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JEE Chemistry Formulas
Complete Formula Sheet

All Physical Chemistry Chapters — JEE Main & Advanced 2026 | 9 Topics | 120+ Formulas | MathJax Rendered

⚛️ Atomic Structure ⚗️ Gaseous State 🌡️ Thermodynamics ⚖️ Equilibrium 🔋 Electrochemistry 💧 Solutions 🔷 Solid State ⏱️ Chemical Kinetics
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Table of Contents

1
Atomic Structure
2
Stoichiometry
3
Gaseous State
4
Thermodynamics
5
Chemical Equilibrium
6
Electrochemistry
7
Solutions & Colligative
8
Solid State
9
Chemical Kinetics
⚛️

1. Atomic Structure

14 Formulas
Key
Nuclear Radius
\[ R = R_0 A^{1/3} \]
R₀ = 1.2×10⁻¹³ cm, A = mass number
Important
Planck's Quantum Theory
\[ E = h\nu = \frac{hc}{\lambda} \]
h = 6.626×10⁻³⁴ J·s
Important
Photoelectric Effect (Einstein)
\[ h\nu = h\nu_0 + \frac{1}{2}mv^2 \]
ν₀ = threshold frequency; ½mv² = max KE of electron
Key
Bohr's Quantization (Angular Momentum)
\[ mvr = \frac{nh}{2\pi} \]
Important
Bohr's Energy of Electron
\[ E_n = -\frac{13.6\,Z^2}{n^2}\text{ eV/atom} \]
Z = atomic number, n = principal quantum number
Important
Bohr's Radius
\[ r_n = \frac{0.529\,n^2}{Z}\text{ Å} \]
Velocity of Electron in Bohr Orbit
\[ v_n = \frac{2.18\times10^6\, Z}{n}\text{ m/s} \]
Key
de Broglie Wavelength
\[ \lambda = \frac{h}{mv} = \frac{h}{p} \]
Heisenberg Uncertainty Principle
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
Important
Rydberg Formula (Spectral Lines)
\[ \frac{1}{\lambda} = R_H Z^2\!\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \]
R_H = 1.097×10⁷ m⁻¹
Orbital Angular Momentum
\[ L = \sqrt{l(l+1)}\,\frac{h}{2\pi} \]
Spin Multiplicity
\[ \text{Spin Mult.} = 2|S| + 1 \]
Hydrogen Spectral Series
Seriesn₁n₂Spectral Region
Lyman12, 3, 4…UV
Balmer23, 4, 5…Visible
Paschen34, 5, 6…IR
Brackett45, 6, 7…IR
Pfund56, 7, 8…Far IR
⚗️

2. Stoichiometry & Concentration

12 Formulas
Key
Molarity
\[ M = \frac{w \times 1000}{M_w \times V(\text{mL})} \]
w = solute mass (g), Mw = molar mass, V = vol in mL
Molality
\[ m = \frac{w \times 1000}{M_w \times W_s(\text{g})} \]
Ws = mass of solvent in grams
Normality
\[ N = M \times n\text{-factor} \]
Important
Mole Fraction
\[ x_1 = \frac{n_1}{n_1 + n_2} \]
Vapour Density
\[ V.D. = \frac{M}{2} \]
M = molar mass of gas
Density of Gas (Ideal)
\[ d = \frac{PM}{RT} \]
Important
Dilution Law
\[ N_1V_1 = N_2V_2 \]
Also: M₁V₁ = M₂V₂
Parts per Million
\[ \text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6 \]
Equivalent Weight
\[ E = \frac{M_w}{n\text{-factor}} \]
% by Mass
\[ \%w/w = \frac{m_{solute}}{m_{solution}} \times 100 \]
💨

