Class 11 Chemistry Formula Sheet (CBSE 2026-27)

Sub-atomic particles

• \(e/m_e = 1.758820 \times 10^{11}\) C kg\(^{-1}\) (Thomson)
• \(e = 1.602 \times 10^{-19}\) C (Millikan); \(m_e = 9.1094 \times 10^{-31}\) kg
• Mass number \(A = Z + n\) (protons + neutrons)
• Isotopes: same \(Z\); isobars: same \(A\)

Waves and quanta

• \(c = \nu\lambda\); wavenumber \(\bar{\nu} = 1/\lambda\)
• Planck: $$E = h\nu = \frac{hc}{\lambda}$$
• Photoelectric effect: \(h\nu = h\nu_0 + \tfrac{1}{2}m_ev^2\) (\(h\nu_0\) = work function)
• No electrons are emitted below the threshold frequency \(\nu_0\), however intense the light.

Hydrogen spectrum

• $$\bar{\nu} = 109677\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)\ \text{cm}^{-1}$$
• 109677 cm\(^{-1}\) = Rydberg constant for hydrogen; \(n_2 = n_1 + 1, n_1 + 2, \dots\)

Bohr model

• Angular momentum: \(m_evr = \dfrac{nh}{2\pi}\)
• Energy: \(E_n = -R_H\left(\dfrac{1}{n^2}\right)\), \(R_H = 2.18 \times 10^{-18}\) J
• Hydrogen-like ion: $$E_n = -2.18 \times 10^{-18}\left(\frac{Z^2}{n^2}\right)\ \text{J}$$
• Radius: \(r_n = \dfrac{52.9\,n^2}{Z}\) pm (\(a_0 = 52.9\) pm)
• \(\Delta E = 2.18 \times 10^{-18}\left(\dfrac{1}{n_i^2} - \dfrac{1}{n_f^2}\right)\) J; \(\ \nu = \Delta E/h\)

Dual nature and uncertainty

• de Broglie: $$\lambda = \frac{h}{mv} = \frac{h}{p}$$
• Heisenberg: $$\Delta x \times \Delta p_x \ge \frac{h}{4\pi}$$ equivalently \(\Delta x \times \Delta v_x \ge \dfrac{h}{4\pi m}\)

Quantum numbers

• \(n = 1, 2, 3, \dots\) (shell); max electrons in a shell \(= 2n^2\)
• \(l = 0, 1, \dots, n-1\) (s, p, d, f); orbitals in a subshell \(= 2l + 1\)
• \(m_l = -l, \dots, 0, \dots, +l\); \(\ m_s = \pm\tfrac{1}{2}\)
• Nodes: radial \(= n - l - 1\), angular \(= l\), total \(= n - 1\)

Filling orbitals

• Aufbau: lower \((n + l)\) fills first; equal \((n + l)\): lower \(n\) first
• Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s
• Pauli: no two electrons have all four quantum numbers the same
• Hund: pairing starts only after each orbital of the subshell has one electron
• Half-filled and fully filled subshells are extra stable: Cr is [Ar]3d\(^5\)4s\(^1\), Cu is [Ar]3d\(^{10}\)4s\(^1\).

Modern periodic law

• Properties are periodic functions of atomic number
• 7 periods, 18 groups; period number = highest \(n\)
• s-block: \(ns^{1-2}\); p-block: \(ns^2np^{1-6}\); d-block: \((n-1)d^{1-10}ns^{0-2}\); f-block: \((n-2)f^{1-14}(n-1)d^{0-1}ns^2\)

Naming elements with \(Z > 100\)

• Add "ium": \(Z = 120\) is unbinilium (Ubn).

Formal charge

• $$\text{F.C.} = V - L - \tfrac{1}{2}S$$
• \(V\) = valence electrons in the free atom, \(L\) = non-bonding (lone pair) electrons, \(S\) = bonding (shared) electrons
• The lowest-energy Lewis structure has the smallest formal charges.

