ChemistryJEE Main & Advanced

Chemistry Formulas

Formulas and cheat sheets for chemical equilibrium, thermodynamics, crystal lattices, kinetics, coordination complexes, and reaction mechanisms.

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Chapter Directory (21 Chapters)

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Physical Chemistry471 Qs

Mole Concept & Stoichiometry

Mole concept, molarity, molality, normality, mole fraction, limiting reagent, and empirical formula.

8 Formulas

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Physical Chemistry568 Qs

Structure of Atom

Planck's quantum theory, photoelectric effect, de Broglie relation, Heisenberg uncertainty principle, and quantum numbers.

8 Formulas Diagram

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Physical Chemistry703 Qs

Chemical Thermodynamics & Energetics

Enthalpy, entropy, Gibbs free energy, Hess law, Kirchhoff equation, and equilibrium constant temperature dependence.

8 Formulas Diagram

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Physical Chemistry486 Qs

Chemical & Ionic Equilibrium

K_p & K_c relations, pH calculations of weak acids/bases, buffer solutions, Henderson equation, and solubility product K_sp.

8 Formulas

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Physical Chemistry685 Qs

Electrochemistry & Conductance

Nernst equation, Gibbs energy of cell, Kohlrausch law, Faraday laws of electrolysis, and molar conductivity.

8 Formulas Diagram

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Physical Chemistry671 Qs

Solutions & Colligative Properties

Raoult's law, relative lowering of vapor pressure, elevation in boiling point, depression in freezing point, and van 't Hoff factor.

8 Formulas

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Physical Chemistry464 Qs

Chemical Kinetics

Rate laws, order and molecularity, integrated rate equations for zero and first order, half-life, and Arrhenius equation.

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Physical Chemistry430 Qs

Solid State Chemistry

Unit cell geometry, density formula, packing efficiency of SC/BCC/FCC, radius ratios, and crystal defects.

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Inorganic Chemistry367 Qs

Periodic Table & Periodic Properties

Ionization enthalpy, electron gain enthalpy, electronegativity (Pauling & Mulliken scales), screening effect, and atomic radii trends.

7 Formulas

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Inorganic Chemistry894 Qs

p-Block Elements

Group 15 (N, P, As), Group 16 (O, S), Group 17 (Halogens), Group 18 (Noble Gases) — oxoacids, interhalogen compounds, allotropes, and trend rules.

9 Formulas

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Inorganic Chemistry698 Qs

Chemical Bonding & VSEPR

VSEPR molecular geometries, steric number hybridization, bond order from MOT, dipole moments, and hydrogen bonding.

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Inorganic Chemistry772 Qs

Coordination Compounds

Werner theory, crystal field splitting (CFT), spectrochemical series, magnetic moments, and isomerism.

9 Formulas

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Inorganic Chemistry589 Qs

d- & f-Block Elements

Transition element trends, variable oxidation states, lanthanide contraction, catalytic properties, and potassium permanganate/dichromate reactions.

8 Formulas

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Organic Chemistry377 Qs

General Organic Chemistry (GOC)

Inductive effect, resonance & mesomeric effect, hyperconjugation, aromaticity (Hückel's 4n+2 rule), and carbocation stability.

7 Formulas

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Organic Chemistry514 Qs

Hydrocarbons (Alkanes, Alkenes, Alkynes)

Markovnikov & anti-Markovnikov additions, ozonolysis, Wurtz reaction, Friedel-Crafts alkylation/acylation, and acidic nature of alkynes.

8 Formulas

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Organic Chemistry527 Qs

Haloalkanes & Haloarenes

SN1 and SN2 nucleophilic substitutions, E1 and E2 eliminations, Saytzeff rule, and Grignard reagent synthesis.

8 Formulas

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Organic Chemistry594 Qs

Alcohols, Phenols & Ethers

Lucas test, Reimer-Tiemann reaction, Kolbe reaction, Williamson ether synthesis, and acidic strength of phenols.

8 Formulas

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Organic Chemistry395 Qs

Aldehydes, Ketones & Carboxylic Acids

Nucleophilic addition, Aldol condensation, Cannizzaro reaction, Tollens/Fehling test, Hell-Volhard-Zelinsky (HVZ) reaction.

9 Formulas

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Organic Chemistry585 Qs

Amines & Diazonium Salts

Basicity of amines in gas/aqueous phase, Hoffmann bromamide degradation, Gabriel phthalimide synthesis, and Sandmeyer reaction.

7 Formulas

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Organic Chemistry572 Qs

Biomolecules & Polymers

Carbohydrates (glucose, fructose, mutarotation), amino acids, peptide bonds, isoelectric point, and nucleic acids (DNA/RNA).

8 Formulas

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Inorganic Chemistry512 Qs

Principles of Practical Chemistry & Salt Analysis

Systematic qualitative analysis of cations (Groups 0 to VI) and anions, confirmatory tests, flame tests, borax bead test, and organic functional group identification.

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Formulas Reference (All)

21 Chapters match

Physical ChemistryHigh Yield (1-2 Qs in JEE)471 PYQs

Mole Concept & Stoichiometry

Mole concept, molarity, molality, normality, mole fraction, limiting reagent, and empirical formula.

Chapter

Concentration Units (Molarity, Molality, Normality)

M = \frac{n_{\text{solute}}}{V_{\text{solution (L)}}}, \quad m = \frac{n_{\text{solute}}}{w_{\text{solvent (kg)}}}, \quad N = M \times n\text{-factor}

Fundamental quantitative measures of solution concentration.

Normality equals Molarity times valence n-factor.

Mole Fraction & Relation with Molality

X_A + X_B = 1, \quad m = \frac{X_B \times 1000}{(1 - X_B) M_A}

Converts mole fraction of solute X_B to molality m.

M_A is the molar mass of the solvent.

Average Molar Mass & Vapor Density

M_{\text{avg}} = \frac{\sum n_i M_i}{\sum n_i}, \quad \text{Molar Mass} = 2 \times \text{Vapor Density}

Molecular weight calculation for gas mixtures and unknown volatile compounds.

Vapor density is measured relative to Hydrogen gas.

Equivalent Weight & n-Factor Rules

E = \frac{\text{Molar Mass}}{n\text{-factor}}, \quad n\text{-factor}(\text{KMnO}_4): \begin{cases} 5 & \text{Acidic } (\text{Mn}^{2+}) \\ 3 & \text{Neutral } (\text{MnO}_2) \\ 1 & \text{Alkaline } (\text{MnO}_4^{2-}) \end{cases}

Calculates chemical equivalent weight. For acids: replaceable H⁺ count; bases: replaceable OH⁻ count; redox: change in oxidation state per molecule.

For K₂Cr₂O₇ in acidic medium: Cr goes from +6 to +3, giving n-factor = 2 × 3 = 6 (E = M / 6).

Law of Chemical Equivalence & Titration

N_1 V_1 = N_2 V_2, \quad \text{mEq} = N \times V_{\text{mL}} = \frac{\text{mass (g)}}{E} \times 1000

In any complete stoichiometric reaction, the number of gram-equivalents of all reactants and products are identical.

Does NOT require balancing the stoichiometric reaction equation beforehand.

Empirical Formula & Dulong-Petit Law

\text{MF} = (\text{EF})_n \quad \left(n = \frac{\text{Molar Mass}}{\text{EF Mass}}\right), \quad \text{Atomic Weight} \times \text{Specific Heat (cal/g)} \approx 6.4

Determination of true molecular formula from simplest atomic ratio and Dulong-Petit approximate atomic mass estimation for solid metals.

Valence of metal = (Approximate Atomic Weight) / (Equivalent Weight).

Limiting Reagent, Percentage Yield & Purity

\text{LR: Smallest } \frac{\text{Moles}}{\text{Coefficient}}, \quad \% \text{ Yield} = \frac{\text{Actual}}{\text{Theoretical}} \times 100\%, \quad \% \text{ Purity} = \frac{m_{\text{pure}}}{m_{\text{sample}}} \times 100\%

Limiting reagent is consumed first and dictates the maximum theoretical amount of product formed.

Always balance the chemical reaction before dividing moles by stoichiometric coefficients.

Volume Strength of H₂O₂ & Parts Per Million (ppm)

\text{Volume Strength} = 11.2 \times M = 5.6 \times N, \quad \text{ppm} = \frac{w_{\text{solute}}}{w_{\text{solution}}} \times 10^6

Volume of O₂ liberated at STP from 1 volume of hydrogen peroxide solution upon decomposition, and ppm trace concentration unit.

20 volume H₂O₂ has molarity M = 20 / 11.2 ≈ 1.78 M and normality N = 20 / 5.6 ≈ 3.57 N.

Physical ChemistryHigh Yield (2 Qs in JEE)568 PYQs

Structure of Atom

Planck's quantum theory, photoelectric effect, de Broglie relation, Heisenberg uncertainty principle, and quantum numbers.

Chapter

Planck Quantum Energy & de Broglie Wavelength

E = h\nu = \frac{hc}{\lambda}, \quad \lambda = \frac{h}{mv} = \frac{h}{\sqrt{2m(KE)}}

Wave-particle duality relations.

Energy of one mole of photons (Einstein): E = N_A h ν.

Heisenberg's Uncertainty Principle

\Delta x \cdot \Delta p \ge \frac{h}{4\pi} = \frac{\hbar}{2}, \quad \Delta x \cdot \Delta v \ge \frac{h}{4\pi m}

Fundamental limit on simultaneous measurement of conjugate variables.

Also applies to energy and time: ΔE · Δt ≥ h / (4π).

Quantum Numbers & Nodal Surfaces

\text{Radial Nodes} = n - l - 1, \quad \text{Angular Nodes} = l, \quad \text{Total Nodes} = n - 1

Characterization of electronic orbitals (n, l, m, s).

Orbital angular momentum L = √(l(l+1)) ħ.

Bohr Model for Hydrogenic Atoms

r_n = 0.529 \frac{n^2}{Z} \text{ \AA}, \quad v_n = 2.18 \times 10^6 \frac{Z}{n} \text{ m/s}, \quad E_n = -13.6 \frac{Z^2}{n^2} \text{ eV/atom} = -\frac{2.18 \times 10^{-18} Z^2}{n^2} \text{ J}

Quantized orbital radius, electron orbital velocity, and total electronic energy levels for single-electron species (H, He⁺, Li²⁺, Be³⁺).

Kinetic Energy K = -E_n = +13.6 Z²/n² eV; Potential Energy U = 2E_n = -27.2 Z²/n² eV.

Einstein's Photoelectric Equation

h\nu = \Phi_0 + KE_{\text{max}} = h\nu_0 + e V_s, \quad KE_{\text{max}} = hc\left(\frac{1}{\lambda} - \frac{1}{\lambda_0}\right)

Conservation of energy in photoelectric emission where Φ₀ = hν₀ is work function and V_s is stopping potential.

Slope of stopping potential V_s versus incident frequency ν is universal constant h/e.

Orbital & Spin Angular Momentum

L_{\text{orbital}} = \sqrt{l(l+1)}\frac{h}{2\pi} = \sqrt{l(l+1)}\hbar, \quad \mu_s = \sqrt{n(n+2)} \text{ BM} \quad (n = \text{unpaired } e^-)

Spatial angular momentum of atomic orbitals and spin-only magnetic moment in Bohr Magnetons.

For s-orbital (l = 0), orbital angular momentum is strictly ZERO.

Rydberg Formula & Hydrogen Emission Spectral Series

\bar{\nu} = \frac{1}{\lambda} = R_H Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right), \quad N_{\text{lines}} = \frac{(n_2 - n_1)(n_2 - n_1 + 1)}{2}

Wavenumbers of emitted spectral lines. Lyman (n₁=1, UV), Balmer (n₁=2, visible), Paschen (n₁=3, IR), Brackett (n₁=4, IR), Pfund (n₁=5, far-IR).

Only the Balmer series falls in the human-visible region of electromagnetic spectrum.

