Chemistry Comprehensive Formula Sheet - JEE/NEET Essential Formulas

📋 Introduction

This comprehensive chemistry formula sheet contains all essential formulas, equations, and constants needed for JEE Advanced and NEET preparation. Formulas are organized by branch and topic with units, conditions, and applications.

🧪 Physical Chemistry

Basic Concepts and Mole Concept

Mole Concept:
Number of moles: n = given mass/molar mass = N/N_A
Number of particles: N = n × N_A
Mass of substance: m = n × M
N_A = 6.022 × 10²³ mol⁻¹ (Avogadro's number)

Concentration Terms:
Molarity (M): M = moles of solute/volume of solution (L)
Molality (m): m = moles of solute/mass of solvent (kg)
Normality (N): N = equivalents of solute/volume of solution (L)
Mole fraction (X): X_A = n_A/(n_A + n_B)

Percentage Composition:
% by mass = (mass of element/mass of compound) × 100
% by volume = (volume of component/total volume) × 100
% by moles = (moles of component/total moles) × 100

Stoichiometry:
Limiting reactant: Reactant that produces least product
% yield = (actual yield/theoretical yield) × 100
Stoichiometric calculations based on balanced equations

Atomic Structure and Periodic Properties

Atomic Structure:
Rutherford model: Nuclear atom with electrons
Bohr model: E_n = -13.6/n² eV (hydrogen)
de Broglie wavelength: λ = h/p = h/(mv)
Heisenberg uncertainty: Δx·Δp ≥ h/(4π)

Quantum Numbers:
Principal (n): n = 1, 2, 3, ...
Azimuthal (l): l = 0 to n-1
Magnetic (m_l): m_l = -l to +l
Spin (m_s): m_s = +½ or -½

Electronic Configuration:
Aufbau principle: (n+l) rule
Hund's rule: Maximum multiplicity
Pauli exclusion principle: No two electrons with same four quantum numbers

Periodic Trends:
Atomic radius: Decreases across period, increases down group
Ionization energy: Increases across period, decreases down group
Electron affinity: Generally increases across period
Electronegativity: Increases across period, decreases down group

Chemical Bonding

Bond Parameters:
Bond length: Distance between nuclei
Bond angle: Angle between bonds
Bond enthalpy: Energy required to break bond
Bond order: (Number of bonding electrons - antibonding electrons)/2

VSEPR Theory:
AX_mE_n: A = central atom, X = surrounding atoms, E = lone pairs
Geometry determined by electron pair repulsion
Common geometries: Linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral

Molecular Orbital Theory:
Bond order = (n_b - n_a)/2
Homonuclear diatomic molecules energy diagrams
Paramagnetic vs diamagnetic based on unpaired electrons

Hybridization:
sp: linear, 180°
sp²: trigonal planar, 120°
sp³: tetrahedral, 109.5°
sp³d: trigonal bipyramidal, 90°, 120°
sp³d²: octahedral, 90°

States of Matter

Gas Laws:
Boyle's Law: P₁V₁ = P₂V₂ (constant T, n)
Charles's Law: V₁/T₁ = V₂/T₂ (constant P, n)
Gay-Lussac's Law: P₁/T₁ = P₂/T₂ (constant V, n)
Avogadro's Law: V₁/n₁ = V₂/n₂ (constant P, T)

Ideal Gas Equation:
PV = nRT
Combined gas law: (P₁V₁)/T₁ = (P₂V₂)/T₂
Gas constant: R = 8.314 J/(mol·K) = 0.0821 L·atm/(mol·K)

Van der Waals Equation:
(P + a/V²)(V - b) = RT
a accounts for intermolecular forces
b accounts for molecular volume

Kinetic Theory of Gases:
Pressure: P = (1/3)ρv²_rms = (2/3)(KE)/V
v_rms = √(3RT/M) = √(3kT/m)
KE_avg = (3/2)kT per molecule = (3/2)RT per mole

Thermodynamics

First Law of Thermodynamics:
ΔU = Q - W
For cyclic process: ΔU = 0, Q = W
Work done by gas: W = ∫PdV