3. Gaseous State

14 Formulas
Important
Ideal Gas Law
\[ PV = nRT \]
R = 8.314 J mol⁻¹ K⁻¹; R = 0.0821 L·atm mol⁻¹ K⁻¹
Boyle's Law (Isothermal)
\[ P_1V_1 = P_2V_2 \]
Charles' Law (Isobaric)
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Key
Dalton's Law of Partial Pressure
\[ P_{total} = P_1 + P_2 + P_3 + \cdots \]
Key
Graham's Law of Diffusion
\[ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{d_2}{d_1}} \]
Important
RMS Speed
\[ u_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3kT}{m}} \]
Average Speed
\[ u_{avg} = \sqrt{\frac{8RT}{\pi M}} \]
Most Probable Speed
\[ u_{mp} = \sqrt{\frac{2RT}{M}} \]
Speed Ratio
\[ u_{rms} : u_{avg} : u_{mp} = \sqrt{3} : \sqrt{\tfrac{8}{\pi}} : \sqrt{2} \approx 1.73 : 1.60 : 1.41 \]
Important
Van der Waals Equation
\[ \left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT \]
a = intermolecular attraction, b = volume correction
Key
Critical Constants
\[ V_c = 3b,\quad P_c = \frac{a}{27b^2},\quad T_c = \frac{8a}{27Rb} \]
Compressibility Factor
\[ Z = \frac{PV}{nRT} \]
Z = 1 for ideal gas; Z > 1 repulsion dominant; Z < 1 attraction dominant
Mean Free Path
\[ \lambda = \frac{kT}{\sqrt{2}\pi d^2 P} \]
🌡️

4. Thermodynamics & Thermochemistry

16 Formulas
Important
First Law of Thermodynamics
\[ \Delta U = q + w \]
q = heat absorbed; w = work done ON system
Work Done by Gas
\[ w = -P_{ext}\Delta V \]
Key
Enthalpy
\[ H = U + PV,\quad \Delta H = \Delta U + \Delta nRT \]
Δn = moles of gaseous products − moles of gaseous reactants
Hess's Law
\[ \Delta H_{rxn} = \sum \Delta H_f(\text{products}) - \sum \Delta H_f(\text{reactants}) \]
Kirchhoff's Equation
\[ \Delta H_2 - \Delta H_1 = \Delta C_p (T_2 - T_1) \]
Important
Entropy Change
\[ \Delta S = \frac{q_{rev}}{T} = \sum S_{products} - \sum S_{reactants} \]
Important
Gibbs Free Energy
\[ \Delta G = \Delta H - T\Delta S \]
ΔG < 0: spontaneous; ΔG = 0: equilibrium; ΔG > 0: non-spontaneous
Key
ΔG° and Equilibrium Constant
\[ \Delta G^\circ = -RT\ln K = -2.303\,RT\log K \]
ΔG° and Cell EMF
\[ \Delta G^\circ = -nFE^\circ_{cell} \]
Spontaneity Conditions
ΔHΔSSpontaneity
Negative (−)Positive (+)Always spontaneous
Positive (+)Negative (−)Never spontaneous
Negative (−)Negative (−)Spontaneous at low T
Positive (+)Positive (+)Spontaneous at high T
Bond Enthalpy Method
\[ \Delta H_{rxn} = \sum BE(\text{Reactants}) - \sum BE(\text{Products}) \]
Lattice Enthalpy (Born-Haber Cycle)
\[ \Delta H_{lattice} = \Delta H_f - (\text{sum of all steps}) \]
⚖️

