All JEE Advanced Chemistry Formulas 2026: Your Ultimate Guide for Exam Preparation

ENTHALPY FORMULAS

Enthalpy Definition:

H = U + pV U = Internal energy of system p = Pressure of system V = Volume of system

Change in Enthalpy (ΔH) under different conditions:

At isobaric condition (Δp = 0): ΔH = Cₚ(T₂ − T₁)

At isochoric condition (ΔV = 0): ΔH = Qᵥ + VΔp

At isothermal condition (ΔT = 0): ΔH = 0

At adiabatic condition (Q = 0): ΔH = Cₚ(T₂ − T₁)

Enthalpy Change of a Reaction:

ΔH_reaction = H_products − H_reactants ΔH° = H°_products − H°_reactants Positive ΔH → endothermic Negative ΔH → exothermic

Enthalpy of Reaction from Enthalpies of Formation:

ΔH°_r = Σ ν_B ΔH°_f,products − Σ ν_B ΔH°_f,reactants (ν_B = stoichiometric coefficient)

Estimation of Enthalpy from Bond Enthalpies:

ΔH = (Enthalpy required to break reactant bonds into gaseous atoms) − (Enthalpy released to form product bonds from gaseous atoms)

Resonance Energy:

ΔH°_resonance = ΔH°_f,experimental − ΔH°_f,calculated ΔH°_resonance = ΔH°_c,calculated − ΔH°_c,experimental

ENTROPY FORMULAS

Entropy:

ΔS_system = ∫(A→B) dq_rev / T

Entropy Calculation for an Ideal Gas:

ΔS_system = nCᵥ ln(T₂/T₁) + nR ln(V₂/V₁)

Also: ΔS_system = nCₚ ln(T₂/T₁) + nR ln(V₂/V₁)

Entropy of Reaction from Standard Entropy Values:

ΔS_rxn = Σ ΔS_products − Σ ΔS_reactants

ΔS_rxn = standard entropy values ΣΔS_products = sum of ΔS of products ΣΔS_reactants = sum of ΔS of reactants

Gibbs Free Energy:

G_system = H_system − TS_system

ATOMIC MASS FORMULAS

Atomic Mass:

Atomic Mass = Mass of protons + Mass of neutrons + Mass of electrons

Mass Number:

Mass number = number of protons + number of neutrons

Relative Atomic Mass (R.A.M.):

R.A.M. = Mass of one atom of an element / (1/12 × mass of one carbon atom)

Specific Gravity:

Specific gravity = density of the substance/density of water at 4°C

Absolute Density (for gases):

Absolute density = Molar mass of the gas / Molar volume of the gas ρ = PM/(RT)

Vapour Density:

V.D. = d_gas / d_H₂ = (PM_gas/RT) / (PM_H₂/RT) = M_gas / M_H₂ = M_gas / 2 Therefore: M_gas = 2 × V.D.

Molarity:

M = (w × 1000) / (Mol. wt. of solute × V_in mL)

Molality:

m = (number of moles of solute/mass of solvent in grams) × 1000 m = (1000 × w₁) / (M₁ × w₂)

Mole Fraction:

Mole fraction of solute (x₁) = n/(n + N) Mole fraction of solvent (x₂) = N/(n + N) x₁ + x₂ = 1

Percentage Calculations:

% w/w = (mass of solute in gm/mass of solution in gm) × 100 % w/v = (mass of solute in gm/volume of solution in mL) × 100 % v/v = (volume of solute in mL/volume of solution) × 100

Interconversion of Concentration Terms:

(M₁ = molar mass of solvent, M₂ = molar mass of solute, ρ = density of solution in g/mL, M = Molarity, m = Molality, x₁ = mole fraction of solvent, x₂ = mole fraction of solute)

Mole fraction of solute → Molarity: M = (x₂ × ρ × 1000) / (x₁M₁ + M₂x₂)

Molarity → Mole fraction: x₂ = (MM₁) / (ρ × 1000 − MM₂)

Mole fraction → Molality: m = (x₂ × 1000) / (x₁M₁)

Molality → Mole fraction: x₂ = (mM₁) / (1000 + mM₁)

Molality → Molarity: M = (mρ × 1000) / (1000 + mM₂)

Molarity → Molality: m = (M × 1000) / (1000ρ − MM₂)

Average Atomic Mass:

Ā_x = (a₁x₁ + a₂x₂ + ... + aₙxₙ) / 100

Mean Molar Mass:

M_avg = (n₁M₁ + n₂M₂ + ... + nₙMₙ) / (n₁ + n₂ + ... + nₙ)

Normality:

N = Number of equivalents of solute / Volume of solution (in litres) N = Molarity × v.f.