Radial Probability Distribution Function

P(r)\,dr = 4\pi r^2 R_{n,l}^2(r)\,dr, \quad r_{\text{max probability}}(1s) = a_0 = 0.529\,\text{\AA}

Probability of finding an electron in a spherical shell of radius r and thickness dr surrounding the nucleus.

At r = 0, probability density ψ² is maximum for s-orbitals, but radial probability P(r) is zero due to the 4πr² geometric factor.

Physical ChemistryTop Priority (3-4 Qs in JEE)703 PYQs

Chemical Thermodynamics & Energetics

Enthalpy, entropy, Gibbs free energy, Hess law, Kirchhoff equation, and equilibrium constant temperature dependence.

Chapter

First Law & Enthalpy Relation

\Delta U = q + w = q - P_{\text{ext}}\Delta V, \quad \Delta H = \Delta U + \Delta n_g R T

First law formulation with enthalpy-internal energy gaseous conversion.

Δn_g = (moles of gaseous products) - (moles of gaseous reactants).

Gibbs Free Energy & Spontaneity

\Delta G = \Delta H - T\Delta S, \quad \Delta G^\circ = -RT \ln K = -2.303 RT \log_{10} K

Universal thermodynamic criterion for spontaneity and chemical equilibrium.

Spontaneous if ΔG < 0; at equilibrium ΔG = 0; non-spontaneous if ΔG > 0.

Kirchhoff's Thermochemical Equation

\Delta H_{T_2} = \Delta H_{T_1} + \Delta C_p(T_2 - T_1), \quad \Delta U_{T_2} = \Delta U_{T_1} + \Delta C_v(T_2 - T_1)

Temperature dependence of standard reaction enthalpy and internal energy.

ΔC_p = ∑ C_p(products) - ∑ C_p(reactants).

Entropy Changes in Physical Processes

\Delta S = \frac{q_{\text{rev}}}{T}, \quad \Delta S_{\text{gas}} = n C_v \ln\frac{T_2}{T_1} + n R \ln\frac{V_2}{V_1} = n C_p \ln\frac{T_2}{T_1} - n R \ln\frac{P_2}{P_1}

Entropy change for state transitions of ideal gas.

In isothermal process, ΔS = n R ln(V₂/V₁) = -n R ln(P₂/P₁).

Van 't Hoff Isochore Equation

\ln\frac{K_2}{K_1} = \frac{\Delta H^\circ}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Temperature variation of equilibrium constant K.

For endothermic reactions (ΔH° > 0), K increases as T increases; for exothermic, K decreases.

Work Done: Reversible vs Irreversible (Isothermal & Adiabatic)

w_{\text{iso, rev}} = -2.303 n R T \log_{10}\left(\frac{V_2}{V_1}\right), \quad w_{\text{adiab, rev}} = \frac{n R(T_2 - T_1)}{\gamma - 1} = \frac{P_2 V_2 - P_1 V_1}{\gamma - 1}

Pressure-volume work for fundamental paths. In expansion, reversible work output is strictly greater than irreversible work.

Free expansion against vacuum (P_ext = 0) has w = 0, q = 0, ΔT = 0 for ideal gas (both isothermal and adiabatic).

Standard Enthalpy via Bond Energies & Hess's Law

\Delta_r H^\circ = \sum \text{B.E.}_{\text{reactants}} - \sum \text{B.E.}_{\text{products}} = \sum \Delta_f H^\circ_{\text{products}} - \sum \Delta_f H^\circ_{\text{reactants}}

Enthalpy calculation from chemical bond dissociation energies or standard enthalpies of formation.

Standard enthalpy of formation Δ_f H° of elements in their reference standard states (e.g. C_graphite, O₂ gas, Br₂ liquid) is zero by convention.

Molar Heat Capacities & Degrees of Freedom

C_p - C_v = R, \quad \gamma = \frac{C_p}{C_v} = 1 + \frac{2}{f} \implies \begin{cases} \text{Monoatomic } (f=3): \gamma = 5/3 \approx 1.67 \\ \text{Diatomic } (f=5): \gamma = 7/5 = 1.40 \end{cases}

Mayer's relation and adiabatic exponent γ connection to molecular translational and rotational degrees of freedom.

At high temperatures, vibrational modes become active, contributing an additional R to C_v.

Physical ChemistryTop Priority (3 Qs in JEE)486 PYQs

Chemical & Ionic Equilibrium

K_p & K_c relations, pH calculations of weak acids/bases, buffer solutions, Henderson equation, and solubility product K_sp.

Chapter

Kp and Kc Relation

K_p = K_c (RT)^{\Delta n_g}, \quad \Delta n_g = \sum n_{\text{gas (prod)}} - \sum n_{\text{gas (react)}}

Connects partial pressure equilibrium constant K_p and molarity constant K_c.

If Δn_g = 0, K_p = K_c and equilibrium is independent of total pressure.

Ostwald's Dilution Law & pH of Weak Acid

\alpha = \sqrt{\frac{K_a}{C}}, \quad [H^+] = \sqrt{K_a C} = C\alpha, \quad \text{pH} = \frac{1}{2}[\text{p}K_a - \log_{10} C]

Degree of dissociation and hydronium concentration for weak monoprotic acid.

Valid only when degree of dissociation α ≤ 0.05 (5%).

Henderson-Hasselbalch Equation (Buffer Solutions)

\text{pH} = \text{p}K_a + \log_{10}\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right), \quad \text{pOH} = \text{p}K_b + \log_{10}\left(\frac{[\text{Salt}]}{[\text{Base}]}\right)

Calculates pH of acidic and basic buffer solutions resistent to pH change.

Maximum buffer capacity occurs when [Salt] = [Acid], giving pH = pKa.

Salt Hydrolysis pH Formulas

\text{Weak Acid + Strong Base: } \text{pH} = 7 + \frac{1}{2}(\text{p}K_a + \log_{10} C), \quad \text{Weak Acid + Weak Base: } \text{pH} = 7 + \frac{1}{2}(\text{p}K_a - \text{p}K_b)

Hydrolysis of salts producing alkaline or acidic aqueous solutions.

Salt of weak acid and weak base pH is independent of concentration C.

Solubility Product (K_sp) & Common Ion Effect

A_x B_y (s) \rightleftharpoons x A^{y+} + y B^{x-} \implies K_{\text{sp}} = x^x y^y S^{x+y}, \quad S' = \frac{K_{sp}}{[\text{Common Ion}]^y}

Equilibrium constant for sparingly soluble salts, and suppression of solubility in presence of shared ions.

Common ion effect drastically decreases solubility S without altering K_sp.

Strong Acid + Weak Base Salt Hydrolysis

\text{pH} = 7 - \frac{1}{2}(\text{p}K_b + \log_{10} C), \quad K_h = \frac{K_w}{K_b}, \quad h = \sqrt{\frac{K_w}{K_b C}}

Cationic hydrolysis producing an acidic solution (e.g. NH₄Cl).

Degree of hydrolysis h increases upon dilution.

Buffer Capacity & Effective Buffer Range

\beta = \frac{d B}{d\text{pH}} = 2.303 \frac{C_{\text{acid}} C_{\text{salt}}}{C_{\text{acid}} + C_{\text{salt}}}, \quad \text{Effective Range: } \text{pH} = \text{p}K_a \pm 1

Quantitative measure of buffer resistance to pH change upon addition of strong acid/base.

Maximum buffer capacity occurs at pH = pKa (equimolar ratio of conjugate acid-base pair).

Van 't Hoff Isochore & Temperature Dependence

\ln\left(\frac{K_2}{K_1}\right) = \frac{\Delta H^\circ}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right), \quad \text{Inert gas at const. } V: \Delta n_g \text{ no shift}

Variation of equilibrium constant K with absolute temperature T governed by standard enthalpy of reaction ΔH°.

Endothermic reactions (ΔH° > 0) have higher K at higher temperatures; exothermic reactions have lower K.

Physical ChemistryTop Priority (3-4 Qs in JEE)685 PYQs

Electrochemistry & Conductance

Nernst equation, Gibbs energy of cell, Kohlrausch law, Faraday laws of electrolysis, and molar conductivity.

Chapter

Nernst Equation (at 298 K)

E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log_{10} Q

Computes non-standard cell potential under varying ion concentrations.

At equilibrium, E_cell = 0 and Q = K_eq.

Standard Cell Potential & Free Energy

\Delta G^\circ = -n F E^\circ_{\text{cell}}, \quad \log_{10} K = \frac{n E^\circ_{\text{cell}}}{0.0591}

Connects electrochemical cell voltage to standard Gibbs energy and equilibrium constant.

F = Faraday constant ≈ 96500 C/mol.

Molar Conductivity & Kohlrausch's Law

\Lambda_m = \frac{\kappa \times 1000}{M} \; (\text{S cm}^2\text{mol}^{-1}), \quad \Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ

Independent migration of ions at infinite dilution.

Degree of dissociation of weak electrolyte: α = Λ_m / Λ_m°.

Faraday's Laws of Electrolysis

w = Z I t = \left(\frac{E}{96500}\right) I t, \quad \frac{w_1}{E_1} = \frac{w_2}{E_2}

Mass w of substance liberated at electrode by current I in time t.

Equivalent weight E = Molar mass / n-factor.

Concentration Cell EMF

E_{\text{cell}} = \frac{0.0591}{n} \log_{10}\frac{C_2}{C_1} \quad (C_2 > C_1)

EMF generated purely by concentration difference of identical electrodes.

E°_cell is identically ZERO for concentration cells.

Debye-Hückel-Onsager Equation (Strong Electrolytes)

\Lambda_m = \Lambda_m^\circ - A\sqrt{C}

Linear variation of molar conductance with square root of concentration for completely dissociated strong electrolytes.

Extrapolation to C → 0 gives limiting molar conductance Λ_m° for strong electrolytes (cannot be extrapolated for weak electrolytes).

Solubility of Sparingly Soluble Salts via Conductance

S = \frac{\kappa \times 1000}{\Lambda_m^\circ} \; (\text{mol/L}), \quad K_{sp} = [M^{z+}]^x [X^{z-}]^y

Determining microscopic solubility S and solubility product K_sp from electrolytic specific conductance κ.

Specific conductance of salt alone is κ_salt = κ_solution - κ_water.

Cell Thermodynamics & Fuel Cell Efficiency

\Delta S = n F \left(\frac{\partial E}{\partial T}\right)_P, \quad \Delta H = -nFE + nFT\left(\frac{\partial E}{\partial T}\right)_P, \quad \eta_{\text{fuel cell}} = \frac{\Delta G^\circ}{\Delta H^\circ}

Entropy, enthalpy of cell reaction derived from temperature coefficient (∂E/∂T)_P, and theoretical efficiency of H₂-O₂ fuel cells.

If (∂E/∂T)_P > 0, cell absorbs heat from surroundings during operation and ΔS > 0.

Physical ChemistryHigh Yield (2-3 Qs in JEE)671 PYQs

Solutions & Colligative Properties

Raoult's law, relative lowering of vapor pressure, elevation in boiling point, depression in freezing point, and van 't Hoff factor.

Chapter

Raoult's Law (Liquid-Liquid Solutions)

P_{\text{total}} = P_A^\circ X_A + P_B^\circ X_B, \quad Y_A = \frac{P_A}{P_{\text{total}}} = \frac{P_A^\circ X_A}{P_{\text{total}}}

Partial vapor pressure of volatile components and mole fraction Y_A in vapor phase.

Positive deviation has P_total > Raoult's prediction (ΔH_mix > 0, ΔV_mix > 0).

Relative Lowering of Vapor Pressure (RLVP)

\frac{P_A^\circ - P_A}{P_A^\circ} = i X_B = i \frac{n_B}{n_A + n_B} \approx i \frac{w_B M_A}{M_B w_A}

Vapor pressure reduction caused by dissolving non-volatile solute B.

For dilute solutions: (P° - P)/P = i (n_B / n_A) is exact.