5. Chemical & Ionic Equilibrium

18 Formulas
Important
Kp – Kc Relation
\[ K_p = K_c(RT)^{\Delta n} \]
Δn = moles of gaseous products − moles of gaseous reactants
Van't Hoff Equation
\[ \log\frac{K_2}{K_1} = \frac{\Delta H}{2.303R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right) \]
Key
Reaction Quotient
\[ Q < K \Rightarrow \text{forward};\quad Q > K \Rightarrow \text{backward} \]
Important
pH Definition
\[ \text{pH} = -\log[\text{H}^+] \]
pH + pOH = pKw
\[ \text{pH} + \text{pOH} = 14\quad (at\ 25°C) \]
Kw = [H⁺][OH⁻] = 10⁻¹⁴ at 25°C
Ostwald Dilution Law
\[ \alpha = \sqrt{\frac{K_a}{C}} \]
α = degree of dissociation; C = concentration
pH of Weak Acid
\[ \text{pH} = \frac{1}{2}(pK_a - \log C) \]
pH of Weak Base
\[ \text{pOH} = \frac{1}{2}(pK_b - \log C) \]
Important
Henderson–Hasselbalch (Acid Buffer)
\[ \text{pH} = pK_a + \log\frac{[\text{Salt}]}{[\text{Acid}]} \]
Henderson–Hasselbalch (Base Buffer)
\[ \text{pOH} = pK_b + \log\frac{[\text{Salt}]}{[\text{Base}]} \]
Salt Hydrolysis – Weak Acid + Strong Base
\[ \text{pH} = 7 + \frac{1}{2}(pK_a + \log C) \]
Salt Hydrolysis – Strong Acid + Weak Base
\[ \text{pH} = 7 - \frac{1}{2}(pK_b + \log C) \]
Key
Solubility Product
\[ K_{sp} = [\text{M}^{x+}]^y[\text{X}^{y-}]^x \]
For M_yX_x → yM^x+ + xX^y−
Ksp in Terms of Solubility S
\[ K_{sp} = x^x \cdot y^y \cdot S^{x+y} \]
Degree of Hydrolysis
\[ h = \sqrt{\frac{K_w}{K_a \cdot C}} \]
🔋

6. Electrochemistry

14 Formulas
Important
Cell EMF
\[ E_{cell} = E_{cathode} - E_{anode} \]
Important
Nernst Equation
\[ E_{cell} = E^\circ_{cell} - \frac{0.0591}{n}\log Q \quad (\text{at 298K}) \]
General: E = E° − (RT/nF) ln Q
ΔG and Cell EMF
\[ \Delta G = -nFE_{cell},\quad \Delta G^\circ = -nFE^\circ_{cell} \]
F = 96500 C/mol (Faraday's constant)
Key
Faraday's First Law
\[ W = Z \cdot I \cdot t \]
Z = electrochemical equivalent (g/C)
Faraday's Second Law
\[ \frac{W_1}{E_1} = \frac{W_2}{E_2} \]
E = equivalent weight
Charge Passed
\[ Q = I \times t = n \times F \]
Molar Conductance
\[ \Lambda_m = \frac{\kappa \times 1000}{M} \]
κ = specific conductance (S/cm), M = molarity
Key
Kohlrausch's Law
\[ \Lambda^\circ_m = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_- \]
Debye-Hückel-Onsager Equation
\[ \Lambda_m = \Lambda^\circ_m - b\sqrt{C} \]
Degree of Dissociation from Conductance
\[ \alpha = \frac{\Lambda_m}{\Lambda^\circ_m} \]
Relation: E°cell and K
\[ \log K = \frac{nE^\circ_{cell}}{0.0591} \quad (\text{at 298K}) \]
Resistance of Solution
\[ R = \rho\frac{l}{A},\quad \kappa = \frac{1}{\rho} \]
💧

7. Solutions & Colligative Properties

14 Formulas
Important
Raoult's Law
\[ P_s = P^\circ x_A,\quad \frac{P^\circ - P_s}{P^\circ} = x_B \]
xA = mole fraction of solvent; xB = mole fraction of solute
Relative Lowering of Vapour Pressure
\[ \frac{P^\circ - P_s}{P^\circ} = \frac{n}{n + N} \approx \frac{n}{N} \]
Key
Elevation of Boiling Point
\[ \Delta T_b = i K_b m \]
Kb = ebullioscopic constant; m = molality; i = van't Hoff factor
Key
Depression of Freezing Point
\[ \Delta T_f = i K_f m \]
Kf = cryoscopic constant; used to find molar mass
Important
Osmotic Pressure
\[ \pi = iCRT = i\frac{nRT}{V} \]
π = osmotic pressure; C = molarity; R = 0.0821 L·atm·mol⁻¹·K⁻¹
Molar Mass from Colligative Property
\[ M_b = \frac{1000 \times K_b \times w}{\Delta T_b \times W} \]
w = solute mass (g); W = solvent mass (g)
Important
Van't Hoff Factor (Dissociation)
\[ i = 1 + (n-1)\alpha \]
n = ions per formula unit; α = degree of dissociation
Van't Hoff Factor (Association)
\[ i = 1 + \left(\frac{1}{n} - 1\right)\beta \]
β = degree of association
Henry's Law
\[ p = K_H \cdot x \]
KH = Henry's constant; x = mole fraction of gas in solution
Isotonic Solutions
\[ \pi_1 = \pi_2 \Rightarrow C_1 = C_2 \]
🔷

