{[A]_0}{[A]_t}). Half-life for 1st order $t_{1/2} = \frac{0.693}{k}$ .
Cubic Systems: $SC$ ( $Z=1$ , packing $52 \text{\%}$ ), $BCC$ ( $Z=2$ , packing $68 \text{\%}$ ), $FCC$ ( $Z=4$ , packing $74 \text{\%}$ ).
Density of Crystal: $d = \frac{ZM}{N_A a^3}$ .

Periodic Trends: Atomic radius decreases across a period, increases down a group. Ionization Energy ( $IE$ ) and Electronegativity ( $EN$ ) increase across a period.
Bonding: VBT (sigma and pi bonds); VSEPR theory predicts molecular geometry based on electron repulsion.
Hybridization: $sp$ (linear), $sp^2$ (trigonal planar), $sp^3$ (tetrahedral), $sp^3d$ ( $TBP$ ), $sp^3d^2$ (octahedral).
MOT: Bond order $B.O. = \frac{1}{2}(N_b - N_a)$ .
Coordination Compounds: Werner’s Theory (Primary vs Secondary valency). EAN Rule. Crystal Field Theory (splitting of d-orbitals into $t_{2g}$ and $e_g$ ).
Metallurgy: Processes include roasting (sulfides), calcination (carbonates), smelting (reduction), and refining (Mond’s, Van Arkel).

Nomenclature: IUPAC priority: Carboxylic Acid > Acid Derivative > Nitrile > Aldehyde > Ketone > Alcohol > Amine.
Electronic Effects: Inductive ( $I$ ), Mesomeric ( $M$ ), Resonance ( $R$ ), and Hyperconjugation determine stability of intermediates like carbocations ( $3^{\circ} > 2^{\circ} > 1^{\circ}$ ).
Aromaticity: Huckel’s Rule requires a planar, cyclic system with (4n + 2) \text{\pi} electrons.
Isomerism: Chain, positional, functional, metamerism, tautomerism (structural), and cis-trans/optical (stereo).

Alkanes/Alkenes: Wurtz reaction ( $R-X + Na > R-R$ ). Electrophilic addition in alkenes (Markovnikov rule).
Aldehydes & Ketones: Aldol Condensation (requires $\alpha-H$ ); Cannizzaro Reaction (no $\alpha-H$ ). Grignard Reagent ( $RMgX$ ) adds to carbonyls to form alcohols.
Aromatic Substitution: Nitration ( $HNO_3/H_2SO_4$ ), Sulphonation ( $H_2SO_4/SO_3$ ), Friedel-Crafts alkylation/acylation.
Polymers: Addition polymers (LDPE, HDPE, PVC, Teflon) vs. Condensation polymers (Nylon-6,6, Terylene, Bakelite).