BCS Written Chemistry cheat sheet

Quantum numbers: n (shell, n ≥ 1), l (0 to n−1), m_l (−l to +l), m_s (±½); orbital capacity = 2(2l+1), shell capacity = 2n².

Aufbau order follows (n+l) rule; for equal (n+l) the lower n fills first: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; explains paramagnetism of unpaired-electron species.

Effective nuclear charge Z* = Z − S (Slater's rules); higher Z* across a period contracts radius and raises ionization energy.

Periodic trends: atomic radius decreases across a period, increases down a group; ionization energy and electronegativity show the opposite pattern.

Exceptions: IE(Be) > IE(B) and IE(N) > IE(O) due to 2s² stability and 2p³ half-filled stability respectively.

Photoelectric and Bohr relations: E = hν = hc/λ; for hydrogen E_n = −13.6/n² eV, so ΔE = 13.6(1/n₁² − 1/n₂²) eV.

De Broglie wavelength λ = h/mv; Heisenberg uncertainty Δx·Δp ≥ h/4π; nodes: radial = n−l−1, angular = l.

VSEPR electron-pair repulsion order: lone pair–lone pair > lone pair–bond pair > bond pair–bond pair; gives bent H₂O (104.5°) vs linear CO₂ (180°).

Hybridization from steric number: 2 → sp (linear), 3 → sp² (trigonal planar), 4 → sp³ (tetrahedral), 5 → sp³d, 6 → sp³d².

Bond order = (bonding electrons − antibonding electrons)/2; O₂ has bond order 2 and is paramagnetic (two unpaired π* electrons).

MO filling order for O₂/F₂: σ2s σ2s σ2p π2p π2p σ*2p; for B₂/C₂/N₂ the π2p lies below σ2p.

Polarity: a molecule is nonpolar if bond dipoles cancel by symmetry (CO₂, CCl₄, BF₃) even when individual bonds are polar.

Bond strength and length: triple > double > single bond strength; bond length order single > double > triple.

Fajans' rules: small highly charged cations with large polarizable anions give increased covalent character (e.g., LiI > LiF).

Hydrogen bonding (N–H, O–H, F–H) raises boiling point and water solubility; it explains water's high boiling point and ice's low density.

First law: ΔU = q + w; with pressure–volume work w = −PΔV; enthalpy ΔH = ΔU + Δ(PV), and ΔH = q_p at constant pressure.

Gibbs energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0; at equilibrium ΔG = 0 and ΔG° = −RT ln K.

Second law: ΔS_universe ≥ 0; ΔS = q_rev/T; entropy increases for solid → liquid → gas and for increasing moles of gas.

Arrhenius: k = A e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂); a catalyst lowers Ea without changing ΔH or K.

First-order kinetics: t½ = 0.693/k, independent of initial concentration; integrated form ln[A] = ln[A]₀ − kt.

Nernst equation: E = E° − (0.0592/n) log Q at 25 °C; E°cell = E°cathode − E°anode.

ΔG° = −nFE°cell; positive E°cell means spontaneous reaction; Faraday = 96500 C/mol, and mass deposited m = (MIt)/(nF).

Buffer and pH: Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA]); Kw = 1×10⁻¹⁴ at 25 °C so pH + pOH = 14.

SN1 proceeds via carbocation (rate = k[substrate], racemization, favored by tertiary and polar protic solvent); SN2 is backside attack (rate = k[substrate][nucleophile], inversion, favored by primary).

E2 requires anti-periplanar geometry and strong base; E1 shares the carbocation intermediate with SN1 and is favored by heat.

Markovnikov addition to alkenes puts H on the carbon with more hydrogens; peroxide effect (anti-Markovnikov) occurs via free-radical HBr addition only.

Electrophilic aromatic substitution: activating o/p directors are –OH, –OR, –NH₂, –R; deactivating m directors are –NO₂, –CN, –COOH, –SO₃H; halogens are deactivating but o/p directing.

Aldol condensation: enolate attacks carbonyl giving β-hydroxy carbonyl, dehydration yields α,β-unsaturated product; Cannizzaro occurs for aldehydes lacking α-H.

Grignard reagent RMgX adds to aldehydes (→ secondary alcohol), ketones (→ tertiary alcohol), and CO₂ (→ carboxylic acid after hydrolysis).

Oxidation: primary alcohol → aldehyde → carboxylic acid; secondary alcohol → ketone; tertiary alcohols resist oxidation under mild conditions.