Bond parameters

• Bond order (Lewis) = number of bonds between two atoms
• Higher bond order: higher bond enthalpy, shorter bond length
• Dipole moment: \(\mu = Q \times r\); 1 D \(= 3.33564 \times 10^{-30}\) C m
• \(\mu = 0\) for symmetric molecules (CO\(_2\), BF\(_3\), CH\(_4\)); \(\mu(\ce{NH3}) > \mu(\ce{NF3})\).

Hybridisation

Molecular orbital theory

• $$\text{Bond order} = \tfrac{1}{2}(N_b - N_a)$$
• \(N_b > N_a\): stable; \(N_b \le N_a\): unstable
• H\(_2\) = 1, He\(_2\) = 0, Li\(_2\) = 1, C\(_2\) = 2, N\(_2\) = 3, O\(_2\) = 2
• Unpaired electrons: paramagnetic (O\(_2\)); all paired: diamagnetic
• Up to N\(_2\), \(\pi 2p_x = \pi 2p_y\) lies below \(\sigma 2p_z\); for O\(_2\) and F\(_2\), \(\sigma 2p_z\) lies below.

Hydrogen bonding

• H bonded to F, O or N attracts a nearby electronegative atom
• Intermolecular: HF, water, alcohols
• Intramolecular: o-nitrophenol
• Strength order of H-bonding: solid > liquid > gas.

First law

• $$\Delta U = q + w$$ (\(q\), \(w\) positive when added to the system)
• Expansion work: \(w = -p_{ex}\Delta V\)
• Isothermal reversible: $$w_{rev} = -2.303\,nRT\log\frac{V_f}{V_i}$$
• Free expansion (vacuum): \(w = 0\)
• \(U\), \(H\), \(S\), \(G\) are state functions; \(q\) and \(w\) are not.

Enthalpy and heat capacity

• \(\Delta U = q_V\) (constant volume); \(\Delta H = q_p\) (constant pressure)
• $$\Delta H = \Delta U + \Delta n_g RT$$
• \(q = C\Delta T = mc\,\Delta T\)
• Ideal gas: \(C_p - C_V = R\)

Reaction enthalpies

• $$\Delta_r H^\circ = \sum a_i\,\Delta_f H^\circ(\text{products}) - \sum b_i\,\Delta_f H^\circ(\text{reactants})$$
• Gases: \(\Delta_r H^\circ = \sum\) bond enthalpies (reactants) \(- \sum\) bond enthalpies (products)
• Hess's law: \(\Delta_r H = \Delta_r H_1 + \Delta_r H_2 + \dots\) (path-independent)
• \(\Delta_f H^\circ\) of an element in its standard state = 0

Types of enthalpy change

• Phase changes: fusion, vaporisation, sublimation (always positive, at constant \(T\))
• Combustion, atomization, bond dissociation, solution, lattice enthalpy
• Lattice enthalpy from the Born-Haber cycle; \(\Delta_{sol}H = \Delta_{lattice}H + \Delta_{hyd}H\)

Entropy and Gibbs energy

• \(\Delta S = \dfrac{q_{rev}}{T}\); spontaneous change: \(\Delta S_{total} > 0\)
• $$\Delta_r G = \Delta_r H - T\Delta_r S$$
• \(\Delta G < 0\): spontaneous; \(\Delta G = 0\): equilibrium
• $$\Delta_r G^\circ = -RT\ln K = -2.303\,RT\log K$$
• Third law: entropy of a perfect crystal \(\to 0\) as \(T \to 0\) K

Effect of temperature on spontaneity

Equilibrium constants

• \(\ce{aA + bB <=> cC + dD}\): $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$
• \(K_p\): same form with partial pressures
• $$K_p = K_c(RT)^{\Delta n}$$ (\(\Delta n\) = moles of gaseous products \(-\) reactants)
• Reverse reaction: \(K'_c = 1/K_c\); equation multiplied by \(n\): \(K''_c = K_c^{\,n}\)
• Pure solids and liquids are left out of \(K\) (heterogeneous equilibria).