8. Solid State

12 Formulas
Important
Density of Unit Cell
\[ d = \frac{Z \times M}{N_A \times a^3} \]
Z = atoms/unit cell; M = molar mass; a = edge length; NA = 6.022×10²³
Unit Cell Types
TypeAtoms/cell (Z)Packing EfficiencyAtomic Radius
Simple Cubic (SC)152.4%\(r = a/2\)
Body Centred Cubic (BCC)268%\(r = \frac{\sqrt{3}}{4}a\)
Face Centred Cubic (FCC/CCP)474%\(r = \frac{a}{2\sqrt{2}}\)
Hexagonal Close Packed (HCP)674%—
Key
Bragg's Law (X-ray Diffraction)
\[ n\lambda = 2d\sin\theta \]
d = interplanar spacing; θ = angle of diffraction
Ionic Radii Ratio & Coordination Number
r⁺/r⁻ RangeCoordination NumberGeometry
0.155 – 0.2253Triangular Planar
0.225 – 0.4144Tetrahedral
0.414 – 0.7326Octahedral
0.732 – 1.0008Body Centred Cubic
Packing Fraction (SC)
\[ \text{PE} = \frac{\frac{4}{3}\pi r^3}{a^3} = \frac{\pi}{6} \approx 52.4\% \]
Schottky & Frenkel Defects
Schottky: \(n_s = N\,e^{-E_s/2kT}\)
Frenkel: \(n_f = \sqrt{NN_i}\,e^{-E_f/2kT}\)
⏱️

9. Chemical Kinetics

16 Formulas
Key
Rate Law
\[ \text{Rate} = k[A]^m[B]^n \]
m, n = orders; (m+n) = overall order; k = rate constant
Unit of Rate Constant
\[ [k] = (\text{mol/L})^{1-n}\text{s}^{-1} \]
n = order of reaction
Integrated Rate Laws
OrderIntegrated LawHalf-life (t½)Unit of k
Zero\([A]_t = [A]_0 - kt\)\(\frac{[A]_0}{2k}\)mol L⁻¹ s⁻¹
First\(k = \frac{2.303}{t}\log\frac{[A]_0}{[A]_t}\)\(\frac{0.693}{k}\)s⁻¹
Second\(\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt\)\(\frac{1}{k[A]_0}\)L mol⁻¹ s⁻¹
Important
First Order t½
\[ t_{1/2} = \frac{0.693}{k} \]
Independent of initial concentration
Important
Arrhenius Equation
\[ k = A\,e^{-E_a/RT} \]
A = pre-exponential factor; Ea = activation energy
Key
Arrhenius (Logarithmic Form)
\[ \log k = \log A - \frac{E_a}{2.303\,RT} \]
Important
Effect of Temperature on k
\[ \log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\!\left(\frac{1}{T_1} - \frac{1}{T_2}\right) \]
Temperature Coefficient
\[ \mu = \frac{k_{T+10}}{k_T} \approx 2\text{ to }3 \]
Radioactive Decay (First Order)
\[ N = N_0\,e^{-\lambda t},\quad t_{1/2} = \frac{0.693}{\lambda} \]
Concentration after n Half-lives
\[ [A]_t = \frac{[A]_0}{2^n} \]
Time for n half-lives
\[ t = n \times t_{1/2} \]
Rate of Reaction
\[ r = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} \]
For: aA + bB → cC + dD