At Equivalence Point:

N₁V₁ = N₂V₂ n₁M₁V₁ = n₂M₂V₂

Equivalent Weight:

E = Atomic weight / Valency factor

Number of Equivalents:

No. of equivalents = Wt/Eq.wt. = W/E = W/(M/n) No. of equivalents = No. of moles × v.f.

Measurement of Hardness:

Hardness in ppm = (mass of CaCO₃ / Total mass of water) × 10⁶

ATOMIC STRUCTURE FORMULAS

Planck's Quantum Theory:

Energy of one photon = hν = hc/λ

Photoelectric Effect:

hν = hν₀ + ½m_e v²

Bohr's Model for Hydrogen-like Atoms:

1. Quantization of angular momentum: mvr = nh/(2π)

2. Energy of nth orbit: Eₙ = −E₁/n² × Z² = −2.178 × 10⁻¹⁸ × Z²/n² J/atom = −13.6 × Z²/n² eV E₁ = −2π²me⁴/n²

3. Radius of nth orbit: rₙ = (n²/Z) × h²/(4π²e²m) = 0.529 × n²/Z Å

4. Velocity of electron: v = 2πZe²/(nh) = 2.18 × 10⁶ × Z/n m/s

de Broglie Wavelength:

λ = h/(mc) = h/p (for photon)

Wavelength of Emitted Photon:

1/λ = RZ²(1/n₁² − 1/n₂²)

Number of Photons Emitted by a Sample of H Atoms:

E = nhν (n = number of photons, h = Planck's constant, ν = frequency)

Heisenberg's Uncertainty Principle:

Δx · Δp ≥ h/(4π) mΔx · Δv ≥ h/(4π) Δx · Δv ≥ h/(4πm)

Quantum Numbers:

Principal quantum number: n = 1, 2, 3, 4, 5, ... ∞ Orbital angular momentum in any orbit = nh/(2π) Azimuthal quantum number (l) = 0, 1, 2, 3, ...(n − 1) Magnetic quantum number (m) = −l, ..., −1, 0, 1, ..., +l Spin quantum number (s) = +½, −½ Number of orbitals in subshell = 2l + 1 Maximum electrons in particular subshell = 2(2l + 1) Orbital angular momentum: L = (h/2π)√[l(l+1)] = ℏ√[l(l+1)] ℏ = h/(2π)

MOLAR MASS FORMULAS

Molar Mass:

M = m/n M = molar mass, m = mass of substance (in grams), n = number of moles

Molar Mass of an Element:

Molar mass = Molar mass constant × Relative atomic mass

Molar Mass from Colligative Properties:

M = ΔT_f / K_f (from freezing point depression)

When the Elevation of the Boiling Point is Given:

ΔT_b = K_b × m m = 1000 × w₂ / (w₁ × M₂) ΔT_b = K_b × 1000 × w₂ / (w₁ × M₂)

When the Depression of Freezing Point is Given:

ΔT_f = K_f × m ΔT_f = K_f × 1000 × w₂ / (w₁ × M₂)

STOICHIOMETRY FORMULAS

Relative Atomic Mass:

R.A.M. = Mass of one atom of element / (1/12 × mass of one Carbon atom) = Total number of nucleons

Density:

Specific gravity = density of substance/density of water at 4°C

For Gases:

Absolute density (mass/volume) = Molar mass of gas / Molar volume of gas ρ = PM/(RT)

Vapour Density:

V.D. = d_gas/d_H₂ = (PM_gas/RT)/(PM_H₂/RT) = M_gas/M_H₂ M_gas = 2 × V.D.