Chirality requires four different groups on a carbon; a racemic mixture has zero optical rotation; R/S assigned by CIP priority rules.

Coordination number and geometry: 2 linear, 4 tetrahedral or square planar, 6 octahedral; isomerism includes geometrical, optical, ionization, and linkage types.

Crystal field splitting: Δo (octahedral) > Δt (tetrahedral); high-spin versus low-spin depends on whether Δo exceeds pairing energy.

Spectrochemical series (weak to strong): I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.

Magnetic moment μ = √(n(n+2)) BM where n = number of unpaired electrons; e.g., n = 4 gives ≈ 4.9 BM.

EAN rule: stable complexes often reach 36, 54, or 86 electrons about the metal; e.g., [Fe(CN)₆]⁴⁻ achieves 36.

Chelate effect: polydentate ligands (EDTA, en) give higher stability and entropy-driven formation than comparable monodentate ligands.

Lanthanide contraction: poor 4f shielding causes a small radius decrease, making Zr and Hf nearly identical in size and chemistry.

Transition metals show variable oxidation states (Mn: +2 to +7), catalytic activity, and colored ions from d–d transitions.

Beer–Lambert law: A = εbc; absorbance is linear in concentration only at low concentration and monochromatic light.

Standardization: primary standards are pure, stable, non-hygroscopic (K₂C₂O₄, KHP, Na₂CO₃); molarity from titration uses M₁V₁/n₁ = M₂V₂/n₂.

Iodometry uses liberated I₂ titrated with thiosulfate (starch indicator); iodimetry titrates with standard I₂ directly.

Acid–base indicators change over pKa ± 1; phenolphthalein (8.3–10) suits strong base titrations, methyl orange (3.1–4.4) suits strong acid.

Flame emission (AES) measures excited-state emission; AAS measures ground-state absorption; both use calibration curves for trace metals.

Chromatography: Rf = distance solute/distance solvent front in TLC; GC and HPLC separate by differential partitioning between mobile and stationary phases.

Gravimetric analysis requires a pure, filterable, weighable precipitate; BaSO₄ for sulfate and AgCl for chloride are standard examples.

Errors: systematic errors shift results consistently and can be corrected by calibration; random errors reduce by replicate measurement and averaging.

Contact process: S + O₂ → SO₂, V₂O₅ catalyst at ~450 °C converts SO₂ + ½O₂ ⇌ SO₃, absorbed in H₂SO₄ (not water) to give oleum.

Haber process: N₂ + 3H₂ ⇌ 2NH₃, exothermic, high pressure (~200 atm) and moderate temperature (~450 °C) with iron catalyst.

Ostwald process: NH₃ oxidized over Pt/Rh to NO, then NO₂, absorbed in water to give HNO₃.

Solvay process: NaCl + NH₃ + CO₂ → NaHCO₃ + NH₄Cl; NaHCO₃ calcined to Na₂CO₃, ammonia recovered.

Water quality: BOD measures oxygen consumed by microbes; COD uses strong oxidant; DO below ~4 mg/L harms aquatic life.

Greenhouse gases: CO₂, CH₄, N₂O, and CFCs absorb IR; CFCs also deplete ozone via Cl radicals in a catalytic cycle.

Eutrophication is driven by excess nitrate and phosphate causing algal blooms, oxygen depletion, and fish kills.

Air pollution control: electrostatic precipitators and bag filters remove particulates; lime scrubbing removes SO₂ from flue gas.

Urea (46% N) is the dominant nitrogen fertilizer in Bangladesh; TSP and DAP supply phosphorus, and MoP supplies potassium.

Urea hydrolysis and nitrification acidify soil; lime (CaCO₃) is applied to correct acidity in the Barind and tea-garden soils.

Karnafuli and Shitalakshya river pollution from tanneries, textiles, and fertilizer plants raises heavy-metal and COD loads.

Arsenic contamination of shallow tubewells exceeds 0.05 mg/L in many districts; testing and deep tubewells are the mitigation route.

Natural gas at Titas and Bakhrabad feeds fertilizer (urea) and power plants; gas is mainly methane with H₂S removed by amine scrubbing.

Sugarcane mills (Ishwardi, Joypurhat) and cement, paper, and textile industries are major chemical-processing sectors.

Groundwater salinity in coastal Khulna and Satkhira districts affects drinking water and crop choice.

Public health: fluoride and arsenic in drinking water, pesticide residues on vegetables, and lead exposure are priority chemical hazards.