Boiling Point Elevation & Freezing Depression

\Delta T_b = i K_b m, \quad \Delta T_f = i K_f m \quad \left(m = \text{molality} = \frac{1000 w_B}{M_B w_A}\right)

Thermal colligative shifts dependent strictly on particle concentration.

For water: K_b = 0.52 K kg/mol, K_f = 1.86 K kg/mol.

Osmotic Pressure

\pi = i C R T = i \left(\frac{n_B}{V}\right) R T

Hydrostatic pressure required to stop inward osmosis through semipermeable membrane.

Best colligative property for determining molar mass of polymers and biomolecules.

Van 't Hoff Factor (Dissociation & Association)

i = 1 + (n - 1)\alpha \; (\text{Dissociation}), \quad i = 1 - \left(1 - \frac{1}{n}\right)\alpha \; (\text{Association}), \quad i = \frac{M_{\text{theoretical}}}{M_{\text{observed}}}

Ratio of observed colligative property to theoretical calculated colligative property.

For complete dimerization (n = 2, α = 1), i = 0.5.

Henry's Law of Gas Solubility

P = K_H \cdot \chi, \quad K_H \propto T \implies \text{Solubility decreases as } T \text{ increases}

Partial pressure of gas above liquid is proportional to mole fraction χ of gas dissolved in the liquid.

Aquatic species are more comfortable in cold water because higher dissolved O₂ is present at lower temperatures (smaller K_H).

Thermodynamic Expressions for K_b and K_f

K_b = \frac{R T_b^2 M_{\text{solvent}}}{1000 \Delta H_{\text{vap}}} = \frac{R T_b^2}{1000 l_v}, \quad K_f = \frac{R T_f^2 M_{\text{solvent}}}{1000 \Delta H_{\text{fus}}} = \frac{R T_f^2}{1000 l_f}

Ebullioscopic and cryoscopic constants determined solely by properties of the pure solvent.

K_b and K_f are independent of the nature of the solute dissolved.

Azeotropes & Deviations from Raoult's Law

\text{Positive Dev: } \Delta H_{\text{mix}} > 0, \; \Delta V > 0 \to \text{Min-Boiling Az.}; \quad \text{Negative Dev: } \Delta H < 0, \; \Delta V < 0 \to \text{Max-Boiling Az.}

Constant-boiling binary liquid mixtures that distill without changing composition in liquid and vapor phases.

Acetone + Chloroform shows negative deviation due to intermolecular C-H···O hydrogen bonding.

Physical ChemistryHigh Yield (2-3 Qs in JEE)464 PYQs

Chemical Kinetics

Rate laws, order and molecularity, integrated rate equations for zero and first order, half-life, and Arrhenius equation.

Chapter

Rate of Reaction & Rate Law

\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = k [A]^x [B]^y, \quad \text{Order} = x + y

Stoichiometric rate definition and experimental power dependence.

Order can be zero, fractional, or negative; molecularity is always integer.

Integrated Rate Laws (Zero & First Order)

[A]_t = [A]_0 - kt \; (\text{Zero Order}), \quad \ln\frac{[A]_0}{[A]_t} = kt \iff [A]_t = [A]_0 e^{-kt} \; (\text{First Order})

Concentration-time profiles for fundamental reaction mechanisms.

First-order equation in log10: k = (2.303/t) * log10([A]₀ / [A]_t).

Half-Life Formulas

t_{1/2} = \frac{[A]_0}{2k} \; (\text{Zero Order}), \quad t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{k} \; (\text{First Order}), \quad t_{1/2} \propto \frac{1}{[A]_0^{n-1}}

Time required for reactant concentration to reduce to half its initial value.

For first-order: t_75% = 2 * t_50%, and t_99.9% ≈ 10 * t_50%.

Arrhenius Equation & Activation Energy

k = A e^{-E_a / RT} \iff \log_{10}\frac{k_2}{k_1} = \frac{E_a}{2.303 R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Temperature dependence of rate constant governed by activation energy barrier E_a.

Plot of ln k vs 1/T has slope -E_a / R.

Catalyst Mechanism

\Delta E_a = E_a - E_a', \quad \frac{k_{\text{cat}}}{k_{\text{uncat}}} = e^{\Delta E_a / RT}

A catalyst provides an alternate pathway with lower activation energy, accelerating both forward and backward rates equally.

A catalyst does NOT change equilibrium constant K or ΔG.

Second-Order & General n-th Order Integrated Laws

\text{2nd Order: } \frac{1}{[A]_t} - \frac{1}{[A]_0} = kt \implies t_{1/2} = \frac{1}{k [A]_0}, \quad n\text{-th Order: } \frac{1}{n-1}\left(\frac{1}{[A]_t^{n-1}} - \frac{1}{[A]_0^{n-1}}\right) = kt

Integrated rate law and half-life for second-order and general n-th order reactions (n ≠ 1).

Plot of 1/[A]_t versus t for a second-order reaction yields a straight line with slope +k.

Parallel (Branched) First-Order Reactions

k_{\text{eff}} = k_1 + k_2, \quad \frac{[B]_t}{[C]_t} = \frac{k_1}{k_2}, \quad \% \text{ Yield of } B = \frac{k_1}{k_1 + k_2} \times 100\%, \quad E_{a,\text{eff}} = \frac{k_1 E_{a1} + k_2 E_{a2}}{k_1 + k_2}

Kinetics where reactant A decomposes simultaneously into two distinct products B and C.

Product ratio [B]/[C] is constant and equal to k₁/k₂ at all times throughout the reaction.

Consecutive Reactions & Maximum Intermediate Time

A \xrightarrow{k_1} B \xrightarrow{k_2} C \implies t_{\text{max}} = \frac{\ln(k_2 / k_1)}{k_2 - k_1}, \quad [B]_{\text{max}} = [A]_0 \left(\frac{k_1}{k_2}\right)^{\frac{k_2}{k_2 - k_1}}

Sequential first-order decay. Intermediate concentration [B] rises to a peak and then decays to zero.

If k₂ >> k₁, intermediate B reacts immediately upon formation, validating the Steady State Approximation: d[B]/dt ≈ 0.

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Solid State Chemistry

Unit cell geometry, density formula, packing efficiency of SC/BCC/FCC, radius ratios, and crystal defects.

Chapter

Unit Cell Density Formula

\rho = \frac{Z \cdot M}{N_A \cdot a^3} \quad (\rho \text{ in g/cm}^3, \; a \text{ in cm})

Core formula linking atomic mass M, number of atoms per unit cell Z, and edge length a.

Remember N_A ≈ 6.022 × 10²³.

Lattice Packing Efficiency & Atomic Radii

\text{SC: } a = 2r \; (52.4\%), \quad \text{BCC: } r = \frac{\sqrt{3}a}{4} \; (68\%), \quad \text{FCC: } r = \frac{a}{2\sqrt{2}} \; (74\%)

Geometric packing efficiency and nearest neighbor distance.

FCC / CCP has the maximum possible packing efficiency of 74%.

Limiting Radius Ratios for Voids

\frac{r_+}{r_-} < 0.225 \; (\text{Trigonal}), \quad 0.225 - 0.414 \; (\text{Tetrahedral}), \quad 0.414 - 0.732 \; (\text{Octahedral}), \quad 0.732 - 1.0 \; (\text{Cubic})

Predicts coordination number and void geometry in ionic crystals.

For N close-packed atoms: Octahedral voids = N, Tetrahedral voids = 2N.

Bragg's Law & Interplanar Spacing (Miller Indices)

2d_{hkl} \sin\theta = n\lambda, \quad d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}} \quad (\text{Cubic System})

Constructive interference condition for X-rays reflected from crystal planes with Miller indices (h, k, l).

For cubic crystals: ratio of spacing d₁₀₀ : d₁₁₀ : d₁₁₁ = 1 : 1/√2 : 1/√3 = 1 : 0.707 : 0.577.

Hexagonal Close Packing (HCP) Geometry

Z = 6, \quad c = 4r\sqrt{\frac{2}{3}} = a\sqrt{\frac{8}{3}}, \quad V_{\text{cell}} = 24\sqrt{2}r^3 = \frac{3\sqrt{3}}{2}a^2c, \quad \text{P.E.} = 74\%

Parameters of hexagonal closest packed unit cell. Coordination number is 12 (same as FCC/CCP).

Number of tetrahedral voids = 12, octahedral voids = 6 per HCP unit cell. c/a ratio = √(8/3) ≈ 1.633.

Standard Ionic Crystal Geometries & Radii

\text{NaCl (6:6): } r_+ + r_- = \frac{a}{2}, \quad \text{CsCl (8:8): } r_+ + r_- = \frac{\sqrt{3}a}{2}, \quad \text{ZnS (4:4): } r_+ + r_- = \frac{\sqrt{3}a}{4}

Distance between nearest cation-anion centers in rock-salt, cesium chloride, and zinc blende crystal lattices.

CaF₂ (fluorite) has 8:4 coordination; Na₂O (anti-fluorite) has 4:8 coordination.

Point Defects & Density Effects

\text{Schottky: } \rho_{\text{actual}} < \rho_{\text{theoretical}} \quad | \quad \text{Frenkel: } \rho_{\text{actual}} = \rho_{\text{theoretical}}

Stoichiometric point defects in ionic solids. Schottky forms paired cation-anion vacancies; Frenkel dislocates smaller ion to interstitial site.

AgBr shows BOTH Schottky and Frenkel defects (frequent JEE question). Density decreases in Schottky, remains unchanged in Frenkel.

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Periodic Table & Periodic Properties

Ionization enthalpy, electron gain enthalpy, electronegativity (Pauling & Mulliken scales), screening effect, and atomic radii trends.

Chapter

Effective Nuclear Charge (Slater's Rules)

Z_{\text{eff}} = Z - \sigma, \quad \text{Shielding Power: } s > p > d > f

Net positive nuclear attraction felt by valence electrons after screening.

Poor shielding of 3d and 4f electrons causes scandide and lanthanide contractions.

Electronegativity Scales (Pauling & Mulliken)

\chi_A - \chi_B = 0.208 \sqrt{\Delta} \; (\text{in kcal}), \quad \chi_{\text{Mulliken}} = \frac{\text{IE} + \text{EA}}{2 \text{ (in eV)}} \approx 2.8 \chi_{\text{Pauling}}

Tendency of bonded atom to attract shared electron pair.

Fluorine has maximum electronegativity = 4.0 on Pauling scale.

Ionization Enthalpy & Anomalies

\text{IE}_1(\text{Be}) > \text{IE}_1(\text{B}), \quad \text{IE}_1(\text{N}) > \text{IE}_1(\text{O}), \quad \text{IE}_1(\text{P}) > \text{IE}_1(\text{S})

Penetration effect (2s² > 2p¹) and extra stability of half-filled subshells (2p³ > 2p⁴).

Successive ionization energies strictly increase: IE₁ < IE₂ < IE₃ < IE₄.

Electron Gain Enthalpy (\Delta_{eg}H) Anomalies

|\Delta_{eg}H|: \; \text{Cl} > \text{F} > \text{Br} > \text{I}, \quad \text{S} > \text{Se} > \text{Te} > \text{Po} > \text{O}

Compact 2p orbital in F and O creates strong electron-electron repulsion, making 3p elements (Cl, S) have more negative electron gain enthalpy.

Noble gases have positive Δ_eg H. Nitrogen, Be, and Mg have Δ_eg H close to zero or slightly positive.

Allred-Rochow Scale of Electronegativity

\chi_{\text{AR}} = 0.359 \frac{Z_{\text{eff}}}{r^2} + 0.744 \quad (r \text{ in \AA})

Electrostatic force exerted by effective nuclear charge on an electron at the covalent radius distance.

Pauling scale connection: χ_Pauling ≈ χ_AR ≈ χ_Mulliken / 2.8.