Enthalpy Changes:
ΔH = ΔU + Δ(PV)
Standard enthalpy of formation: ΔH°_f
Hess's Law: ΔH_total = ΣΔH_products - ΣΔH_reactants
Bond enthalpy: Energy required to break bonds

Entropy Changes:
ΔS = Q_rev/T
Standard entropy change: ΔS° = ΣS°_products - ΣS°_reactants
Second law: ΔS_universe > 0 for spontaneous processes

Gibbs Free Energy:
ΔG = ΔH - TΔS
Standard free energy: ΔG° = ΔH° - TΔS°
ΔG = ΔG° + RTln(Q)
ΔG° = -RTln(K)

Spontaneity Criteria:
ΔG < 0: Spontaneous
ΔG = 0: Equilibrium
ΔG > 0: Non-spontaneous

Chemical Equilibrium

Equilibrium Constant:
For aA + bB ⇌ cC + dD:
K_c = [C]^c[D]^d/[A]^a[B]^b
K_p = (P_C)^c(P_D)^d/(P_A)^a(P_B)^b
K_p = K_c(RT)^(Δn)

Le Chatelier's Principle:
If stress applied, equilibrium shifts to relieve stress
Effect of concentration, pressure, temperature, catalyst

Common Ion Effect:
Solubility decreases in presence of common ion
K_sp remains constant

Buffer Solutions:
pH = pKa + log([A-]/[HA]) (Henderson-Hasselbalch)
Buffer capacity: Amount of acid/base that can be added
Optimal buffer: pH = pKa

Solubility Product:
K_sp = [A^+][B^-] for AB ⇌ A^+ + B^-
Common ion effect reduces solubility
pH affects solubility of weak electrolytes

Chemical Kinetics

Rate of Reaction:
Rate = -(1/a)d[A]/dt = -(1/b)d[B]/dt = (1/c)d[C]/dt = (1/d)d[D]/dt
Rate law: Rate = k[A]^m[B]^n
Order of reaction: sum of powers m + n
Molecularity: number of molecules colliding

Rate Laws:
Zero order: Rate = k, [A] = [A]₀ - kt
First order: Rate = k[A], ln[A] = ln[A]₀ - kt
Second order: Rate = k[A]², 1/[A] = 1/[A]₀ + kt
Pseudo first order: Rate = k'[A] when [B] is in excess

Arrhenius Equation:
k = Ae^(-Ea/RT)
ln(k) = ln(A) - Ea/(RT)
log(k₂/k₁) = Ea/(2.303R)(1/T₁ - 1/T₂)
Activation energy: Ea

Catalysis:
Lowers activation energy
Provides alternative pathway
Increases reaction rate
Not consumed in reaction

Electrochemistry

Conductance:
Conductance (G) = 1/Resistance (R)
Specific conductance (κ) = G(l/A) = 1/ρ
Molar conductance (Λ_m) = κ/c
Equivalent conductance (Λ_e) = κ/N

Kohlrausch's Law:
At infinite dilution: Λ⁰_m = λ⁰_+ + λ⁰_-
For weak electrolytes: Λ_m = Λ⁰_m - K√c

Electrochemical Cells:
Cell potential: E_cell = E_cathode - E_anode
Standard cell potential: E°_cell = E°_cathode - E°_anode
Nernst equation: E = E° - (RT/nF)ln(Q)

Electrode Potentials:
Standard hydrogen electrode: E° = 0 V
Reference electrodes: Calomel, Ag/AgCl
Concentration cells: E = (RT/nF)ln([ion]₂/[ion]₁)

Electrolysis:
Faraday's laws: m = (Q/F)(M/n)
Q = I × t
Current efficiency = (actual mass/theoretical mass) × 100

Solutions and Colligative Properties

Solution Concentration:
Molarity: M = n/V (mol/L)
Molality: m = n/mass_solvent (mol/kg)
Mole fraction: X_i = n_i/(n₁ + n₂ + ...)

