Chemistry · Physical Chemistry

Equilibrium formulas for JEE

Every Equilibrium formula you need for JEE, grouped by concept.

FormulasRevision notes
40 formulas4 concepts
01Chemical Equilibrium02Ionic Equilibrium03Buffer Solutions and Salt Hydrolysis04Solubility Product
01

Chemical Equilibrium

15 formulas

Equilibrium Constant (Concentration)

Kc=[C]c[D]d[A]a[B]bK_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}

The equilibrium constant expressed in terms of molar concentrations for a reversible reaction.

applies whenSystem at equilibrium, constant temperature.
equilibriumconcentrationlaw-of-mass-action

Equilibrium Constant (Pressure)

Kp=(PC)c(PD)d(PA)a(PB)bK_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}

The equilibrium constant expressed in terms of partial pressures for gaseous reactions.

applies whenGaseous system at equilibrium, ideal gas behavior.
equilibriumpressuregas

Relation between Kp and Kc

Kp=Kc(RT)ΔnK_p = K_c(RT)^{\Delta n}

Converts equilibrium constant in terms of concentration to partial pressure.

applies whenGaseous systems where Δn\Delta n is the change in gaseous moles.
equilibriumkp-kcthermodynamics

Clausius-Clapeyron Equation

log⁡10P2P1=ΔHvap2.303R(1T1−1T2)\log_{10} \frac{P_2}{P_1} = \frac{\Delta H_{vap}}{2.303 R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)

Relates vapor pressure and temperature for phase equilibria.

applies whenLiquid-Vapor phase equilibrium.
phase-equilibriumvapor-pressurejee-advanced

Standard Gibbs Free Energy and K

ΔG∘=−RTln⁡K\Delta G^\circ = -RT \ln K

Fundamental thermodynamic relation between standard Gibbs energy and equilibrium constant.

applies whenSystem at equilibrium (ΔG=0\Delta G = 0).
thermodynamicsgibbsequilibrium-constant

Gibbs Free Energy and Q

ΔG=ΔG∘+RTln⁡Q\Delta G = \Delta G^\circ + RT \ln Q

Relates the change in Gibbs free energy to standard Gibbs energy and reaction quotient.

applies whenConstant temperature and pressure.
thermodynamicsgibbsreaction-quotient

Ideal Gas Concentration Relation

P=cRT=(nV)RTP = cRT = \left(\frac{n}{V}\right)RT

Relates pressure and molar concentration of an ideal gas.

applies whenIdeal gas behavior.
gas-lawsconcentration

Multiplied Reaction Equilibrium Constant

Kc′′=KcnK''_{c} = K_c^n

Equilibrium constant when the stoichiometric coefficients are multiplied by a factor n.

equilibrium-constantstoichiometry

Reverse Reaction Equilibrium Constant

Kc′=1KcK'_{c} = \frac{1}{K_c}

Equilibrium constant for a reversed reaction is the reciprocal of the forward reaction.

equilibrium-constantreaction-properties

Equilibrium Constant Exponential Form

K=e−ΔG∘/RTK = e^{-\Delta G^\circ / RT}

Exponential representation of the equilibrium constant from standard Gibbs energy.

applies whenConstant temperature.
thermodynamicsgibbsexponential

Net Reaction Equilibrium Constant

Knet=K1×K2×…K_{net} = K_1 \times K_2 \times \dots

The overall equilibrium constant for a reaction obtained by adding multiple steps.

applies whenMultiple sequential equilibrium reactions.
equilibrium-constanthess-law-analog

Kp and Alpha Relation

Kp=4α21−α2PtotK_p = \frac{4\alpha^2}{1-\alpha^2} P_{tot}

A specific relation between partial pressure, total pressure and degree of dissociation.

applies whenSpecific to A(g)⇌2B(g)A(g) \rightleftharpoons 2B(g) gaseous dissociations (e.g., N2O4⇌2NO2N_2O_4 \rightleftharpoons 2NO_2).
degree-of-dissociationpartial-pressurejee-advanced

Reaction Quotient (Qc)

Qc=[C]c[D]d[A]a[B]bQ_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}

Calculates the ratio of product to reactant concentrations at any arbitrary time.