Lanthanide Contraction & Pairs with Identical Radii

r(\text{Zr}^{4+}) \approx r(\text{Hf}^{4+}) \approx 0.80\,\text{\AA}, \quad r(\text{Nb}^{5+}) \approx r(\text{Ta}^{5+}), \quad r(\text{Mo}^{6+}) \approx r(\text{W}^{6+})

Poor shielding of 14 inner 4f electrons causes atomic/ionic radii of 4d and 5d transition series to be almost identical.

Explains why separation of Zr and Hf is extremely difficult chemically.

Hydration Enthalpy & Aqueous Ionic Mobility

\Delta H_{\text{hyd}} \propto \frac{z}{r} \implies \text{Hydrated Radius: } \text{Li}^+_{\text{aq}} > \text{Na}^+_{\text{aq}} > \text{K}^+_{\text{aq}} > \text{Cs}^+_{\text{aq}}, \quad \text{Mobility: } \text{Cs}^+ > \text{Rb}^+ > \text{K}^+ > \text{Na}^+ > \text{Li}^+

Smaller gaseous cations have higher charge density, attract more water molecules, and become bulkier with slower electrical conductivity in aqueous solution.

Li⁺ has smallest gaseous ionic radius but largest hydrated radius in water.

Inorganic ChemistryTop Priority (3-4 Qs in JEE)894 PYQs

p-Block Elements

Group 15 (N, P, As), Group 16 (O, S), Group 17 (Halogens), Group 18 (Noble Gases) — oxoacids, interhalogen compounds, allotropes, and trend rules.

Chapter

Oxidation States of Group 15, 16, 17 Elements

\text{Group 15: } -3, +1, +2, +3, +4, +5 \quad \text{Group 16: } -2, +2, +4, +6 \quad \text{Group 17: } -1, +1, +3, +5, +7

p-Block elements exhibit multiple oxidation states due to availability of d-orbitals (from 3rd period onward). Fluorine has fixed OS = −1 (no d-orbital, most electronegative).

Nitrogen does NOT show +5 OS in fluoride (NF₅ does not exist) because N has no d-orbitals to expand octet. Maximum OS of N is +4 in NO₂ (and +5 only in N₂O₅ / NO₃⁻).

Phosphorus Oxoacids — Basicity & Reducing Power

\begin{array}{lcc} \text{Acid} & \text{Basicity} & \text{Reducing?} \\ H_3PO_4 & 3 & \text{No} \\ H_3PO_3 & 2 & \text{Yes} \\ H_3PO_2 & 1 & \text{Yes (strong)} \\ H_4P_2O_7 & 4 & \text{No} \end{array}

Basicity = number of ionisable P−OH groups. P−H bonds are not ionisable. Reducing power arises from P−H bond which donates H to oxidising agent.

Memory rule: Count only OH groups directly bonded to P. H₃PO₂ has one −OH and two P−H bonds → monobasic, strong reducing agent. All metaphosphoric acids (HPO₃)ₙ have basicity 1.

Nitrogen Oxides Oxidation State Ladder

N_2O \xrightarrow{+1} NO \xrightarrow{+2} N_2O_3 \xrightarrow{+3} NO_2 \xrightarrow{+4} N_2O_4 \xrightarrow{+4} N_2O_5 \xrightarrow{+5}

Nitrogen oxides in increasing oxidation state. NO and NO₂ are paramagnetic (odd-electron species). N₂O₄ is the dimer of NO₂ (diamagnetic).

Only NO₂ (brown gas) and N₂O₄ (colourless) are in equilibrium: 2NO₂ ⇌ N₂O₄ (K_p decreases with temperature → more NO₂ at high T, Le Chatelier). N₂O is laughing gas (+1 OS), used as anaesthetic.

Oxoacids of Sulphur — Structure & OS

H_2S_2O_7 \text{ (pyrosulphuric, oleum, OS +7)}, \quad H_2SO_4 \text{ (+6)}, \quad H_2SO_3 \text{ (+4)}, \quad H_2S_2O_8 \text{ (peroxodisulphuric, Marshall's acid, OS +6)}

Key sulphur oxoacids with S oxidation states. Oleum (H₂S₂O₇) = SO₃ dissolved in H₂SO₄. Marshall's acid contains -O-O- peroxo linkage. Thiosulphate Na₂S₂O₃ contains S in OS 0 and +5 (average +2).

H₂S₂O₃ (thiosulphuric acid): average OS of S = +2 but one S is -2 and other is +6 (non-equivalent). Hot conc. H₂SO₄ acts as oxidising agent (reduces to SO₂); cold dil. H₂SO₄ acts as acid.

Interhalogen Compounds — Formula & Geometry

\text{Type XY: ClF, BrF, BrCl} \quad \text{XY}_3\text{: ClF}_3 \text{ (T-shape)} \quad \text{XY}_5\text{: ClF}_5\text{, BrF}_5 \text{ (Square pyramidal)} \quad \text{XY}_7\text{: IF}_7 \text{ (Pentagonal bipyramidal)}

Interhalogen compounds XYₙ where X is the heavier halogen and n = 1, 3, 5, 7. Geometry determined by VSEPR including lone pairs.

ClF₃ has 2 lone pairs on Cl → T-shape (sp³d). BrF₅ has 1 lone pair on Br → square pyramidal (sp³d²). IF₇ has 0 lone pairs on I → pentagonal bipyramidal (sp³d³). All are powerful fluorinating agents.

Noble Gas Compounds of Xenon — Structure & Shape

\begin{array}{lll} \text{Compound} & \text{Hybridisation} & \text{Shape} \\ XeF_2 & sp^3d & \text{Linear} \\ XeF_4 & sp^3d^2 & \text{Square planar} \\ XeF_6 & sp^3d^3 & \text{Distorted octahedral} \\ XeO_3 & sp^3 & \text{Pyramidal} \\ XeO_4 & sp^3 & \text{Tetrahedral} \end{array}

Xenon fluorides and oxides. XeF₂ and XeF₄ have lone pairs on Xe making them linear and square planar respectively (VSEPR).

XeF₂ is a mild fluorinating agent. XeF₄ reacts with water to give Xe + O₂ + HF (disproportionation): 6XeF₄ + 12H₂O → 4Xe + 2XeO₃ + 24HF + 3O₂. Never confuse XeF₄ (sp³d²) with SF₄ (sp³d, seesaw).

Disproportionation of Halogen Acids & Oxyhalogen Acids

\text{Hot NaOH: } 3Cl_2 + 6NaOH \xrightarrow{\Delta} 5NaCl + NaClO_3 + 3H_2O

Disproportionation of halogens in alkali. In cold dilute NaOH: Cl₂ + 2NaOH → NaCl + NaOCl + H₂O (hypohalite formation). Bleaching powder: Ca(OCl)Cl formed by Cl₂ + Ca(OH)₂ → Ca(OCl)Cl + H₂O.

Oxidising power order of oxyacids: HOCl > HOBr > HOI. Acid strength order (opposite to oxidising power): HClO₄ > HClO₃ > HClO₂ > HOCl. HOCl is the strongest oxidising halogen oxyacid.

Allotropes of Phosphorus & Sulphur — Key Properties

\text{P}_4 \text{ (white, P−P−P angle } 60°, \text{most reactive)}, \quad \text{Red P} \text{ (polymer)}, \quad \text{Black P} \text{ (graphite-like, most stable)}

Sulphur allotropes: rhombic S₈ (stable below 96°C), monoclinic S₈ (stable 96–119°C), plastic S (amorphous, above 160°C). White phosphorus is soluble in CS₂ and is poisonous; red phosphorus is non-toxic polymer.

White P₄ has tetrahedral structure with bond angle 60° (highly strained → very reactive). Reacts with conc. NaOH: P₄ + 3NaOH + 3H₂O → 3NaH₂PO₂ + PH₃↑ (disproportionation). Contact process for H₂SO₄: 2SO₂ + O₂ ⇌ 2SO₃ (V₂O₅ catalyst, 450°C, 2 atm).

Acidic Strength & Reducing Power Trends in Group 16, 17

\text{Acid strength: HF} < \text{HCl} < \text{HBr} < \text{HI (bond energy ↓)} \quad \text{Reducing power: HF} < \text{HCl} < \text{HBr} < \text{HI}

Hydrohalic acid strength increases down the group as H−X bond dissociation enthalpy decreases. HF is the weakest acid but forms strongest H-bonds. HF etches glass: SiO₂ + 4HF → SiF₄ + 2H₂O.

Bond angle in H₂O > H₂S > H₂Se > H₂Te (O uses pure p-orbitals; as we go down, angles → 90° as pure p-orbitals used for bonding). Thermal stability of hydrides: H₂O > H₂S > H₂Se > H₂Te (bond energy ↓ down group).

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Chemical Bonding & VSEPR

VSEPR molecular geometries, steric number hybridization, bond order from MOT, dipole moments, and hydrogen bonding.

Chapter

Steric Number & Hybridization

\text{Steric No} = \frac{1}{2}[V + M - C + A] = \sigma\text{-bonds} + \text{lone pairs}

V: valence e⁻, M: monovalent atoms (H, F, Cl), C: positive charge, A: negative charge.

SN: 2 = sp (180°), 3 = sp² (120°), 4 = sp³ (109.5°), 5 = sp³d, 6 = sp³d².

Molecular Orbital Theory (MOT) Bond Order

\text{Bond Order} = \frac{N_b - N_a}{2}, \quad \text{Bond Length} \propto \frac{1}{\text{Bond Order}}

N_b: bonding electrons, N_a: antibonding electrons.

14 electrons (N₂) has BO = 3. Each added or removed electron changes BO by ±0.5.

Dipole Moment & Percentage Ionic Character

\mu = q \times d, \quad \% \text{ Ionic Character} = \frac{\mu_{\text{observed}}}{\mu_{\text{theoretical}}} \times 100\%

Measures molecular bond polarity (1 Debye = 3.336 × 10⁻³⁰ C m).

Symmetric molecules with no lone pairs (like CCl₄, BF₃, CO₂) have net μ = 0.

Formal Charge Calculation

\text{Formal Charge} = V - L - \frac{1}{2}S

V: valence electrons in free atom, L: lone pair non-bonding electrons, S: shared bonding electrons.

Lowest formal charge configuration represents the most stable Lewis resonance structure.

Fajan's Rules (Covalent Character in Ionic Bonds)

\text{Polarizing Power} \propto \frac{\text{Charge}}{\text{Cation Radius}}, \quad \text{Polarizability} \propto \text{Anion Radius}

Covalent character increases with: (1) high charge on cation/anion, (2) smaller cation, (3) larger anion, and (4) pseudo-inert gas electron configuration 18e⁻ (Cu⁺, Ag⁺) over 8e⁻ (Na⁺, K⁺).

Higher covalent character lowers melting point and increases solubility in non-polar organic solvents (e.g. AgI is yellow/covalent, AgF is white/ionic).

Bond Angle Hierarchy Rules

\text{Hybridization } (sp > sp^2 > sp^3) \to \text{No. of Lone Pairs } \downarrow \to \text{EN of Central Atom } \uparrow \to \text{EN of Surrounding Atoms } \downarrow

Systematic order for comparing bond angles across molecules.

Drago's Rule: In PH₃, AsH₃, H₂S, H₂Se, no hybridization occurs; bond angles are close to 90° pure p-orbital angles.

Back-Bonding & 3-Center-2-Electron Bonds

p\pi - p\pi \; (\text{in } BF_3), \quad p\pi - d\pi \; (\text{in } N(SiH_3)_3), \quad B_2H_6 \; (\text{Banana } 3c-2e^- \text{ bridge bonds})

Transfer of lone pair electrons from filled orbital into adjacent empty p or d orbital increases bond order and reduces Lewis acidity.

N(CH₃)₃ is pyramidal with sp³ N, whereas N(SiH₃)₃ is planar with sp² N due to pπ-dπ back-donation into empty d-orbitals of Si.

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Coordination Compounds

Werner theory, crystal field splitting (CFT), spectrochemical series, magnetic moments, and isomerism.