Molarity (M):

Molarity(M) = (w × 1000) / (Mol.wt. of Solute × V_in mL)

Molality (m):

Molality = (number of moles of solute/mass of solvent in grams) × 1000 = 1000 × W₁ / (M₁ × W₂)

Percentage Calculations:

% w/w = (mass of solute in gm/mass of solution in gm) × 100 % w/v = (mass of solute in gm/volume of solution in mL) × 100 % v/v = (volume of solute in mL/volume of solution) × 100

Average/Mean Atomic Mass:

Ā_x = (a₁x₁ + a₂x₂ + ... + aₙXₙ) / 100

Mean Molar Mass or Molecular Mass:

M_avg = (n₁M₁ + n₂M₂ + ... + nₙMₙ) / (n₁ + n₂ + n₃ + ... + nₙ)

Normality (N):

N = Number of equivalents of solute / Volume of Solution (in litres)

Measurement of Hardness:

Hardness in ppm = (mass of CaCO₃ / Total Mass of water) × 10⁶

Molarity to Mole Fraction:

x₂ = (MM₁) / (ρ × 1000 − MM₂)

Mole Fraction to Molality:

m = (x₂ × 1000) / (x₁M₁)

Molality to Mole Fraction:

x₂ = (mM₁) / (1000 + mM₁)

Molality to Molarity:

M = (mρ × 1000) / (1000 + mM₂)

Molarity to Molality:

m = (M × 1000) / (1000ρ − MM₁) (ρ = density of solution in g/mL, M₁ = molecular weight of solute)

THERMODYNAMICS FORMULAS 

Thermodynamic Processes:

Isothermal: T = constant, dT = 0, ΔT = 0 Isochoric: V = constant, dV = 0, ΔV = 0 Isobaric: P = constant, dP = 0, ΔP = 0 Adiabatic: q = 0, heat exchange with surrounding = zero

Sign Convention:

Work done on the system = Positive Work done by the system = Negative

Laws of Thermodynamics:

1st Law: ΔU = (U₂ − U₁) = q + w

2nd Law: ΔS_universe = ΔS_system + ΔS_surrounding > 0 (for spontaneous processes)

3rd Law: S − S₀ = k_B ln Ω S = entropy of the system S₀ = initial entropy k_B = Boltzmann constant Ω = total number of microstates consistent with macroscopic configuration

Law of Equipartition of Energy:

U = (f/2)nRT ΔE = (f/2)nR(ΔT) f = degrees of freedom

Total Heat Capacity:

C_T = Δq/ΔT = dq/dT

Molar Heat Capacity:

C = Δq/(nΔT) = dq/(ndT) Cₚ = γR/(γ − 1) Cᵥ = R/(γ − 1)

Specific Heat Capacity:

S = Δq/(mΔT) = dq/(mdT)

Application of 1st Law:

ΔU = ΔQ + ΔW ΔW = −PΔV Therefore: ΔU = ΔQ − PΔV

Isothermal Reversible Expansion/Compression (Ideal Gas):

W = −nRT ln(V_f/V_i)

Reversible/Irreversible Isochoric Processes:

dV = 0, so dW = −P_ext · dV = 0

Reversible Isobaric Process:

W = P(V_f − V_i)

Adiabatic Reversible Expansion:

T₂V₂^(γ−1) = T₁V₁^(γ−1)

Reversible Adiabatic Work:

W = (P₂V₂ − P₁V₁)/(γ − 1) = nR(T₂ − T₁)/(γ − 1)

Irreversible Adiabatic Work:

W = (P₂V₂ − P₁V₁)/(γ − 1) = nR(T₂ − T₁)/(γ − 1) = nCᵥ(T₂ − T₁) = −P_ext(V₂ − V₁) Use: P₁V₁/T₁ = P₂V₂/T₂

GASEOUS STATE FORMULAS 

Temperature Conversions:

(C − 0)/(100 − 0) = (K − 273)/(373 − 273) (K − 273)/(373 − 273) = (F − 32)/(212 − 32)

Boyle's Law (constant T):

V ∝ 1/P P₁V₁ = P₂V₂

Charles's Law (constant P):

V ∝ T V₁/T₁ = V₂/T₂

Derivation of Charles's Law:

