Chemistry

Periodic Table & Periodic Properties

• Electronic configuration model used ⇒ Aufbau, n+l rule (lower n+l ⇒ lower E; if equal, lower n fills first).
  • Example: 3d vs 4s → 3d : n+l = 3+2 =5, 4s : 4+0 =4 ⇒ 4s fills before 3d.
• Sample configurations
  • Zn (30): [Ar]4s^23d^{10}
  • Sc(21): [Ar]4s^23d^1
• Cation–anion size trend
  • Cation < parent atom (loss of e⁻, ↑Z_eff). • Anion > parent atom (gain of e⁻, ↓Z_eff).
• Iso-electronic series radius (same e⁻ count) ⇒ higher nuclear charge → smaller radius.
  e.g. N^{3-} > O^{2-} > F^- > Ne > Na^+.
• Atomic radius trend: ↓ down group (n↑), ↑ left→right contracted (Z_eff↑).
• Electronegativity (χ): ↑ up & right; relates inversely with size, directly with ionisation energy (I.E.).
• Electron affinity (EA): generally ↑ across period, ↓ down group except anomalies (e.g. Be, N low EA due to stable subshell).

Quantum Numbers & Orbitals

• 4 quantum numbers describe each e⁻:
  • Principal n (1,2,3…) – shell/size.
  • Azimuthal l (0 → n-1) – subshell/shape (s,p,d,f).
  • Magnetic ml (-l…+l) – orientation. • Spin ms (+\tfrac12 or -\tfrac12).
• Tabulated examples (4th shell):
  n=4\;\Rightarrow\; l=0(s),1(p),2(d),3(f) with corresponding m_l spreads.
• Example for outermost e⁻ of Cu: n=4, l=0, ml =0, ms = +\tfrac12.

Hybridisation & Molecular Geometry

• Hybrid index = (no. of σ-bonds + lone pairs).
  • 2 ⇒ sp (linear) – e.g. BeF2. • 3 ⇒ sp^2 (trigonal planar) – BF3.
  • 4 ⇒ sp^3 (tetrahedral) – CH4 (109.5°); pyramidal NH3 (107°); bent H2O (104.5°). • 5 ⇒ sp^3d (trigonal bipyramidal) – PF5.
  • 6 ⇒ sp^3d^2 (octahedral) – SF_6.
• σ-bond: head-on overlap, π-bond: sidewise overlap (p–p or p–d).

Bond Character & Fajans’ Rules

• Covalent character ↑ with:
  • Small, highly charged cation.
  • Large, highly charged anion.
• Sequence: LiF < LiCl < LiBr < LiI (polarisation ↑ → covalency ↑).
• Solubility/lattice-energy order in chlorides: LiCl > NaCl > KCl > RbCl (larger ions → lower L.E. → ↑ solubility).

Lattice Energy vs Solubility

• L.E \propto \dfrac{z^+ z^-}{r^+ + r^-}; solubility inversely related except where hydration enthalpy (H.E.) compensates.
• Alkali carbonates: Li2CO3 < Na2CO3 < K2CO3 (Li⁺ high L.E. → least soluble).
• Alkali sulphates: Li2SO4 > Na2SO4 > K2SO4 (opposite trend due to H.E.).

Acid–Base Theories & pH

• Arrhenius: Acid → H^+ donor in water; Base → OH^- donor.
• Brønsted–Lowry: Acid donor, base acceptor of H^+.
• Lewis: Acid = e⁻ pair acceptor, Base = e⁻ pair donor (species with lone pair = base; e-deficient, octet-incomplete = acid).
• pH = -\log[H^+] , pOH = -\log[OH^-] , pH + pOH =14 (25 °C).
  pKa = -\log Ka,\; pKb = -\log Kb,\; pK_w =14.
• Weak acid dissociation: for HA\rightleftharpoons H^+ + A^-
  Ka = \dfrac{c\alpha^2}{1-\alpha}\approx c\alpha^2 if \alpha

Buffer Solutions

• Acidic buffer = weak acid + salt of its conjugate base.
• Henderson–Hasselbalch: pH = pK_a + \log\dfrac{[\text{salt}]}{[\text{acid}]}.

Solubility Product (K{sp}) & Ionic Product (K{ip})

• K_{sp} depends only on T; defines saturated solution.
• Example: Fe(OH)3 \rightleftharpoons Fe^{3+}+3OH^- K{sp}=4\times10^{-38} = s(3s)^3 ⇒ s=1.96\times10^{-10} mol L⁻¹.
• Precipitation criteria:
  • K{ip} > K{sp} ⇒ ppt forms.
  • K{ip} = K{sp} ⇒ saturated.
  • K{ip} < K{sp} ⇒ unsaturated.

Flame Test Colours (Platinum/Nichrome wire)

• Li^+ – crimson red.
• Na^+ – golden yellow.
• K^+ – violet.
• Rb^+ – reddish-violet.
• Ca^{2+} – brick red.
• Cu^{2+} – blue-green.

Classification: Isotope, Isobar, Isotone, Iso-electronic, Iso-steric

• Isotope: same Z, diff A → {}1^1H, {}1^2H, {}_1^3H.
• Isobar: same A, diff Z → {}{29}^{64}Cu, {}{30}^{64}Zn.
• Isotone: same neutrons.
• Iso-electronic: identical e⁻ count (e.g. N_2, CO, CN^-).
• Iso-steric: same steric demand (identical total of ne + nN).

Gas Laws & Quantitative Chemistry

• Ideal gas: PV = nRT ; R=0.0821\;L\,atm\,mol^{-1}K^{-1} = 8.314\;J\,mol^{-1}K^{-1}.
• STP: 273 K, 1 atm ⇒ 1 mol occupies 22.4\,L; at 298 K ⇒ 24.78\,L.
• Real gas (van der Waals): \left(P+\dfrac{a}{V^2}\right)(V-b)=RT.
• Parts-per-million: ppm = \dfrac{mass\;solute}{mass\;solution}\times10^6.

Organic Chemistry Fundamentals

Nomenclature Scheme

prefix 2 + prefix 1 + parent + suffix 1 + suffix 2.
Priority: Functional group > multiple bonds > substituents; nearest locant, alphabetical order for identical priority.

• Common F.G. hierarchy: –COOH > –SO3H > –COOR > –COCl > –CONH2 > –CN > –CHO > >C=O > –OH > –NH_2 > –C=C– > –C≡C– > halo.

Stereochemistry

• Chiral C = attached to 4 different groups → optically active.

Reactivity Trends

• Alcohol acidity: 1^° > 2^° > 3^° (opposite for bases).
• Amines basic