Chapter

Crystal Field Splitting (Octahedral & Tetrahedral)

\Delta_t = \frac{4}{9}\Delta_o, \quad \text{CFSE}_{\text{oct}} = (-0.4 n_{t_{2g}} + 0.6 n_{e_g})\Delta_o + m P

Splitting of degenerate d-orbitals into t_2g and e_g sets.

If Δ_o > P (strong field), electrons pair up in t_2g (low spin).

Spin-Only Magnetic Moment

\mu = \sqrt{n(n + 2)} \text{ BM} \quad (n = \text{number of unpaired electrons})

Bohr Magneton (BM) value indicating paramagnetism.

n = 1 -> 1.73 BM, n = 2 -> 2.83 BM, n = 3 -> 3.87 BM, n = 4 -> 4.90 BM, n = 5 -> 5.92 BM.

Spectrochemical Series of Ligands

\text{I}^- < \text{Br}^- < \text{Cl}^- < \text{F}^- < \text{OH}^- < \text{C}_2\text{O}_4^{2-} < \text{H}_2\text{O} < \text{NCS}^- < \text{EDTA}^{4-} < \text{NH}_3 < \text{en} < \text{CN}^- < \text{CO}

Empirical ordering of ligands by their crystal field splitting power Δ.

Carbonyl (CO) and cyanide (CN⁻) are the strongest field ligands.

Effective Atomic Number (EAN Rule)

\text{EAN} = Z - (\text{Oxidation State}) + 2 \times (\text{Coordination Number})

Sidgwick's stability rule: complex is exceptionally stable when EAN equals the atomic number of the next noble gas.

Metals in low or zero oxidation states (metal carbonyls) obey the 18-electron rule.

Synergic Bonding in Metal Carbonyls

M \xleftarrow{\sigma} \text{CO} \quad + \quad M(d) \xrightarrow{\pi} \text{CO}(\pi^*), \quad \text{Bond Length } (\text{C-O}) \propto \frac{1}{\nu_{\text{CO}}} \propto \text{Negative charge on } M

Dual bonding: ligand-to-metal σ donation and metal d-to-CO π* back-donation strengthens M-C bond while weakening C-O bond.

Decreasing order of C-O bond strength (and stretching frequency): [Mn(CO)₆]⁺ > [Cr(CO)₆] > [V(CO)₆]⁻.

Square Planar Crystal Field Splitting (d⁸ Ions)

\Delta_{sp} \approx 1.3 \Delta_o, \quad \text{Energy Order: } d_{x^2-y^2} \gg d_{xy} > d_{z^2} > d_{xz} \approx d_{yz}

Extreme tetragonal elongation removes axial ligands, placing d_{x²-y²} at highest energy. Characteristic of Pt(II), Pd(II), and [Ni(CN)₄]²⁻.

All 4d and 5d metals form square planar low-spin diamagnetic complexes with coordination number 4 regardless of ligand strength.

Octahedral & Square Planar Isomerism Summary

[Ma_2b_2] \to \text{cis/trans (2)}, \quad [Mabcd] \to 3\,\text{GI}, \quad [Ma_3b_3] \to \text{fac/mer (2)}, \quad [M(AA)_2b_2] \to \text{cis (chiral) } + \text{ trans (achiral)}

Geometrical (GI) and Optical (OI) isomer counts. Square planar complexes cannot show optical activity due to molecular plane.

Tris-bidentate complex [M(AA)₃] (like [Co(en)₃]³⁺) has NO plane of symmetry and exists as an enantiomeric pair (d and l).

CFSE Values for Octahedral d^n Configurations

\text{CFSE (oct, high spin): } d^1\!=\!-0.4, d^2\!=\!-0.8, d^3\!=\!-1.2, d^4\!=\!-0.6, d^5\!=\!0, d^6\!=\!-0.4, d^7\!=\!-0.8, d^8\!=\!-1.2, d^9\!=\!-0.6, d^{10}\!=\!0 \;(\times\Delta_o)

Crystal Field Stabilisation Energy in units of Δ_o for high-spin octahedral complexes (no extra pairing energy P). Low-spin complexes have greater CFSE (more electrons in t_2g): e.g. d⁶ low-spin = -2.4Δ_o + P.

d³ and d⁸ have maximum CFSE in high-spin octahedral field (-1.2Δ_o) → most stable complexes (Cr³⁺ and Ni²⁺ form very stable octahedral complexes). d⁰, d⁵ (HS), d¹⁰ have zero CFSE.

Stability Constant (K_f) & Lability of Complexes

K_f = \frac{[\text{ML}_n]}{[\text{M}][\text{L}]^n}, \quad \log K_f \propto \text{Stability}, \quad \beta_n = K_{f1} \times K_{f2} \times \cdots \times K_{fn} \; (\text{overall stability})

Formation constant K_f (also called stability constant) measures thermodynamic stability of a complex. β_n is the cumulative/overall stability constant for stepwise addition of n ligands.

EDTA forms highly stable 1:1 chelate complexes (log K_f ~ 18 for Ca²⁺). Chelate effect: polydentate ligands are more stable than monodentate equivalents due to entropy gain. Lability ≠ thermodynamic stability (e.g., [Co(NH₃)₆]³⁺ is thermodynamically stable but kinetically inert).

Inorganic ChemistryHigh Yield (2-3 Qs in JEE)589 PYQs

d- & f-Block Elements

Transition element trends, variable oxidation states, lanthanide contraction, catalytic properties, and potassium permanganate/dichromate reactions.

Chapter

Oxidation States & Redox Equivalent Weights

\text{KMnO}_4 (\text{Acidic}): \text{Mn}^{7+} + 5e^- \to \text{Mn}^{2+} \implies n = 5, \quad \text{K}_2\text{Cr}_2\text{O}_7 (\text{Acidic}): \text{Cr}_2^{6+} + 6e^- \to 2\text{Cr}^{3+} \implies n = 6

Stoichiometric electron transfer in analytical volumetric titrations.

Equivalent weight = Molar mass / n-factor (M/5 for acidic KMnO₄, M/6 for acidic K₂Cr₂O₇).

Lanthanide Contraction Phenomenon

r(\text{Zr}) \approx r(\text{Hf}) \approx 1.60 \text{ \AA}, \quad r(\text{Nb}) \approx r(\text{Ta})

Poor shielding effect of 4f electrons causes abnormal similarity in 4d and 5d series atomic and ionic sizes.

Causes extreme difficulty in chemical separation of Zr and Hf.

Chromate-Dichromate Equilibrium

2 \text{CrO}_4^{2-} \; (\text{Yellow}) + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} \; (\text{Orange}) + \text{H}_2\text{O}

pH-dependent equilibrium: yellow chromate in base, orange dichromate in acid.

Oxidation state of Chromium remains +6 throughout the interconversion.

Standard Electrode Potentials & Thermodynamic Cycle

E^\circ_{M^{2+}/M} \propto -(\Delta H_{\text{sub}} + \text{IE}_1 + \text{IE}_2 + \Delta H_{\text{hyd}}), \quad E^\circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34\,\text{V} > 0

Standard reduction potential determined by balance between sublimation, ionization enthalpies and hydration enthalpy. Cu cannot liberate H₂ from dilute acids.

E°(Mn³⁺/Mn²⁺) = +1.57 V is unusually high because Mn²⁺ achieves stable half-filled 3d⁵ configuration.

Chromyl Chloride Test (Confirmatory Test for Cl⁻)

\text{K}_2\text{Cr}_2\text{O}_7 + 4\text{NaCl} + 6\text{H}_2\text{SO}_4 \to 2\text{CrO}_2\text{Cl}_2\uparrow \; (\text{Red Vapor}) \xrightarrow{\text{NaOH}} \text{Na}_2\text{CrO}_4 \xrightarrow{\text{Pb(OAc)}_2} \text{PbCrO}_4\downarrow \; (\text{Yellow})

Qualitative test for ionic chlorides. Covalent chlorides and AgCl, Hg₂Cl₂, HgCl₂, PbCl₂ do NOT respond to this test.

Fluorides, bromides, and iodides do not form volatile chromyl halides.

KMnO₄ in Neutral & Strongly Alkaline Media

\text{Neutral/Weak Base: } \text{MnO}_4^- + 3e^- + 2\text{H}_2\text{O} \to \text{MnO}_2\downarrow + 4\text{OH}^- \; (n=3), \quad \text{Strong Base: } \text{MnO}_4^- + e^- \to \text{MnO}_4^{2-} \; (n=1)

In neutral/faintly alkaline medium, KMnO₄ oxidizes iodide to iodate (I⁻ → IO₃⁻) and thiosulfate to sulfate (S₂O₃²⁻ → SO₄²⁻).

In acidic medium, I⁻ is oxidized to I₂ (not IO₃⁻).

Interstitial Compounds & Catalytic Properties

\text{Compounds: } \text{TiC}, \; \text{Mn}_4\text{N}, \; \text{Fe}_3\text{H}, \; \text{VH}_{0.56} \implies \text{Higher M.P., Hardness, Metallic Conduction}

Transition metals trap small non-metal atoms (H, B, C, N) inside octahedral/tetrahedral voids of the metallic lattice without changing lattice type.

Transition elements are excellent catalysts (V₂O₅, finely divided Fe, Raney Ni) due to variable oxidation states and surface d-orbital adsorption.

Actinoid Contraction & Variable Oxidation States

\text{Contraction: } 5f > 4f \implies \text{Actinoid Contraction} > \text{Lanthanoid Contraction}, \quad \text{Max ON: } \text{Np, Pu } (+7)

Poorer shielding of 5f electrons causes steeper radius decrease across actinoid series than 4f across lanthanoids.

5f, 6d, and 7s energy levels are extremely close in energy, allowing actinoids to exhibit variable oxidation states from +3 up to +7.

Organic ChemistryTop Priority (3-4 Qs in JEE)377 PYQs

General Organic Chemistry (GOC)

Inductive effect, resonance & mesomeric effect, hyperconjugation, aromaticity (Hückel's 4n+2 rule), and carbocation stability.

Chapter

Hückel's Rule of Aromaticity

4n + 2 \; \pi\text{-electrons} \; (n = 0, 1, 2, \dots) \implies \text{Aromatic}

Requires cyclic, planar, fully conjugated ring system with (4n + 2) π-electrons.

4n π-electrons in cyclic planar conjugated ring = Anti-aromatic (least stable).

Carbocation & Carbanion Stability Order

\text{Carbocation: } 3^\circ > 2^\circ > 1^\circ > \text{CH}_3^+, \quad \text{Carbanion: } \text{CH}_3^- > 1^\circ > 2^\circ > 3^\circ

Carbocations are stabilized by +I, +M, and hyperconjugation (α-hydrogens).

Stability of carbocation increases with number of α-hydrogens for hyperconjugation.

Electronic Effects Order (+M / -M & +I / -I)

+M: \; -O^- > -NH_2 > -OH > -OR; \quad -M: \; -NO_2 > -CN > -CHO > -COOH

Relative strength of resonance and inductive donor/acceptor substituents.

Mesomeric effect M operates at ortho/para positions, NOT meta positions.

Acidic Strength Comparison

\text{Acidic Strength } \propto K_a \propto \frac{1}{pK_a} \propto \text{Stability of Conjugate Base (Anion)}

Anion stability is increased by -I and -M electron-withdrawing groups.

Ortho-substituted benzoic acids are stronger acids regardless of whether the group is +I or -I (ortho effect).

Hyperconjugation & Heat of Hydrogenation

\text{Alkene Stability} \propto \text{No. of } \alpha\text{-H atoms} \propto \frac{1}{\Delta H_{\text{hydrogenation}}}

σ(C-H) to empty p or π* orbital overlap stabilizes alkenes and free radicals. More stable alkenes release less heat upon hydrogenation.

Trans-alkene is generally more stable than cis-alkene due to lower steric hindrance.

Tautomerism & Keto-Enol Equilibrium

\% \text{ Enol Content} \propto \text{Aromatic Enol Driving Force} > \text{Intramolecular H-Bonding (Chelation)}

Spontaneous interconversion between constitutional isomers differing in position of hydrogen atom and double bond.