Raoult's Law:
P_solution = X_solvent × P°_solvent
For non-ideal solutions: P = X × P° + correction term

Colligative Properties:
Elevation of boiling point: ΔT_b = K_b × m
Depression of freezing point: ΔT_f = K_f × m
Osmotic pressure: π = iMRT (Van't Hoff equation)

Van't Hoff Factor:
i = actual colligative effect/normal colligative effect
For electrolytes: i = number of ions produced

🧪 Organic Chemistry

Basic Principles and Hydrocarbons

Organic Chemistry Basics:
Hybridization: sp, sp², sp³
Inductive effect: +I, -I
Mesomeric effect: +M, -M
Hyperconjugation: Delocalization of σ electrons

IUPAC Nomenclature:
Identify longest carbon chain (parent)
Identify substituents (alkyl groups)
Number the carbon chain
Name the compound according to rules

Hydrocarbon Reactions:
Alkanes: Substitution (free radical mechanism)
Alkenes: Addition, polymerization
Alkynes: Addition, polymerization
Aromatics: Electrophilic substitution

Reaction Mechanisms

Reaction Mechanisms:
SN1: Two-step, carbocation intermediate, racemic mixture
SN2: One-step, backside attack, inversion of configuration
E1: Two-step elimination, carbocation intermediate
E2: One-step elimination, anti-periplanar requirement

Electrophilic Aromatic Substitution:
General mechanism: Formation of σ complex, deprotonation
Directing effects: Ortho/para directors, meta directors
Activating groups: Electron donating
Deactivating groups: Electron withdrawing

Important Reactions:
Aldol condensation: Aldol → α,β-unsaturated carbonyl
Cannizzaro reaction: Disproportionation of non-enolizable aldehydes
Grignard reaction: Formation of carbon-carbon bonds
Wittig reaction: Formation of alkenes from carbonyl compounds

Biomolecules and Polymers

Biomolecules:
Carbohydrates: General formula Cₙ(H₂O)ₙ
Proteins: Polymers of amino acids
Nucleic acids: DNA, RNA
Lipids: Fats and oils

Amino Acids:
General formula: H₂N-CH(R)-COOH
Essential amino acids: Cannot be synthesized by body
pKa values: COOH (~2), NH₃⁺ (~9)
Isoelectric point: pI = (pKa₁ + pKa₂)/2

Polymers:
Addition polymers: Polyethylene, polystyrene
Condensation polymers: Nylon, polyester
Natural polymers: Cellulose, proteins, nucleic acids

🔬 Inorganic Chemistry

Periodic Classification

Periodic Trends:
Atomic radius: Decreases across period, increases down group
Ionization energy: Increases across period, decreases down group
Electron affinity: Generally increases across period
Electronegativity: Increases across period, decreases down group

Blocks of Elements:
s-block: Groups 1, 2 (alkali and alkaline earth metals)
p-block: Groups 13-18
d-block: Transition elements (Groups 3-12)
f-block: Lanthanides and actinides

Classification based on properties:
Metals, non-metals, metalloids
Representative elements, transition elements, inner transition elements

s-Block Elements

Alkali Metals (Group 1):
General formula: M (ns¹)
Low ionization energies
Highly reactive
Form +1 ions
Compounds: oxides, hydroxides, halides

Alkaline Earth Metals (Group 2):
General formula: M (ns²)
Higher ionization energies than alkali metals
Form +2 ions
Compounds: oxides, hydroxides, sulfates

General Trends:
Reactivity increases down group
Ionic radii increase down group
Solubility varies with compound type

p-Block Elements

Group 13 (Boron Family):
General formula: M (ns²np¹)
+3 oxidation state common
Boron shows different properties
Compounds: boranes, borates

Group 14 (Carbon Family):
General formula: M (ns²np²)
+4 and +2 oxidation states
Catenation (especially carbon)
Compounds: oxides, halides, hydrides

Group 15 (Nitrogen Family):
General formula: M (ns²np³)
-3 to +5 oxidation states
Nitrogen fixation important
Compounds: ammonia, nitrogen oxides

Group 16 (Chalcogens):
General formula: M (ns²np⁴)
-2 to +6 oxidation states
Oxygen and sulfur most important
Compounds: oxides, sulfides, acids