Reaction quotient and Gibbs energy

• \(Q_c < K_c\): net forward; \(Q_c > K_c\): net reverse; \(Q_c = K_c\): at equilibrium
• \(\Delta G = \Delta G^\circ + RT\ln Q\)
• \(\Delta G^\circ = -RT\ln K\), so \(K = e^{-\Delta G^\circ/RT}\)
• \(\Delta G^\circ < 0\) gives \(K > 1\) (products favoured).

Le Chatelier's principle

• Adding reactant / removing product: shifts forward
• Higher pressure: shifts to fewer gas moles
• Higher temperature: favours the endothermic direction (and changes \(K\))
• Catalyst: no shift, equilibrium reached sooner
• Inert gas at constant volume: no effect

Acids and bases

• Arrhenius: gives H\(^+\) / OH\(^-\) in water
• Brönsted-Lowry: proton donor / proton acceptor; conjugate pairs differ by one H\(^+\)
• Lewis: electron-pair acceptor / electron-pair donor

Water and pH

• \(K_w = [\ce{H3O+}][\ce{OH-}] = 1.0 \times 10^{-14}\) at 298 K
• $$\text{pH} = -\log[\ce{H3O+}]$$
• \(\text{pH} + \text{pOH} = \text{p}K_w = 14\) (298 K)
• Neutral pH 7; acidic < 7; basic > 7 (298 K)

Weak acids and bases

• $$K_a = \frac{c\alpha^2}{1 - \alpha}$$ (\(\alpha\) = degree of ionization); same form for \(K_b\)
• \(\text{p}K_a = -\log K_a\); \(\ \text{p}K_b = -\log K_b\)
• Conjugate pair: \(K_a \times K_b = K_w\); \(\ \text{p}K_a + \text{p}K_b = 14\)
• Adding a common ion suppresses ionization of a weak electrolyte.

Salt hydrolysis and buffers

• Salt of weak acid + weak base: $$\text{pH} = 7 + \tfrac{1}{2}(\text{p}K_a - \text{p}K_b)$$
• Strong acid + weak base salt: acidic; weak acid + strong base salt: basic
• Henderson-Hasselbalch (acidic buffer): $$\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}$$
• Basic buffer: \(\text{pOH} = \text{p}K_b + \log\dfrac{[\ce{BH+}]}{[\ce{B}]}\)

Solubility product

• \(\ce{M_xX_y <=> xM^{p+} + yX^{q-}}\): \(K_{sp} = [\ce{M^{p+}}]^x[\ce{X^{q-}}]^y\)
• With molar solubility \(S\): $$K_{sp} = x^x y^y S^{x+y}$$
• Precipitation when ionic product \(Q_{sp} > K_{sp}\)
• A common ion lowers solubility.

Definitions

• Oxidation: loss of electrons, increase in oxidation number
• Reduction: gain of electrons, decrease in oxidation number
• Oxidant is itself reduced; reductant is itself oxidised
• e.g. \(\ce{Zn(s) + Cu^2+(aq) -> Zn^2+(aq) + Cu(s)}\)

Oxidation number rules

• Free element: 0; monatomic ion: its charge
• O: \(-2\) (peroxides \(-1\), superoxides \(-\tfrac{1}{2}\), OF\(_2\) \(+2\))
• H: \(+1\) (metal hydrides \(-1\)); F: always \(-1\)
• Sum = 0 for a molecule, = charge for a polyatomic ion

Types of redox reactions

• Combination: \(\ce{C(s) + O2(g) -> CO2(g)}\)
• Decomposition: \(\ce{2H2O(l) -> 2H2(g) + O2(g)}\)
• Displacement (metal or non-metal): \(\ce{Zn + CuSO4 -> ZnSO4 + Cu}\)
• Disproportionation: \(\ce{2H2O2(aq) -> 2H2O(l) + O2(g)}\) (O: \(-1 \to -2\) and 0)

Balancing redox equations

• Oxidation number method: equalise total increase and decrease in O.N.
• Half-reaction (ion-electron) method: balance each half for atoms, then O with H\(_2\)O, H with H\(^+\) (acid) or OH\(^-\) (base), then charge with e\(^-\); add halves