Phenol enol content is ~100% due to aromatic resonance; acetylacetone (CH₃COCH₂COCH₃) enol content is ~76% in gas phase due to 6-membered quasi-ring H-bonding.

Stereochemistry & Specific Optical Rotation

[\alpha]_\lambda^T = \frac{\alpha_{\text{observed}}}{l \text{ (dm)} \times c \text{ (g/mL)}}, \quad \% ee = \frac{|d - l|}{d + l} \times 100\%, \quad \text{Stereoisomers} = 2^n

Optical rotation of chiral molecules in polarimeter tube of length l and concentration c, and enantiomeric excess (% ee).

Meso compounds contain chiral carbons with an internal plane of symmetry (C_s) or inversion center (C_i) and are optically inactive by internal compensation.

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Hydrocarbons (Alkanes, Alkenes, Alkynes)

Markovnikov & anti-Markovnikov additions, ozonolysis, Wurtz reaction, Friedel-Crafts alkylation/acylation, and acidic nature of alkynes.

Chapter

Markovnikov & Anti-Markovnikov Addition

R-\text{CH}=\text{CH}_2 + \text{HX} \longrightarrow R-\text{CH(X)}-\text{CH}_3 \quad (\text{Markovnikov})

Electrophile H⁺ adds to form the more stable carbocation intermediate.

In presence of peroxide (R₂O₂), HBr adds anti-Markovnikov via free radical mechanism.

Ozonolysis of Alkenes

R_1 R_2 \text{C}=\text{C} R_3 R_4 \xrightarrow{\text{1. } O_3, \; \text{2. } Zn / H_2O} R_1 R_2 \text{C}=\text{O} + R_3 R_4 \text{C}=\text{O}

Cleaves carbon-carbon double bonds to form carbonyl compounds.

Reductive ozonolysis uses Zn/H₂O or (CH₃)₂S to prevent oxidation of aldehydes to carboxylic acids.

Wurtz Reaction & Corey-House Synthesis

2 \text{ R-X} + 2 \text{Na} \xrightarrow{\text{dry ether}} \text{R-R} + 2 \text{NaX}

Coupling of alkyl halides to produce symmetrical alkanes.

Methane (CH₄) cannot be prepared by the Wurtz reaction.

Friedel-Crafts Alkylation & Acylation

\text{C}_6\text{H}_6 + \text{R-Cl} \xrightarrow{\text{anh. AlCl}_3} \text{C}_6\text{H}_5\text{R}, \quad \text{C}_6\text{H}_6 + \text{RCOCl} \xrightarrow{\text{anh. AlCl}_3} \text{C}_6\text{H}_5\text{COR}

Electrophilic aromatic substitution on benzene ring.

Acylation avoids carbocation rearrangement and polyalkylation.

Acidic Nature of Terminal Alkynes

\text{R-C}\equiv\text{CH} + \text{NaNH}_2 \longrightarrow \text{R-C}\equiv\text{C}^- \text{Na}^+ + \text{NH}_3

Terminal alkyne hydrogen is acidic due to 50% s-character of sp hybridized carbon.

Gives red precipitate with ammoniacal Cu₂Cl₂ and white precipitate with Tollen's reagent.

Stereoselective Reduction of Alkynes (cis vs trans)

\text{R-C}\equiv\text{C-R}' \xrightarrow{\text{H}_2 / \text{Pd-CaCO}_3 \text{ (Lindlar)}} \text{cis-alkene}, \quad \text{R-C}\equiv\text{C-R}' \xrightarrow{\text{Na / liq. } \text{NH}_3 \text{ (Birch)}} \text{trans-alkene}

Syn-addition catalytic hydrogenation versus anti-addition dissolving metal reduction to control alkene geometry.

Birch reduction of benzene gives non-conjugated 1,4-cyclohexadiene.

Hydration of Alkenes: OMDM vs Hydroboration-Oxidation

\text{OMDM: } \text{R-CH=CH}_2 \xrightarrow{\text{1. Hg(OAc)}_2/\text{H}_2\text{O}, \; \text{2. NaBH}_4} \text{Markovnikov (no rearr.)}, \quad \text{HBO: } \xrightarrow{\text{1. B}_2\text{H}_6, \; \text{2. H}_2\text{O}_2/\text{OH}^-} \text{Anti-Markovnikov (syn)}

Two non-rearranging pathways for regioselective water addition across carbon-carbon double bonds.

OMDM avoids carbocation ring expansions and hydride/methyl shifts.

Hückel's Rule of Aromaticity & Anti-Aromaticity

\text{Aromatic: Planar, cyclic, conjugated, } (4n + 2)\pi e^-, \quad \text{Anti-Aromatic: Planar, cyclic, conjugated, } 4n\pi e^-

Stability criteria based on cyclic π-electron delocalization. Anti-aromatic compounds are destabilized relative to open-chain analogs.

Cyclooctatetraene (8 π electrons) adopts a non-planar tub conformation to avoid anti-aromaticity, behaving as non-aromatic.

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Haloalkanes & Haloarenes

SN1 and SN2 nucleophilic substitutions, E1 and E2 eliminations, Saytzeff rule, and Grignard reagent synthesis.

Chapter

SN1 vs SN2 Nucleophilic Substitution

\text{S}_\text{N}1: \; \text{Rate} = k[\text{R-X}] \; (3^\circ > 2^\circ > 1^\circ), \quad \text{S}_\text{N}2: \; \text{Rate} = k[\text{R-X}][\text{Nu}^-] \; (\text{CH}_3\text{X} > 1^\circ > 2^\circ > 3^\circ)

Two-step unimolecular vs one-step concerted bimolecular substitution.

Polar protic solvents favor SN1; polar aprotic solvents (DMSO, DMF, acetone) favor SN2.

Saytzeff vs Hofmann Elimination Rule

\text{Saytzeff: More substituted alkene (more } \alpha\text{-H)}, \quad \text{Hofmann: Less substituted alkene (bulky base like } t\text{-BuO}^-)

Regioselectivity in dehydrohalogenation reactions.

Alcoholic KOH promotes E2 elimination.

Grignard Reagent Preparation & Reactions

\text{R-X} + \text{Mg} \xrightarrow{\text{dry ether}} \text{R-MgX} \xrightarrow{\text{H}_2\text{O}} \text{R-H} + \text{Mg(OH)X}

Organomagnesium halide organometallic reagent acts as powerful carbanion nucleophile and strong base.

Reacts with active hydrogen compounds (water, alcohol, amine) instantly to give alkane.

Halogen Exchange: Finkelstein & Swarts Reactions

\text{Finkelstein: } \text{R-Cl}/\text{Br} + \text{NaI} \xrightarrow{\text{acetone}} \text{R-I} + \text{NaCl}\downarrow, \quad \text{Swarts: } \text{R-Cl}/\text{Br} + \text{AgF}/\text{SbF}_3 \to \text{R-F} + \text{AgX}\downarrow

Specific pathways for synthesizing alkyl iodides (precipitation drives equilibrium) and alkyl fluorides (using heavy metal fluorides).

Swarts fluorinating agents: AgF, Hg₂F₂, CoF₃, SbF₃.

Nucleophilic Aromatic Substitution (S_NAr & Benzyne)

\text{S}_\text{N}\text{Ar Rate: } \text{Ar-F} \gg \text{Ar-Cl} > \text{Ar-Br} > \text{Ar-I} \; (\text{with } -\text{NO}_2 \text{ at } o/p), \quad \text{Benzyne: } \text{Ph-Cl} + \text{NaNH}_2 \xrightarrow{\text{liq } \text{NH}_3} [\text{C}_6\text{H}_4] \to \text{Ph-NH}_2

S_NAr proceeds via Meisenheimer complex (rate-determining addition). Strong base on unactivated haloarene proceeds via benzyne intermediate.

Benzyne mechanism leads to cine substitution (50:50 mixture of substituted products).

Haloform Reaction Mechanism & Specificity

\text{R-CO-CH}_3 + 3\text{X}_2 + 4\text{OH}^- \to \text{R-COO}^- + \text{CHX}_3\downarrow + 3\text{X}^- + 3\text{H}_2\text{O} \quad (\text{CHI}_3 \text{ Yellow ppt})

Characteristic test for methyl ketones (CH₃-C=O) and secondary alcohols oxidizable to them (CH₃-CH(OH)-R), plus ethanol and acetaldehyde.

Tertiary alcohols and methanol DO NOT give the haloform test.

Elimination Reaction Spectrum (E1, E2, E1cB)

\text{E1: Carbocation intermediate}, \quad \text{E2: Anti-periplanar concerted TS}, \quad \text{E1cB: Carbanion intermediate (poor leaving group like F)}

Mechanistic comparison of β-eliminations. E1cB occurs when strong electron-withdrawing groups stabilize conjugate carbanion base with poor leaving group.

E2 dehydrohalogenation requires strictly anti-coplanar alignment of β-hydrogen and α-halogen.

Coupling Reactions: Wurtz, Fittig & Ullmann Synthesis

\text{Wurtz: } 2\text{R-X} + 2\text{Na} \to \text{R-R}, \quad \text{Fittig: } 2\text{Ar-X} + 2\text{Na} \to \text{Ar-Ar}, \quad \text{Ullmann: } 2\text{Ar-I} + \text{Cu} \xrightarrow{\Delta} \text{Ar-Ar}

Reductive coupling reactions forming symmetric carbon-carbon bonds. Ullmann reaction specifically synthesizes biaryls using copper powder.

Ullmann reaction works best with ortho-halonitrobenzenes.

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Alcohols, Phenols & Ethers

Lucas test, Reimer-Tiemann reaction, Kolbe reaction, Williamson ether synthesis, and acidic strength of phenols.

Chapter

Lucas Test for Alcohol Distinction

\text{R-OH} + \text{conc. HCl} \xrightarrow{\text{anh. ZnCl}_2} \text{R-Cl} \downarrow \; (\text{Turbidity})

Differentiates 1°, 2°, 3° alcohols via SN1 rate.

3° alcohol turbidity appears immediately; 1° alcohol shows no turbidity at room temperature.

Reimer-Tiemann & Kolbe Reactions of Phenol

\text{Ph-OH} \xrightarrow{\text{CHCl}_3 + \text{NaOH}} \text{Salicylaldehyde}, \quad \text{Ph-OH} \xrightarrow{\text{CO}_2 + \text{NaOH}} \text{Salicylic Acid}

Electrophilic aromatic substitutions on highly activated phenoxide ring.

Reimer-Tiemann intermediate is electrophilic dichlorocarbene (:CCl₂).

Williamson's Ether Synthesis

\text{R-O}^- \text{Na}^+ + \text{R'-X} \longrightarrow \text{R-O-R'} + \text{NaX} \quad (\text{R' must be } 1^\circ)

SN2 displacement by alkoxide ion on alkyl halide.

If R' is 3°, elimination (alkene) occurs exclusively instead of ether formation.

Pinacol-Pinacolone Rearrangement

\text{R}_2\text{C(OH)-C(OH)R}_2 \xrightarrow{\text{H}^+, \Delta} \text{R}_3\text{C-CO-R} + \text{H}_2\text{O}

Acid-catalyzed dehydration of vicinal diols accompanied by 1,2-migratory shift to form a stable ketone.

Migratory aptitude order: p-anisyl > p-tolyl > phenyl > 3° alkyl > 2° alkyl > 1° alkyl > H.

Cleavage of Ethers with Hydrogen Halides (HI)

\text{R-O-R'} + \text{HI} \longrightarrow \begin{cases} \text{SN2: } \text{R-I (smaller)} + \text{R'OH (larger)} & (1^\circ / 2^\circ) \\ \text{SN1: } \text{R-I (from } 3^\circ / \text{benzyl)} + \text{R'OH} & (3^\circ) \end{cases}

Nucleophilic attack on protonated ether oxonium ion. Excess HI yields two moles of alkyl iodides.