Quantum numbers: n (shell, n ≥ 1), l (0 to n−1), m_l (−l to +l), m_s (±½); orbital capacity = 2(2l+1), shell capacity = 2n².

Aufbau order follows (n+l) rule; for equal (n+l) the lower n fills first: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; explains paramagnetism of unpaired-electron species.

Effective nuclear charge Z* = Z − S (Slater's rules); higher Z* across a period contracts radius and raises ionization energy.

Periodic trends: atomic radius decreases across a period, increases down a group; ionization energy and electronegativity show the opposite pattern.

Exceptions: IE(Be) > IE(B) and IE(N) > IE(O) due to 2s² stability and 2p³ half-filled stability respectively.

Photoelectric and Bohr relations: E = hν = hc/λ; for hydrogen E_n = −13.6/n² eV, so ΔE = 13.6(1/n₁² − 1/n₂²) eV.

De Broglie wavelength λ = h/mv; Heisenberg uncertainty Δx·Δp ≥ h/4π; nodes: radial = n−l−1, angular = l.

VSEPR electron-pair repulsion order: lone pair–lone pair > lone pair–bond pair > bond pair–bond pair; gives bent H₂O (104.5°) vs linear CO₂ (180°).

Hybridization from steric number: 2 → sp (linear), 3 → sp² (trigonal planar), 4 → sp³ (tetrahedral), 5 → sp³d, 6 → sp³d².

Bond order = (bonding electrons − antibonding electrons)/2; O₂ has bond order 2 and is paramagnetic (two unpaired π* electrons).

MO filling order for O₂/F₂: σ2s σ2s σ2p π2p π2p σ*2p; for B₂/C₂/N₂ the π2p lies below σ2p.

Polarity: a molecule is nonpolar if bond dipoles cancel by symmetry (CO₂, CCl₄, BF₃) even when individual bonds are polar.

Bond strength and length: triple > double > single bond strength; bond length order single > double > triple.

Fajans' rules: small highly charged cations with large polarizable anions give increased covalent character (e.g., LiI > LiF).

Hydrogen bonding (N–H, O–H, F–H) raises boiling point and water solubility; it explains water's high boiling point and ice's low density.

First law: ΔU = q + w; with pressure–volume work w = −PΔV; enthalpy ΔH = ΔU + Δ(PV), and ΔH = q_p at constant pressure.

Gibbs energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0; at equilibrium ΔG = 0 and ΔG° = −RT ln K.

Second law: ΔS_universe ≥ 0; ΔS = q_rev/T; entropy increases for solid → liquid → gas and for increasing moles of gas.

Arrhenius: k = A e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂); a catalyst lowers Ea without changing ΔH or K.

First-order kinetics: t½ = 0.693/k, independent of initial concentration; integrated form ln[A] = ln[A]₀ − kt.

Nernst equation: E = E° − (0.0592/n) log Q at 25 °C; E°cell = E°cathode − E°anode.

ΔG° = −nFE°cell; positive E°cell means spontaneous reaction; Faraday = 96500 C/mol, and mass deposited m = (MIt)/(nF).

Buffer and pH: Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA]); Kw = 1×10⁻¹⁴ at 25 °C so pH + pOH = 14.

SN1 proceeds via carbocation (rate = k[substrate], racemization, favored by tertiary and polar protic solvent); SN2 is backside attack (rate = k[substrate][nucleophile], inversion, favored by primary).

E2 requires anti-periplanar geometry and strong base; E1 shares the carbocation intermediate with SN1 and is favored by heat.

Markovnikov addition to alkenes puts H on the carbon with more hydrogens; peroxide effect (anti-Markovnikov) occurs via free-radical HBr addition only.

Electrophilic aromatic substitution: activating o/p directors are –OH, –OR, –NH₂, –R; deactivating m directors are –NO₂, –CN, –COOH, –SO₃H; halogens are deactivating but o/p directing.

Aldol condensation: enolate attacks carbonyl giving β-hydroxy carbonyl, dehydration yields α,β-unsaturated product; Cannizzaro occurs for aldehydes lacking α-H.

Grignard reagent RMgX adds to aldehydes (→ secondary alcohol), ketones (→ tertiary alcohol), and CO₂ (→ carboxylic acid after hydrolysis).

Oxidation: primary alcohol → aldehyde → carboxylic acid; secondary alcohol → ketone; tertiary alcohols resist oxidation under mild conditions.