Group 17 (Halogens):
General formula: M (ns²np⁵)
-1 oxidation state common
High electronegativity
Compounds: halides, interhalogen compounds

Group 18 (Noble Gases):
General formula: M (ns²np⁶)
Generally inert
Few compounds under special conditions

d-Block Elements (Transition Metals)

General Properties:
Partially filled d orbitals
Multiple oxidation states
Colored compounds
Catalytic properties
Formation of complex compounds

Important Series:
3d series: Sc to Zn
4d series: Y to Cd
5d series: La to Hg

Electronic Configuration:
(n-1)d¹⁻¹⁰ns² (exceptions exist)
d-block elements show variable oxidation states

Complex Formation:
Coordination number: 2, 4, 6 common
Geometry: Linear, tetrahedral, square planar, octahedral
Ligands: Monodentate, bidentate, polydentate
Stability: Chelate effect, macrocyclic effect

Coordination Compounds

Werner's Theory:
Primary valences: Oxidation state, satisfied by anions
Secondary valences: Coordination number, satisfied by ligands
Geometry determined by coordination number

Valence Bond Theory:
Hybridization determines geometry
sp³: tetrahedral
dsp²: square planar
d²sp³: octahedral
Magnetic properties from unpaired electrons

Crystal Field Theory:
d-orbital splitting in octahedral field
t₂g (lower energy), e_g (higher energy)
Crystal field splitting energy: Δ₀
High spin vs low spin complexes

Stability Constants:
Formation constant: β_f = [ML_n]/[M][L]^n
Stepwise formation constants: K₁, K₂, K₃...
Overall formation constant: β = K₁ × K₂ × K₃...

Qualitative Analysis

Systematic Analysis:
Group I: Ag⁺, Pb²⁺, Hg₂²⁺ (precipitated by HCl)
Group II: Pb²⁺, Bi³⁺, Cu²⁺, Cd²⁺, As³⁺, Sb³⁺, Sn²⁺ (H₂S in acidic medium)
Group III: Fe³⁺, Al³⁺, Cr³⁺ (NH₄OH in presence of NH₄Cl)
Group IV: Co²⁺, Ni²⁺, Mn²⁺, Zn²⁺ (H₂S in basic medium)
Group V: Ba²⁺, Sr²⁺, Ca²⁺ ((NH₄)₂CO₃)
Group VI: Mg²⁺, Na⁺, K⁺, NH₄⁺ (soluble group)

Confirmatory Tests:
Flame test: Specific colors for different cations
Precipitation tests: Characteristic precipitates
Complex formation tests: Color changes

📊 Essential Constants and Data

Physical Constants

Gas constant: R = 8.314 J/(mol·K) = 0.0821 L·atm/(mol·K)
Avogadro's number: N_A = 6.022 × 10²³ mol⁻¹
Faraday constant: F = 96485 C/mol
Planck's constant: h = 6.626 × 10⁻³⁴ J·s
Speed of light: c = 3 × 10⁸ m/s
Electron charge: e = 1.602 × 10⁻¹⁹ C
Boltzmann constant: k = 1.381 × 10⁻²³ J/K

Atomic Masses (Approximate)

H = 1, C = 12, N = 14, O = 16, Na = 23, Mg = 24
Al = 27, Si = 28, P = 31, S = 32, Cl = 35.5, K = 39
Ca = 40, Fe = 56, Cu = 63.5, Zn = 65, Ag = 108, I = 127
Ba = 137, Au = 197, Pb = 207

🎯 Usage Tips

Formula Selection Strategy:

1. Identify the concept involved in the problem
2. Check the conditions required for formula validity
3. Ensure correct units before substitution
4. Verify the answer using alternative methods

Memory Techniques:

1. Group related formulas by topic or concept
2. Create acronyms for formula sequences
3. Practice dimensional analysis to verify formulas
4. Use real-world examples to understand applications
5. Create formula flashcards for quick review

Use this comprehensive chemistry formula sheet as your quick reference guide for JEE/NEET preparation! Regular practice with these formulas will significantly enhance your problem-solving speed and accuracy. 🎯