Bond fission and intermediates

• Homolytic fission: free radicals
• Heterolytic fission: carbocation (sp\(^2\), planar) and carbanion (sp\(^3\), pyramidal)
• Carbocation stability: $$\ce{CH3+} < \ce{CH3CH2+} < \ce{(CH3)2CH+} < \ce{(CH3)3C+}$$
• Electrophile: electron-pair acceptor (\(\ce{H+}\), \(\ce{NO2+}\)); nucleophile: electron-pair donor (OH\(^-\), CN\(^-\), NH\(_3\))

Electron displacement effects

• Inductive effect (\(-I\): NO\(_2\), CN, halogens; \(+I\): alkyl groups); permanent, along \(\sigma\) bonds
• Resonance effect (\(+R\): halogens, OH, NH\(_2\); \(-R\): COOH, CHO, CN, NO\(_2\))
• Electromeric effect: temporary, only while the reagent is present
• Hyperconjugation: \(\sigma\)(C-H) delocalisation; more \(\alpha\)-H gives more stability

Isomerism

• Structural: chain, position, functional group, metamerism
• Stereoisomerism: geometrical and optical

Purification

• Sublimation, crystallisation, distillation (fractional, under reduced pressure, steam), differential extraction, chromatography
• Retardation factor: $$R_f = \frac{\text{distance moved by substance}}{\text{distance moved by solvent}}$$

Preparation of alkanes

• Hydrogenation: \(\ce{CH2=CH2 + H2 ->[Pt/Pd/Ni] CH3-CH3}\)
• Alkyl halide reduction: \(\ce{CH3Cl + H2 ->[Zn, H+] CH4 + HCl}\)
• Wurtz reaction: \(\ce{2CH3Br + 2Na ->[dry ether] CH3-CH3 + 2NaBr}\) (even-carbon alkanes)
• Decarboxylation: \(\ce{CH3COONa + NaOH ->[CaO][\Delta] CH4 + Na2CO3}\)
• Kolbe's electrolysis: \(\ce{2CH3COONa + 2H2O -> CH3-CH3 + 2CO2 + H2 + 2NaOH}\) (ethane at anode; methane cannot be made)

Reactions of alkanes

• Halogenation (free radical, \(h\nu\)): \(\ce{CH4 + Cl2 -> CH3Cl + HCl}\) and further to CCl\(_4\); rate F\(_2\) > Cl\(_2\) > Br\(_2\) > I\(_2\); H replaced 3° > 2° > 1°
• Combustion: \(\text{C}_n\text{H}_{2n+2} + \dfrac{3n+1}{2}\,\text{O}_2 \longrightarrow n\,\text{CO}_2 + (n+1)\,\text{H}_2\text{O}\)
• Controlled oxidation: \(\ce{2CH4 + O2 ->[Cu/523 K/100 atm] 2CH3OH}\); \(\ce{CH4 + O2 ->[Mo2O3] HCHO + H2O}\); \(\ce{2CH3CH3 + 3O2 ->[(CH3COO)2Mn] 2CH3COOH + 2H2O}\)
• KMnO\(_4\): \(\ce{(CH3)3CH -> (CH3)3COH}\)
• Isomerisation (anhyd. AlCl\(_3\)/HCl): n-hexane \(\to\) 2- and 3-methylpentane
• Aromatization (V, Mo or Cr oxides on alumina, 773 K): n-hexane \(\to\) benzene
• Steam: \(\ce{CH4 + H2O ->[Ni][1273 K] CO + 3H2}\); pyrolysis (cracking) of higher alkanes

Conformations of ethane

• Staggered (most stable) and eclipsed (least stable); skew in between
• Shown by Sawhorse and Newman projections
• Torsional strain: rotation barrier about 12.5 kJ mol\(^{-1}\)