applies whenAt any time t during the reaction.
reaction-quotientdirectionle-chatelier

Van't Hoff Isochore

ln⁡(K2K1)=ΔH∘R(1T1−1T2)\ln\left(\frac{K_2}{K_1}\right) = \frac{\Delta H^\circ}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Relates the variation of equilibrium constant with temperature to the standard enthalpy change.

applies whenAssuming ΔH∘\Delta H^\circ is constant over the temperature range.
thermodynamicsvant-hofftemperature-dependencejee-advanced

Alpha from Vapor Density

α=D−d(n−1)d\alpha = \frac{D - d}{(n-1)d}

Calculates degree of dissociation using initial and equilibrium vapor densities.

applies whenGaseous dissociation reactions where 1 mole yields n moles.
vapor-densitydegree-of-dissociationjee-advanced
02

Ionic Equilibrium

13 formulas

Acid Ionization Constant

Ka=cα21−α=[H+][A−][HA]K_a = \frac{c\alpha^2}{1-\alpha} = \frac{[H^+][A^-]}{[HA]}

Equilibrium expression for the dissociation of a weak acid in water.

applies whenAqueous weak acid solution.
weak-aciddissociationalpha

Base Ionization Constant

Kb=cα21−α=[M+][OH−][MOH]K_b = \frac{c\alpha^2}{1-\alpha} = \frac{[M^+][OH^-]}{[MOH]}

Equilibrium expression for the dissociation of a weak base in water.

applies whenAqueous weak base solution.
weak-basedissociationalpha

Ionic Product of Water

Kw=[H3O+][OH−]=1.0×10−14K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}

Auto-ionization constant for pure water.

applies whenAqueous solutions at 298 K.
waterauto-ionizationconstant

pH Definition

pH=−log⁡10[H+]pH = -\log_{10}[H^+]

Logarithmic scale for hydrogen ion concentration.

applies whenDilute aqueous solutions.
pHhydrogen-ion

pOH Definition

pOH=−log⁡10[OH−]pOH = -\log_{10}[OH^-]

Logarithmic scale for hydroxide ion concentration.

applies whenDilute aqueous solutions.
pOHhydroxide-ion

Percent Dissociation

Percent dissociation=[HA]dissociated[HA]initial×100%\text{Percent dissociation} = \frac{[HA]_{\text{dissociated}}}{[HA]_{\text{initial}}} \times 100\%

Formula to calculate the percentage dissociation of an electrolyte.

dissociationpercentageweak-electrolyte

Conjugate Pair Constant Relation

Ka×Kb=KwK_a \times K_b = K_w

The product of ionization constants for a conjugate acid-base pair.

applies whenConjugate acid-base pairs in water.
conjugate-pairionization-constants

Ostwald's Dilution Law Approximation

α=Kac\alpha = \sqrt{\frac{K_a}{c}}

Degree of dissociation for a very weak electrolyte.

applies whenFor very weak electrolytes where α≪1\alpha \ll 1.
ostwalddilutiondegree-of-dissociation

pH of Amphiprotic Salt

pH=pKa1+pKa22pH = \frac{pK_{a1} + pK_{a2}}{2}

Calculates the pH of an amphiprotic salt solution (e.g., NaHCO3).

applies whenConcentration is reasonably high so water autoionization is negligible.
amphiproticpHpolyproticjee-advanced

pKa Definition

pKa=−log⁡10(Ka)pK_a = -\log_{10}(K_a)

Logarithmic representation of acid dissociation constant.

weak-acidpKa

Log Conjugate Pair Relation

pKa+pKb=pKw=14pK_a + pK_b = pK_w = 14

Logarithmic relation for conjugate acid-base pairs.

applies whenConjugate acid-base pairs in water at 298K.
conjugate-pairlogarithmic

pKb Definition

pKb=−log⁡10(Kb)pK_b = -\log_{10}(K_b)

Logarithmic representation of base dissociation constant.

weak-basepKb

pKw Relation

pKw=pH+pOH=14pK_w = pH + pOH = 14

Relationship between pH and pOH in aqueous solutions.