V ∝ T → V/T = constant = k V₁/T₁ = k ... (I) V₂/T₂ = k ... (II) Equating: V₁/T₁ = V₂/T₂ = k

Gay-Lussac's Law (constant V):

P ∝ T P₁/T₁ = P₂/T₂

Ideal Gas Equation:

PV = nRT PV = (w/m)RT or Pm = dRT

Dalton's Law of Partial Pressure:

P₁ = n₁RT/V, P₂ = n₂RT/V Total Pressure = P₁ + P₂ + ... Partial pressure = Mole fraction × Total Pressure

Average Molecular Mass of Gaseous Mixture:

M_mix = Total mass of mixture / Total no. of moles in mixture = (n₁M₁ + n₂M₂ + n₃M₃) / (n₁ + n₂ + n₃)

Graham's Law:

Rate of diffusion r ∝ 1/√d (d = density of gas) r₁/r₂ = √(d₂/d₁) = √(M₂/M₁) = √(V.D.₂/V.D.₁)

Van der Waals Equation:

(P + an²/V²)(V − nb) = nRT P = pressure, a and b = gas constants, V = molar volume R = universal gas constant, T = temperature, n = number of moles

Relations with Critical Constants:

V_c = 3b P_c = a/(27b²) T_c = 8a/(27Rb)

Kinetic Theory of Gases — Molecular Speeds:

Root mean square speed: U_rms = √(3RT/M) (Molar mass in kg/mole)

Average speed: U_avg = (U₁ + U₂ + U₃ + ... + Uₙ)/N U_avg = √(8RT/πM) = √(8KT/πm) (K = Boltzmann constant)

Most probable speed: U_MPS = √(2RT/M) = √(2KT/m)

Amagat's Law of Partial Volume:

V = V₁ + V₂ + V₃ + ... + Vₙ

CHEMICAL EQUILIBRIUM FORMULAS 

At Equilibrium:

Rate of forward reaction = rate of backward reaction ΔG = 0 Q = K_eq

Equilibrium Constant (K):

K = rate constant of forward reaction/rate constant of backward reaction = K_f/K_b

K_c (in terms of concentration):

K_f/K_b = K_c = [C]^c[D]^d / ([A]^a[B]^b)

K_p (in terms of partial pressure):

K_p = [P_C]^c[P_D]^d / ([P_A]^a[P_B]^b)

K_x (in terms of mole fraction):

K_x = (X_C^c × X_D^d) / (X_A^a × X_B^b)

Relations between K_p, K_c, K_x:

K_p = K_c(RT)^Δn K_p = K_x(P)^Δn

Van't Hoff Equation:

log(K₂/K₁) = (ΔH/2.303R)(1/T₁ − 1/T₂) ΔH = Enthalpy of reaction

Standard Free Energy and Equilibrium Constant:

ΔG° = −2.303 RT log K

Reaction Quotient (Q):

Q = [C]^c[D]^d / ([A]^a[B]^b)

Degree of Dissociation (α):

α = number of moles dissociated / initial number of moles taken

Vapour Pressure of Liquid:

Relative Humidity = Partial pressure of H₂O vapours / Vapour pressure of H₂O at that temperature

Thermodynamics of Equilibrium:

ΔG = ΔG° + 2.303 RTQ

Van't Hoff Equation (alternative form):

log(K₁/K₂) = (ΔH°/2.303R)(1/T₂ − 1/T₁)

IONIC EQUILIBRIUM FORMULAS 

Ostwald Dilution Law:

For weak acid: K_a = [H⁺][A⁻]/[HA] = [Cα][Cα]/[C(1−α)] = Cα²/(1−α)

If α << 1: K_a ≈ Cα² α = √(K_a/C) = √(K_a × V)

For weak base: α = √(K_b/C) Higher K_a/K_b → stronger acid/base

pH Scale:

pH = −log a_H⁺ (a_H⁺ = activity of H⁺ = molar concentration for dilute solutions) pH = −log[H⁺]; [H⁺] = 10^(−pH) pOH = −log[OH⁻]; [OH⁻] = 10^(−pOH) pK_a = −log K_a; K_a = 10^(−pK_a) pK_b = −log K_b; K_b = 10^(−pK_b)

pH Calculations for Different Solution Types:

Strong acid (conc > 10⁻⁶ M): H⁺ from water is neglected. Strong acid (conc < 10⁻⁶ M): H⁺ from water cannot be neglected

Strong base: Calculate [OH⁻] first, then use [H⁺][OH⁻] = 10⁻¹⁴

Mixture of two strong acids: [H⁺] = N = (N₁V₁ + N₂V₂)/(V₁ + V₂)

Mixture of two strong bases: [OH⁻] = N = (N₁V₁ + N₂V₂)/(V₁ + V₂)

Mixture of strong acid + strong base: If N₁V₁ > N₂V₂ (acidic): [H⁺] = (N₁V₁ − N₂V₂)/(V₁ + V₂) If N₂V₂ > N₁V₁ (basic): [OH⁻] = (N₂V₂ − N₁V₁)/(V₁ + V₂)

Weak acid (monoprotic): K_a = [H⁺][OH⁻]/[HA] = Cα²/(1−α) If α << 1: K_a ≈ Cα², α = √(K_a/C) Valid when α < 0.1 or 10%

Relative Strength of Two Acids: [H⁺] from I acid / [H⁺] from II acid = (c₁α₁)/(c₂α₂) = √(K_a1 c₁)/√(K_a2 c₂)

Hydrolysis of Polyvalent Anions/Cations:

For Na₃PO₄ [C]: K_a1 × K_h3 = K_w K_a2 × K_h2 = K_w K_a3 × K_h1 = K_w

First step hydrolysis: K_h1 = Ch²/(1−h) ≈ Ch² h = √(K_h1/c) [OH⁻] = ch = √(K_h1 × c) [H⁺] = √(K_w × K_a3 / C) pH = ½[pK_w + pK_a3 + log C]

Buffer Solutions:

Acidic Buffer (e.g., CH₃COOH + CH₃COONa): pH = pK_a + log([Salt]/[Acid]) — Henderson-Hasselbalch equation

Basic Buffer (e.g., NH₄OH + NH₄Cl): pOH = pK_b + log([Salt]/[Base])

Solubility Product:

For A_xB_y: K_sp = (xs)^x(ys)^y = x^x · y^y · (s)^(x+y)

ELECTROCHEMISTRY FORMULAS 

Gibbs Free Energy Change:

ΔG = −nFE_cell ΔG° = −nFE°_cell

Nernst Equation:

(Effect of concentration and temperature on EMF of the cell)

ΔG = ΔG° + RT ln Q ΔG° = −RT ln K_eq

E_cell = E°_cell − (RT/nF) ln Q E_cell = E°_cell − (2.303RT/nF) log Q E_cell = E°_cell − (0.0591/n) log Q (at 298 K)

At Chemical Equilibrium:

ΔG = 0; E_cell = 0 log K_eq = nE°_cell / 0.0591 E°_cell = (0.0591/n) log K_eq

For an Electrode M^n+/M:

E = E° − (2.303RT/nF) log(1/[M^n+])

Concentration Cells:

E°_cell = 0

Electrolyte Concentration Cell (e.g., Zn(s)/Zn²⁺(C₁) ‖ Zn²⁺(C₂)/Zn(s)): E = (0.0591/2) log(C₂/C₁)

Electrode Concentration Cell (e.g., Pt,H₂(P₁ atm)/H⁺(1M)/H₂(P₂ atm)/Pt): E = (0.0591/2) log(P₁/P₂)

Faraday's Laws of Electrolysis:

First Law: w ∝ q → w = Zq → w = Zit Z = Electrochemical equivalent

Second Law: W ∝ E → W/E = constant W₁/E₁ = W₂/E₂ = ... = Wₙ/Eₙ W/E = (i × t × current efficiency factor) / 96500

Current efficiency = (actual mass deposited / theoretical mass deposited) × 100

Conductance:

Conductance = 1/Resistance

Specific conductance (conductivity): κ = 1/ρ (κ = specific conductance)

Equivalent conductance: λ_E = (κ × 1000) / Normality

Molar conductance: λ_m = (κ × 1000) / Molarity

Specific conductance = conductance × (l/a) (l = length, a = area)

Applications of Kohlrausch's Law:

Calculation of λ°_M of weak electrolytes: λ°_M(CH₃COOHI) = λ°_M(CH₃COONa) + λ°_M(HCl) − λ°_M(NaCl)

Degree of dissociation of weak electrolyte: α = λ_m^c / λ_m^0 K_eq = Cα²/(1 − α)

Solubility of sparingly soluble salt & K_sp: λ_M^c = λ_M^∞ = κ × 1000/solubility K_sp = S²

Transport Number: t_c = μ_c/(μ_c + μ_a) [transport number of cation] t_a = μ_a/(μ_a + μ_c) [transport number of anion] (t_c = transport number of cation, t_a = transport number of anion)

IDEAL GAS EQUATION FORMULAS 

Ideal Gas Law:

PV = nRT P = pressure, V = volume, n = amount of substance, R = ideal gas constant, T = temperature

Derivation from Combined Laws:

Boyle's Law: V ∝ 1/P Charles's Law: V ∝ T Avogadro's Law: V ∝ n

Combining: V ∝ nT/P → V = RnT/P → PV = nRT

Molar Form:

n = m/M (m = total mass, M = molar mass) Density ρ = m/V

pV = (m/M)RT p = (m/V)(R/M)T p = ρ(R/M)T

Combined Gas Law:

P₁V₁/T₁ = P₂V₂/T₂

Using Number of Molecules (N) instead of Moles (n):

PV = Nk_bT (k_b = Boltzmann constant)

Kinetic Energy of Gas:

E = (3/2)nRT

Avogadro's Constant:

N_A = N/n = N/(PV/RT) (N_A = ratio of total molecules N to total moles n)

DIFFUSION FORMULAS 

Diffusion Formula:

Q_S = −D_S (ds/dx) Q_S = rate of movement of matter, momentum, or energy through unit normal area D_S = diffusion coefficient ds/dx = gradient of mass, momentum, or energy in the medium

Graham's Law:

Rate of diffusion r ∝ 1/√d (d = density of gas) r₁/r₂ = √(d₂/d₁) = √(M₂/M₁) = √(V.D.₂/V.D.₁)

Graham's Law for Comparison between Two Gases:

r_GasA / r_GasB = (M_GasB)^(1/2) / (M_GasA)^(1/2)

Van der Waals Equation:

(P + an²/V²)(V − nb) = nRT

Critical Constants:

V_c = 3b P_c = a/(27b²) T_c = 8a/(27Rb)

DE BROGLIE'S FORMULAS 

de Broglie's Equation:

λ = h/(mv) λ = wavelength, h = Planck's constant, m = mass of particle, v = velocity

Derivation:

From Planck: E = hν = hc/λ ... (1) From Einstein: E = mc² ... (2) Equating for dual nature: hc/λ = mv² Therefore: h/λ = mv → λ = h/(mv)

de Broglie's Wavelength:

λ = h/(mv) = h/momentum = h/p

Relation between the de Broglie Equation and Bohr's Hypothesis:

mv = nh/(2πr) or mvr = n × (h/2π)

Thermal de Broglie Wavelength:

λ_th = h/√(2πmk_bT) h = Planck constant m = mass of gas particle k_b = Boltzmann constant T = temperature of gas

de Broglie in Terms of Kinetic Energy:

λ = h/√(2mKE)

CHARLES'S LAW 

Charles's Law:

V ∝ T (at constant pressure) V₁/T₁ = V₂/T₂

Derivation:

V ∝ T → V/T = constant = k V₁/T₁ = k ... (I) V₂/T₂ = k ... (II) Equating (I) and (II): V₁/T₁ = V₂/T₂ = k Generalised: (V₁)/(T₁) = (V₂)/(T₂)

V₁, T₁ = initial volume and temperature V₂, T₂ = final volume and temperature

Gay-Lussac's Law (constant V):

P ∝ T P₁/T₁ = P₂/T₂

Ideal Gas Equation:

PV = nRT PV = (w/m)RT or Pm = dRT

Boyle's Law (constant T):

V ∝ 1/P P₁V₁ = P₂V₂

Amagat's Law of Partial Volume:

V = V₁ + V₂ + V₃ + ... + Vₙ

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