Preparation of alkenes

• Alkyne + H\(_2\), Lindlar's catalyst (Pd/C poisoned): cis-alkene; Na in liquid NH\(_3\): trans-alkene
• Dehydrohalogenation (alc. KOH, \(\beta\)-elimination): rate I > Br > Cl and 3° > 2° > 1°
• Dehalogenation: \(\ce{CH2Br-CH2Br + Zn -> CH2=CH2 + ZnBr2}\)
• Acidic dehydration: \(\ce{CH3CH2OH ->[conc. H2SO4][\Delta] CH2=CH2 + H2O}\)

Reactions of alkenes

• Br\(_2\)/CCl\(_4\): vicinal dibromide; orange colour discharged (test for unsaturation)
• HX (HI > HBr > HCl): Markovnikov's rule, \(\ce{CH3CH=CH2 + HBr -> CH3CHBrCH3}\)
• Peroxide (Kharash) effect, HBr only: \(\ce{CH3CH=CH2 + HBr ->[(C6H5CO)2O2] CH3CH2CH2Br}\)
• Cold conc. H\(_2\)SO\(_4\): alkyl hydrogen sulphate; H\(_2\)O/H\(^+\): alcohol (both Markovnikov)
• Baeyer's reagent (cold dil. KMnO\(_4\)): vicinal glycol; KMnO\(_4\)/H\(^+\): \(\ce{CH3CH=CHCH3 -> 2CH3COOH}\)
• Ozonolysis: \(\ce{O3}\), then Zn/H\(_2\)O, gives aldehydes/ketones (locates the double bond)
• Polymerisation: \(n\,\ce{CH2=CH2 -> (-CH2-CH2-)_n}\) (polythene)

Alkynes

• From CaC\(_2\): \(\ce{CaC2 + 2H2O -> Ca(OH)2 + C2H2}\)
• From vicinal dihalide: alc. KOH, then NaNH\(_2\)
• Acidic H: \(\ce{HC#CH + Na -> HC#C^-Na+ + 1/2H2}\); acidity \(\ce{HC#CH} > \ce{H2C=CH2} > \ce{CH3-CH3}\)
• 2 HBr: gem-dihalide, \(\ce{HC#CH -> CH2=CHBr -> CH3CHBr2}\)
• Water (HgSO\(_4\)/dil. H\(_2\)SO\(_4\), 333 K): carbonyl compound
• Cyclic polymerisation: \(\ce{3HC#CH ->[red-hot Fe tube][873 K] C6H6}\)

Benzene and aromaticity

• Hückel rule: planar, fully delocalised, \((4n + 2)\,\pi\) electrons
• All C-C bonds 139 pm (between 154 and 133 pm)
• Preparation: cyclic polymerisation of ethyne; sodium benzoate + soda lime; phenol over heated Zn dust

Electrophilic substitution of benzene

• Nitration (conc. HNO\(_3\) + conc. H\(_2\)SO\(_4\), electrophile \(\ce{NO2+}\)): nitrobenzene
• Halogenation (anhyd. FeCl\(_3\)/AlCl\(_3\)): chlorobenzene
• Sulphonation (oleum): benzenesulphonic acid
• Friedel-Crafts alkylation: \(\ce{C6H6 + CH3Cl ->[anhyd. AlCl3] C6H5CH3 + HCl}\)
• Friedel-Crafts acylation: \(\ce{C6H6 + CH3COCl ->[anhyd. AlCl3] C6H5COCH3 + HCl}\)

Addition and directive influence

• \(\ce{C6H6 + 3H2 ->[Ni] C6H12}\) (cyclohexane); \(\ce{C6H6 + 3Cl2 ->[UV] C6H6Cl6}\) (BHC, gammaxane)
• Combustion: \(\text{C}_x\text{H}_y + \left(x + \dfrac{y}{4}\right)\text{O}_2 \longrightarrow x\,\text{CO}_2 + \dfrac{y}{2}\,\text{H}_2\text{O}\)
• o/p-directing, activating: \(-\)OH, \(-\)NH\(_2\), \(-\)OCH\(_3\), \(-\)CH\(_3\)
• o/p-directing, deactivating: halogens
• m-directing, deactivating: \(-\)NO\(_2\), \(-\)CN, \(-\)CHO, \(-\)COOH, \(-\)SO\(_3\)H