applies whenAt 298 K.
pHpOHwater
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03

Buffer Solutions and Salt Hydrolysis

10 formulas

Henderson-Hasselbalch Equation (Acidic)

pH=pKa+log⁡10[Salt][Acid]pH = pK_a + \log_{10} \frac{[\text{Salt}]}{[\text{Acid}]}

Calculates the pH of an acidic buffer solution.

applies whenAcidic buffer composed of a weak acid and its salt.
bufferhenderson-hasselbalchacidic

Buffer Capacity

β=dnd(pH)\beta = \frac{dn}{d(pH)}

Defines the buffer capacity against addition of strong acid or base.

applies whenAdding dn moles of strong acid/base to 1 L of buffer.
buffer-capacitybetajee-advanced

Henderson-Hasselbalch Equation (Basic)

pOH=pKb+log⁡10[Conjugate Acid][Base]pOH = pK_b + \log_{10} \frac{[\text{Conjugate Acid}]}{[\text{Base}]}

Calculates the pOH of a basic buffer solution.

applies whenBasic buffer composed of a weak base and its salt.
bufferhenderson-hasselbalchbasic

Degree of Hydrolysis

h=Khch = \sqrt{\frac{K_h}{c}}

General approximation for the degree of salt hydrolysis (h).

applies whenWhen h≪1h \ll 1.
hydrolysisdegree-of-hydrolysisjee-advanced

Hydrolysis Constant SA-WB

Kh=KwKbK_h = \frac{K_w}{K_b}

Hydrolysis constant for a salt of strong acid and weak base.

applies whenStrong acid, weak base salt.
hydrolysis-constantsawbjee-advanced

Hydrolysis Constant WA-SB

Kh=KwKaK_h = \frac{K_w}{K_a}

Hydrolysis constant for a salt of weak acid and strong base.

applies whenWeak acid, strong base salt.
hydrolysis-constantwasbjee-advanced

Hydrolysis Constant WA-WB

Kh=KwKaKbK_h = \frac{K_w}{K_a K_b}

Hydrolysis constant for a salt of weak acid and weak base.

applies whenWeak acid, weak base salt.
hydrolysis-constantwawbjee-advanced

pH of SA-WB Salt Hydrolysis

pH=7−12pKb−12log⁡10cpH = 7 - \frac{1}{2}pK_b - \frac{1}{2}\log_{10} c

Calculates the pH of a salt derived from a strong acid and a weak base.

applies whenAqueous solution of SA-WB salt at 298K, degree of hydrolysis h≪1h \ll 1.
hydrolysispHsawbjee-advanced

pH of WA-SB Salt Hydrolysis

pH=7+12pKa+12log⁡10cpH = 7 + \frac{1}{2}pK_a + \frac{1}{2}\log_{10} c

Calculates the pH of a salt derived from a weak acid and a strong base.

applies whenAqueous solution of WA-SB salt at 298K, degree of hydrolysis h≪1h \ll 1.
hydrolysispHwasbjee-advanced

pH of WA-WB Salt Hydrolysis

pH=7+12(pKa−pKb)pH = 7 + \frac{1}{2}(pK_a - pK_b)

Formula for the pH of a salt derived from a weak acid and a weak base.

applies whenAqueous solution of a weak acid-weak base salt at 298K.
hydrolysissaltpHwawb
04

Solubility Product

2 formulas

Solubility Product Constant

Ksp=[Mp+]x[Xq−]y=xxyyS(x+y)K_{sp} = [M^{p+}]^x[X^{q-}]^y = x^x y^y S^{(x+y)}

Relates the solubility product to molar solubility (S) for a salt MxXy.

applies whenSaturated solution of a sparingly soluble salt.
kspsolubilityprecipitation

Solubility and pH Relation

S=Ksp([H+]+KaKa)S = \sqrt{K_{sp} \left( \frac{[H^+] + K_a}{K_a} \right)}

Calculates solubility of a salt of a weak acid in acidic media due to protonation of the anion.

applies whenSparingly soluble salt MX containing a weak acid anion in an acidic medium.
solubilitypHcommon-ion-effect
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