Chirality requires four different groups on a carbon; a racemic mixture has zero optical rotation; R/S assigned by CIP priority rules.

Coordination number and geometry: 2 linear, 4 tetrahedral or square planar, 6 octahedral; isomerism includes geometrical, optical, ionization, and linkage types.

Crystal field splitting: Δo (octahedral) > Δt (tetrahedral); high-spin versus low-spin depends on whether Δo exceeds pairing energy.

Spectrochemical series (weak to strong): I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.

Magnetic moment μ = √(n(n+2)) BM where n = number of unpaired electrons; e.g., n = 4 gives ≈ 4.9 BM.

EAN rule: stable complexes often reach 36, 54, or 86 electrons about the metal; e.g., [Fe(CN)₆]⁴⁻ achieves 36.

Chelate effect: polydentate ligands (EDTA, en) give higher stability and entropy-driven formation than comparable monodentate ligands.

Lanthanide contraction: poor 4f shielding causes a small radius decrease, making Zr and Hf nearly identical in size and chemistry.

Transition metals show variable oxidation states (Mn: +2 to +7), catalytic activity, and colored ions from d–d transitions.

Beer–Lambert law: A = εbc; absorbance is linear in concentration only at low concentration and monochromatic light.

Standardization: primary standards are pure, stable, non-hygroscopic (K₂C₂O₄, KHP, Na₂CO₃); molarity from titration uses M₁V₁/n₁ = M₂V₂/n₂.

Iodometry uses liberated I₂ titrated with thiosulfate (starch indicator); iodimetry titrates with standard I₂ directly.

Acid–base indicators change over pKa ± 1; phenolphthalein (8.3–10) suits strong base titrations, methyl orange (3.1–4.4) suits strong acid.

Flame emission (AES) measures excited-state emission; AAS measures ground-state absorption; both use calibration curves for trace metals.

Chromatography: Rf = distance solute/distance solvent front in TLC; GC and HPLC separate by differential partitioning between mobile and stationary phases.

Gravimetric analysis requires a pure, filterable, weighable precipitate; BaSO₄ for sulfate and AgCl for chloride are standard examples.

Errors: systematic errors shift results consistently and can be corrected by calibration; random errors reduce by replicate measurement and averaging.

Contact process: S + O₂ → SO₂, V₂O₅ catalyst at ~450 °C converts SO₂ + ½O₂ ⇌ SO₃, absorbed in H₂SO₄ (not water) to give oleum.

Haber process: N₂ + 3H₂ ⇌ 2NH₃, exothermic, high pressure (~200 atm) and moderate temperature (~450 °C) with iron catalyst.

Ostwald process: NH₃ oxidized over Pt/Rh to NO, then NO₂, absorbed in water to give HNO₃.

Solvay process: NaCl + NH₃ + CO₂ → NaHCO₃ + NH₄Cl; NaHCO₃ calcined to Na₂CO₃, ammonia recovered.

Water quality: BOD measures oxygen consumed by microbes; COD uses strong oxidant; DO below ~4 mg/L harms aquatic life.

Greenhouse gases: CO₂, CH₄, N₂O, and CFCs absorb IR; CFCs also deplete ozone via Cl radicals in a catalytic cycle.

Eutrophication is driven by excess nitrate and phosphate causing algal blooms, oxygen depletion, and fish kills.

Air pollution control: electrostatic precipitators and bag filters remove particulates; lime scrubbing removes SO₂ from flue gas.

Urea (46% N) is the dominant nitrogen fertilizer in Bangladesh; TSP and DAP supply phosphorus, and MoP supplies potassium.

Urea hydrolysis and nitrification acidify soil; lime (CaCO₃) is applied to correct acidity in the Barind and tea-garden soils.

Karnafuli and Shitalakshya river pollution from tanneries, textiles, and fertilizer plants raises heavy-metal and COD loads.

Arsenic contamination of shallow tubewells exceeds 0.05 mg/L in many districts; testing and deep tubewells are the mitigation route.

Natural gas at Titas and Bakhrabad feeds fertilizer (urea) and power plants; gas is mainly methane with H₂S removed by amine scrubbing.

Sugarcane mills (Ishwardi, Joypurhat) and cement, paper, and textile industries are major chemical-processing sectors.

Groundwater salinity in coastal Khulna and Satkhira districts affects drinking water and crop choice.

Public health: fluoride and arsenic in drinking water, pesticide residues on vegetables, and lead exposure are priority chemical hazards.