Anisole (Ph-O-CH₃) with HI produces Phenol (Ph-OH) and Methyl Iodide (CH₃I) because the Ph-O bond has partial double bond character.

Victor Meyer & Catalytic Dehydrogenation Tests

\text{Victor Meyer: } 1^\circ \to \text{Blood Red}, \; 2^\circ \to \text{Blue}, \; 3^\circ \to \text{Colorless}; \quad \text{Cu / 573 K: } 1^\circ \to \text{Aldehyde}, \; 2^\circ \to \text{Ketone}, \; 3^\circ \to \text{Alkene}

Colorimetric identification of primary, secondary, and tertiary alcohols.

3° alcohol undergoes catalytic elimination (dehydration) with heated Cu yielding an alkene instead of dehydrogenation.

Acidic Strength of Substituted Phenols & Intramolecular H-Bonding

\text{Acidity: } \text{Picric Acid} > p\text{-Nitrophenol} > o\text{-Nitrophenol} > m\text{-Nitrophenol} > \text{Phenol} > \text{Cresols}

Electron-withdrawing groups (-M, -I) disperse phenoxide negative charge and drastically increase acidity.

o-Nitrophenol is steam volatile due to intramolecular H-bonding (chelation); p-nitrophenol has higher boiling point due to intermolecular H-bonding.

Fries & Claisen Rearrangements

\text{Fries: } \text{Ar-OCO-R} \xrightarrow{\text{anh. AlCl}_3} o/p\text{-acylphenol}, \quad \text{Claisen: } \text{Ar-O-CH}_2\text{CH=CH}_2 \xrightarrow{\Delta} o\text{-allylphenol}

Thermal and Lewis-acid catalyzed rearrangements of phenyl esters and allyl aryl ethers into ortho- and para-substituted phenols.

In Fries rearrangement, low temperature (below 60°C) favors para-isomer; high temperature (above 160°C) favors ortho-isomer.

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Aldehydes, Ketones & Carboxylic Acids

Nucleophilic addition, Aldol condensation, Cannizzaro reaction, Tollens/Fehling test, Hell-Volhard-Zelinsky (HVZ) reaction.

Chapter

Aldol Condensation & Cannizzaro Reaction

2 \text{ RCH}_2\text{CHO} \xrightarrow{\text{dil. NaOH}} \text{RCH}_2\text{CH(OH)CH(R)CHO} \xrightarrow{\Delta} \alpha,\beta\text{-unsaturated aldehyde}

Cross-aldol occurs between two different carbonyl compounds with α-hydrogen.

Cannizzaro reaction: 2 HCHO + conc. NaOH -> CH₃OH + HCOONa (disproportionation).

Haloform (Iodoform) Test

\text{R-COCH}_3 \xrightarrow{I_2 + NaOH} \text{R-COONa} + \text{CHI}_3 \downarrow \; (\text{Yellow ppt})

Positive test given by compounds containing CH₃-CO- group or CH₃-CH(OH)- group.

Ethanol gives positive iodoform test, but methanol does not.

Tollens' & Fehling's Distinction Tests

\text{R-CHO} + 2[\text{Ag(NH}_3)_2]^+ + 3\text{OH}^- \longrightarrow \text{R-COO}^- + 2\text{Ag} \downarrow + 4\text{NH}_3 + 2\text{H}_2\text{O}

Aldehydes reduce Tollens' reagent to give silver mirror; ketones do not.

Fehling's solution oxidizes aliphatic aldehydes to give red cuprous oxide Cu₂O precipitate.

Hell-Volhard-Zelinsky (HVZ) Reaction

\text{R-CH}_2\text{-COOH} \xrightarrow{\text{1. } X_2 / \text{Red P}, \; \text{2. } H_2O} \text{R-CH(X)-COOH} \quad (X = Cl, Br)

Halogenation specifically at the α-position of carboxylic acids containing α-hydrogen.

Formic acid (HCOOH) and benzoic acid cannot undergo HVZ reaction (no α-hydrogen).

Clemmensen & Wolff-Kishner Reductions to Hydrocarbons

\text{Clemmensen: } \text{C=O} \xrightarrow{\text{Zn-Hg / conc. HCl}} \text{CH}_2, \quad \text{Wolff-Kishner: } \text{C=O} \xrightarrow{\text{NH}_2\text{NH}_2 / \text{KOH, glycol, } \Delta} \text{CH}_2 + \text{N}_2\uparrow

Total reduction of carbonyl group to methylene (>C=O → >CH₂). Clemmensen for base-sensitive substrates; Wolff-Kishner for acid-sensitive substrates.

Clemmensen cannot be used if molecule contains -OH (undergoes substitution to -Cl) or C=C double bonds.

Rosenmund & DIBAL-H Selective Reductions to Aldehydes

\text{Rosenmund: } \text{R-COCl} + \text{H}_2 \xrightarrow{\text{Pd-BaSO}_4 / \text{quinoline}} \text{R-CHO}, \quad \text{DIBAL-H: } \text{R-COOR}' \xrightarrow{-78^\circ\text{C}} \text{R-CHO}

Controlled partial reduction of acyl chlorides, esters, and nitriles avoiding over-reduction to primary alcohols.

DIBAL-H at -78°C selectively reduces esters and nitriles to aldehydes without affecting isolated C=C double bonds.

Decarboxylation of \beta-Keto Acids & Blanc's Rule for Di-acids

\text{R-CO-CH}_2\text{-COOH} \xrightarrow{\Delta} \text{R-CO-CH}_3 + \text{CO}_2\uparrow \quad (\text{6-membered cyclic TS})

β-dicarboxylic and β-keto acids lose carbon dioxide easily upon gentle heating. Di-acids with 4-5 carbon chains form cyclic anhydrides; 6-7 carbon chains form cyclic ketones.

Oxalic and Malonic acids eliminate CO₂; Succinic and Glutaric acids eliminate H₂O to form cyclic anhydrides.

Perkin & Benzoin Condensation

\text{Perkin: } \text{ArCHO} + (\text{RCH}_2\text{CO})_2\text{O} \xrightarrow{\text{RCH}_2\text{COO}^- / \Delta} \text{ArCH=CRCOOH} \quad (\alpha,\beta\text{-unsaturated acid})

Perkin condensation: aromatic aldehyde + acid anhydride → α,β-unsaturated carboxylic acid (base = sodium salt of the acid). Benzoin condensation: 2 PhCHO → PhCH(OH)COPh (α-hydroxy ketone) catalysed by KCN (CN⁻ acts as nucleophile).

Perkin product undergoes decarboxylation to give cinnamic acid analogs. Benzoin condensation is reversed by NaOH (benzoin oxidation → benzil) and reduced by Raney Ni to give diol.

Nucleophilic Addition Reactivity Order of Carbonyls

\text{Reactivity: } \text{HCHO} > \text{CH}_3\text{CHO} > \text{PhCHO} > \text{CH}_3\text{COCH}_3 > \text{PhCOCH}_3 > \text{PhCOPh}

Carbonyl electrophilicity is governed by steric bulk (alkyl/aryl groups hinder nucleophile approach) and electronic effects (electron-donating groups reduce carbonyl δ⁺ character).

Aldehyde > Ketone always. Benzaldehyde is less reactive than acetaldehyde due to resonance delocalization of carbonyl π-electrons into benzene ring. Ketones can undergo nucleophilic addition only under acidic or basic catalysis.

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Amines & Diazonium Salts

Basicity of amines in gas/aqueous phase, Hoffmann bromamide degradation, Gabriel phthalimide synthesis, and Sandmeyer reaction.

Chapter

Hoffmann Bromamide Degradation

\text{R-CONH}_2 + \text{Br}_2 + 4\text{NaOH} \longrightarrow \text{R-NH}_2 + \text{Na}_2\text{CO}_3 + 2\text{NaBr} + 2\text{H}_2\text{O}

Step-down conversion of primary amide to primary amine with ONE LESS carbon atom.

Intermediate is isocyanate (R-N=C=O).

Basicity Order of Amines in Water

(\text{CH}_3)_2\text{NH} > \text{CH}_3\text{NH}_2 > (\text{CH}_3)_3\text{N} > \text{NH}_3 \quad (2^\circ > 1^\circ > 3^\circ > \text{NH}_3)

Combined result of inductive (+I), steric hindrance, and hydration stabilization.

In gaseous phase with no hydration: 3° > 2° > 1° > NH₃.

Diazotization & Sandmeyer Reaction

\text{Ar-NH}_2 \xrightarrow{\text{NaNO}_2 + \text{HCl, } 0-5^\circ\text{C}} \text{Ar-N}_2^+ \text{Cl}^- \xrightarrow{\text{Cu}_2\text{X}_2} \text{Ar-X} + \text{N}_2 \uparrow

Conversion of primary aromatic amine into benzene diazonium chloride and aryl halides.

Temperature must be strictly between 0°C and 5°C to prevent decomposition of diazonium salt.

Carbylamine (Isocyanide) Test

\text{R-NH}_2 + \text{CHCl}_3 + 3\text{KOH} \xrightarrow{\Delta} \text{R-NC} \; (\text{Foul smell}) + 3\text{KCl} + 3\text{H}_2\text{O}

Specific test given ONLY by primary (1°) aliphatic and aromatic amines.

Secondary and tertiary amines do NOT give carbylamine test.

Gabriel Phthalimide Synthesis

\text{Phthalimide} \xrightarrow{\text{KOH}} \text{K-Phthalimide} \xrightarrow{\text{R-X}} N\text{-alkyl phthalimide} \xrightarrow{\text{NaOH (aq)}} \text{R-NH}_2 \; (1^\circ \text{ Aliphatic Amine})

Clean synthetic preparation of pure 1° aliphatic amines free from 2° and 3° amine impurities.

Aromatic 1° amines (like Aniline) CANNOT be prepared by this method because aryl halides do not undergo SN2 displacement.

Hinsberg Test for Amine Classification

1^\circ: \text{Soluble in KOH}; \quad 2^\circ: \text{Insoluble in KOH}; \quad 3^\circ: \text{Does not react with } \text{PhSO}_2\text{Cl}

Benzene sulfonyl chloride (Hinsberg reagent) distinction between 1°, 2°, and 3° amines based on active hydrogen.

The sulfonamide from 1° amine contains an acidic N-H proton which dissolves in alkaline KOH.

Azo Dye Coupling Reactions

\text{Ph-N}_2^+ \text{Cl}^- + \text{Ph-OH} \xrightarrow{pH \; 9-10} p\text{-Hydroxyazobenzene (Orange Dye)}, \quad \text{Ph-N}_2^+ \text{Cl}^- + \text{Ph-NH}_2 \xrightarrow{pH \; 4-5} p\text{-Aminoazobenzene (Yellow Dye)}

Electrophilic aromatic substitution of diazonium ion on highly activated aromatic rings.

Coupling with phenol requires mildly basic pH (9-10) to form phenoxide; coupling with aniline requires mildly acidic pH (4-5).

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Biomolecules & Polymers

Carbohydrates (glucose, fructose, mutarotation), amino acids, peptide bonds, isoelectric point, and nucleic acids (DNA/RNA).

Chapter

Amino Acid Zwitterion & Isoelectric Point (pI)

\text{H}_3\text{N}^+-\text{CH(R)}-\text{COO}^-, \quad \text{pI} = \frac{\text{p}K_{a1} + \text{p}K_{a2}}{2}

Dipolar ion with zero net charge at its characteristic isoelectric point pI.

At pH = pI, amino acid does not migrate under an applied electric field.

Carbohydrates Classification & Reducing Sugars

\text{Maltose: } \alpha\text{-D-Glc } (1\to 4) \text{ Glc}, \quad \text{Sucrose: } \alpha\text{-D-Glc } (1\to 2) \beta\text{-D-Fru} \; (\text{Non-reducing})

Glycosidic linkages in disaccharides.

Sucrose is non-reducing because both anomeric carbons are locked in the glycosidic bond.

DNA vs RNA Base Complementarity

A = T \; (2 \text{ H-bonds}), \quad G \equiv C \; (3 \text{ H-bonds}) \; (\text{In RNA: } A = U)

Watson-Crick base pairing in double-helix nucleic acids.

G-C base pairs have 3 hydrogen bonds and require higher thermal melting temperature (Tm) than A-T pairs.

Glucose Mutarotation & Equilibrium Specific Rotation

\alpha\text{-D-Glucopyranose } (+112^\circ) \xrightleftharpoons[36\%]{64\%} \text{Open Chain} \xrightleftharpoons{} \beta\text{-D-Glucopyranose } (+19^\circ) \implies [\alpha]_D = +52.7^\circ

Spontaneous change in specific optical rotation until an equilibrium mixture of α and β anomers is reached in aqueous solution.

β-anomer is more stable (64%) because all bulky -OH groups and -CH₂OH occupy equatorial positions in chair conformation.

Inversion of Cane Sugar (Sucrose Hydrolysis)

\text{Sucrose } (+66.5^\circ) + \text{H}_2\text{O} \xrightarrow{\text{invertase}} \text{D-(+)-Glucose } (+52.7^\circ) + \text{D-(-)-Fructose } (-92.4^\circ) \implies [\alpha]_{\text{mix}} = -19.8^\circ

Hydrolysis converts dextrorotatory sucrose into a levorotatory equimolar mixture called invert sugar due to stronger levorotation of D-(-)-fructose.

Follows pseudo-first order kinetics.

Resonance & Planar Geometry of Peptide Bond

-\text{C}(=\text{O})-\text{NH}- \longleftrightarrow -\text{C}(\text{O}^-)=\text{N}^+\text{H}- \quad (\text{Partial double bond character})

Resonance restricts free rotation around C-N bond, causing the six atoms of the peptide unit (C_α, C, O, N, H, C_α) to be coplanar.

Trans-conformation is favored over cis-conformation to minimize steric hindrance between side chains.

Osazone Formation (C-1 & C-2 Identity)

\text{Monosaccharide} + 3 \text{ Ph-NH-NH}_2 \longrightarrow \text{Osazone} + \text{Ph-NH}_2 + \text{NH}_3 + 2\text{H}_2\text{O}

Reaction with excess phenylhydrazine. D-glucose, D-mannose, and D-fructose yield the EXACT same osazone crystal.

Confirms that D-glucose and D-fructose differ configurationally only at C-1 and C-2.

Vitamins Classification & Deficiencies

\text{Fat-Soluble: } A, D, E, K; \quad \text{Water-Soluble: } B\text{-complex, } C; \quad \text{B}_{12} \implies \text{Pernicious Anemia (contains Co)}

Classification by solubility. Water-soluble vitamins must be supplied regularly in diet as they are excreted in urine (except B₁₂).

Vitamin C (ascorbic acid) cannot withstand heat and is easily destroyed during cooking.

Inorganic ChemistryHigh Yield (2 Qs in JEE Main)512 PYQs

Principles of Practical Chemistry & Salt Analysis

Systematic qualitative analysis of cations (Groups 0 to VI) and anions, confirmatory tests, flame tests, borax bead test, and organic functional group identification.

Chapter

Cation Group Separation Scheme (Groups 0 to VI)

\begin{array}{llll} \text{Group} & \text{Reagent} & \text{Cations} & \text{Precipitate Form} \\ \text{0} & \text{NaOH} & \text{NH}_4^+ & \text{NH}_3\uparrow \text{ (Nessler's reagent: brown ppt)} \\ \text{I} & \text{Dil. HCl} & \text{Pb}^{2+}, \text{Ag}^+, \text{Hg}_2^{2+} & \text{Chlorides (PbCl}_2 \text{ white, hot-water sol.)} \\ \text{II-A/B} & \text{H}_2\text{S + dil. HCl} & \text{Cu}^{2+}, \text{Pb}^{2+}, \text{Bi}^{3+}, \text{Cd}^{2+}, \text{As}^{3+} & \text{Sulphides (CuS black, CdS yellow, As}_2\text{S}_3 \text{ yellow)} \\ \text{III} & \text{NH}_4\text{OH + NH}_4\text{Cl} & \text{Fe}^{3+}, \text{Al}^{3+}, \text{Cr}^{3+} & \text{Hydroxides (Fe(OH)}_3 \text{ brown, Al(OH)}_3 \text{ gelatinous, Cr(OH)}_3 \text{ green)} \\ \text{IV} & \text{H}_2\text{S + NH}_4\text{OH} & \text{Co}^{2+}, \text{Ni}^{2+}, \text{Zn}^{2+}, \text{Mn}^{2+} & \text{Sulphides (ZnS dirty white, MnS buff/flesh, CoS/NiS black)} \\ \text{V} & (\text{NH}_4)_2\text{CO}_3 & \text{Ba}^{2+}, \text{Sr}^{2+}, \text{Ca}^{2+} & \text{Carbonates (white)} \\ \text{VI} & \text{Na}_2\text{HPO}_4 & \text{Mg}^{2+} & \text{Mg(NH}_4)\text{PO}_4 \text{ (white crystalline)} \end{array}

Systematic precipitation order governed by solubility product (K_sp). Group II sulphides have very low K_sp and precipitate even with low S²⁻ in acid; Group IV sulphides have higher K_sp and require basic medium.

NH₄Cl is added before NH₄OH in Group III to suppress OH⁻ concentration by common ion effect, preventing premature precipitation of Group IV and Mg(OH)₂.

Confirmatory Tests for Acid Radicals (Anions)

\text{Brown Ring: } \text{Fe}^{2+} + \text{NO}_3^- + \text{H}_2\text{SO}_4 \to [\text{Fe}(\text{H}_2\text{O})_5(\text{NO})]^{2+} \; (\text{Brown ring at interface, Fe in +1 OS})

Key confirmatory tests for anions: Nitrate (Brown Ring test), Chloride (Chromyl Chloride test), Sulphate (BaCl₂ gives white BaSO₄ insoluble in conc. HCl), and Carbonate (CO₂ turns lime water milky).

In [Fe(H₂O)₅(NO)]²⁺, NO exists as NO⁺ (nitrosonium), so oxidation state of Fe is +1 (paramagnetic, 3 unpaired electrons, μ = 3.87 BM).

Chromyl Chloride Test (Chloride Detection)

4\text{NaCl} + \text{K}_2\text{Cr}_2\text{O}_7 + 6\text{H}_2\text{SO}_4 \xrightarrow{\Delta} 2\text{CrO}_2\text{Cl}_2\uparrow \text{ (Deep red-brown vapor)} \xrightarrow{+\text{NaOH}} \text{Na}_2\text{CrO}_4 \text{ (Yellow)} \xrightarrow{+\text{Pb(OAc)}_2} \text{PbCrO}_4\downarrow \text{ (Yellow ppt)}

Confirmatory test for ionic chlorides. Heating solid chloride with potassium dichromate and conc. H₂SO₄ liberates red-brown vapors of chromyl chloride (CrO₂Cl₂).

Bromides and iodides evolve Br₂ (reddish) and I₂ (violet), but their vapors do NOT give a yellow precipitate with lead acetate. Does not work for AgCl, PbCl₂, Hg₂Cl₂.

Flame Test Characteristic Colors

\begin{array}{llll} \text{Metal} & \text{Color} & \text{Metal} & \text{Color} \\ \text{Li} & \text{Crimson red} & \text{Ca} & \text{Brick red} \\ \text{Na} & \text{Golden yellow} & \text{Sr} & \text{Crimson red} \\ \text{K} & \text{Violet / Lilac} & \text{Ba} & \text{Apple green} \\ \text{Rb} & \text{Red-violet} & \text{Cu} & \text{Blue-green} \\ \text{Cs} & \text{Blue} & \text{Pb} & \text{Greyish-white} \end{array}

Excitation of valence electrons by Bunsen flame imparts characteristic emission spectrum colours. Beryllium (Be) and Magnesium (Mg) do NOT give flame colour due to high ionization enthalpy.

Viewing through cobalt blue glass: Sodium yellow is absorbed (invisible); Potassium lilac appears crimson/violet.

Borax Bead Test (Metaborate Formation)

\text{Na}_2\text{B}_4\text{O}_7\cdot 10\text{H}_2\text{O} \xrightarrow{\Delta} \text{Na}_2\text{B}_4\text{O}_7 \xrightarrow{\text{strong }\Delta} 2\text{NaBO}_2 + \text{B}_2\text{O}_3 \; (\text{Glassy bead}) \xrightarrow{+\text{CoO}} \text{Co(BO}_2)_2 \; (\text{Deep Blue})

Heating borax with transition metal salts forms characteristic colored metaborate beads in oxidizing and reducing flames.

Key bead colors in oxidizing flame: Cobalt (Deep Blue), Copper (Blue in hot/cold), Chromium (Green), Iron (Yellow in cold, brown in hot), Manganese (Violet/Amethyst).

Organic Functional Group Detection Tests

\begin{array}{lll} \text{Functional Group} & \text{Test Reagent} & \text{Observation} \\ \text{Unsaturation (C=C)} & \text{Br}_2/\text{CCl}_4 \;\text{or}\; \text{Bayer's (alk. KMnO}_4) & \text{Decolourization} \\ \text{Alcoholic (-OH)} & \text{Ceric Ammonium Nitrate (CAN)} & \text{Red coloration} \\ \text{Phenolic (-OH)} & \text{Neutral FeCl}_3 & \text{Violet/purple coloration} \\ \text{Carbonyl (C=O)} & \text{2,4-DNP (Brady's reagent)} & \text{Orange-yellow precipitate} \\ \text{Aldehyde (-CHO)} & \text{Tollens' reagent } [\text{Ag(NH}_3)_2]^+ & \text{Silver mirror on tube wall} \\ \text{Aldehyde (aliphatic)} & \text{Fehling's solution (A+B)} & \text{Red precipitate (Cu}_2\text{O)} \\ \text{Carboxylic (-COOH)} & \text{Sat. NaHCO}_3 & \text{Brisk effervescence of CO}_2\uparrow \\ \text{1° Amine (-NH}_2) & \text{CHCl}_3 + \text{alc. KOH (Carbylamine)} & \text{Foul smelling isocyanide (R-NC)} \end{array}

Standard organic functional group identification tests prescribed in the JEE practical chemistry curriculum.

Lucas test for alcohol classification: ZnCl₂ + conc. HCl: 3° alcohol gives immediate turbidity; 2° takes 5 mins; 1° does not react at room temperature.

Nessler's Reagent & Ammonium Detection

\text{Nessler's Reagent: } \text{K}_2[\text{HgI}_4] \; (\text{alkaline solution}), \quad 2[\text{HgI}_4]^{2-} + \text{NH}_4^+ + 4\text{OH}^- \to \text{HgO}\cdot\text{Hg}(\text{NH}_2)\text{I}\downarrow \text{ (Brown ppt: Iodide of Millon's base)} + 7\text{I}^- + 3\text{H}_2\text{O}

Potassium tetraiodomercurate(II) in alkaline KOH precipitates brown iodide of Millon's base with trace quantities of ammonium ions or ammonia.

Very sensitive test: even tap water traces of ammonia produce distinct yellow-brown coloration.

Mohr's Salt & Potash Alum Preparation

\text{Mohr's Salt: } \text{FeSO}_4\cdot(\text{NH}_4)_2\text{SO}_4\cdot 6\text{H}_2\text{O}, \quad \text{Potash Alum: } \text{K}_2\text{SO}_4\cdot\text{Al}_2(\text{SO}_4)_3\cdot 24\text{H}_2\text{O}

Standard double salts synthesized by equimolar crystallization in acidic medium to prevent hydrolysis.

Mohr's salt is preferred over FeSO₄ for standard solutions in redox titrations because it is resistant to aerial oxidation (Fe²⁺ remains stable).