Equilibrium revision notes for JEE

01Key Concepts & Definitions

Dynamic Equilibrium

Macroscopic properties are constant, but microscopic forward and reverse processes occur exactly at the same rate.

Isotopic Scrambling

Experimental use of isotopes (

D_2

instead of

H_2

, or radioactive sugar) to prove reactions continue dynamically at equilibrium.

Electrolytes (Strong vs. Weak)

Strong electrolytes dissociate almost completely (

\sim 100\%

) in water; weak electrolytes dissociate only partially (

<5\%

).

Hydronium Ion (

H_3O^+

)

A bare proton (

H^+

) is too intensely charged to exist freely; it bonds with water's lone pairs.

Conjugate Acid-Base Pair

An acid and a base that differ by exactly one proton (

H^+

).

Buffer Solution

A solution resisting pH change upon addition of small amounts of acid/alkali or upon dilution.

02Physical Equilibrium

Physical equilibrium exists when there is a phase transformation and the rates of opposing physical processes become equal.

Dynamic Nature: Physical equilibrium is not static; intense activity occurs at the boundary between phases. Proven experimentally by using radioactive sugar isotopes in a saturated solution; radioactivity soon appears in the solid phase due to continuous exchange.
Solid-Liquid Equilibrium: Occurs at the normal melting/freezing point (at 1 atm/1.013 bar pressure). The mass of the two phases remains constant in an insulated system (no heat exchange).

Liquid-Vapour Equilibrium

Attained when evaporation rate equals condensation rate. The pressure exerted by the vapour in equilibrium with its liquid is the equilibrium vapour pressure.

More volatile liquids have higher vapour pressures and lower boiling points.
JEE Tip Boiling point relies on atmospheric pressure. At high altitudes, atmospheric pressure is lower, causing water to boil at temperatures below 100°C.

Solid-Vapour Equilibrium: Observed in substances that sublime, such as solid iodine (purple vapour), camphor, and $NH_4Cl$ .
Solids in Liquids: Characterized by a saturated solution where the rate of dissolution equals the rate of crystallization. The concentration of solute is constant at a given temperature.

Gases in Liquids (Henry’s Law)

The mass of a gas dissolved in a given mass of a solvent is proportional to the pressure of the gas above the solvent.

JEE Tip Solubility of gases decreases with an increase in temperature. This is why soda becomes "flat" when left open in a warm room.

03Chemical Equilibrium & Reaction Extent

Chemical equilibrium is attained when forward and backward reaction rates become equal, keeping reactant and product concentrations constant.

Dynamic Nature Proof: Demonstrated by Haber using isotopic scrambling. If equilibrium is reached with $H_2, N_2,$ and $NH_3$ , and then $D_2$ (deuterium) is introduced, the system eventually contains scrambled species: $H_2, HD, D_2$ and $NH_3, NH_2D, NHD_2, ND_3$ . JEE Tip This mixing strictly proves that forward and backward reactions continue indefinitely; they do not statically halt.

Extent of Reaction based on

K_c

K_c > 10^3

Products heavily predominate; reaction goes nearly to completion (e.g., $H_2 + O_2 \rightleftharpoons H_2O$ has $K_c = 2.4 \times 10^{47}$ ).

K_c < 10^{-3}

Reactants heavily predominate; reaction rarely proceeds (e.g., $H_2O \rightleftharpoons H_2 + \frac{1}{2}O_2$ has $K_c = 4.1 \times 10^{-48}$ ).

10^{-3} < K_c < 10^3

Appreciable concentrations of both reactants and products exist (e.g., $H_2 + I_2 \rightleftharpoons 2HI$ has $K_c = 57.0$ ).

04Homogeneous and Heterogeneous Equilibria

Homogeneous Equilibria

All reactants and products are in the same phase.

Gas phase: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$
Aqueous phase: $CH_3COOC_2H_5(aq) + H_2O(l) \rightleftharpoons CH_3COOH(aq) + C_2H_5OH(aq)$

Heterogeneous Equilibria

Involves substances in multiple phases.

Example: $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$ .

Example: $Ni(s) + 4CO(g) \rightleftharpoons Ni(CO)_4(g)$ .

05Equilibrium Constants (KcK_cKc, KpK_pKp) & Reaction Quotient (QQQ)

For a reaction $aA + bB \rightleftharpoons cC + dD$ :

$K_c$ and $K_p$ Expressions: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ and $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$ .

Relationship

$K_p = K_c(RT)^{\Delta n}$ .

$\Delta n = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)}$ .
JEE Tip Pressure must strictly be in bar (1 bar = $10^5$ Pa) to align with standard state definitions, and $R = 0.0831 \text{ bar L mol}^{-1} \text{K}^{-1}$ .

Modifying Constants

Reverse reaction: $K_{rev} = 1/K_{fwd}$ .

Multiply by factor $n$ : $K_{new} = (K_{fwd})^n$ .

Adding reactions: $K_{net} = K_1 \times K_2$ .

Reaction Quotient (

Q_c

/

Q_p

)

Calculated using concentrations/pressures at any arbitrary time $t$ .

$Q < K$ : Reaction proceeds forward.

$Q > K$ : Reaction proceeds backward.

$Q = K$ : Equilibrium state.

06Thermodynamics of Equilibrium

Gibbs Free Energy ( $\Delta G$ ): The driving force of a reaction. $\Delta G = \Delta G^\circ + RT \ln Q$ .

\Delta G^\circ = -RT \ln K

or $K = e^{-\Delta G^\circ / RT}$ .

If $\Delta G^\circ < 0$ , $K > 1$ (spontaneous forward, products favored).

If $\Delta G^\circ > 0$ , $K < 1$ (non-spontaneous forward, reactants favored).

07Le Chatelier’s Principle & Industrial Factors

If a system at equilibrium is subjected to a change, it shifts to counteract the effect of the change.

Concentration: Adding reactant/removing product pushes the reaction forward.
Pressure/Volume: Increasing pressure (decreasing volume) shifts equilibrium toward fewer moles of gas. If $\Delta n = 0$ , pressure has no effect.

Temperature

The only factor that alters the numerical value of $K$ .

Exothermic ( $\Delta H < 0$ ): $K$ decreases as $T$ increases. (Cold favored).
Endothermic ( $\Delta H > 0$ ): $K$ increases as $T$ increases. (Hot favored).

Effect of Inert Gas: Adding an inert gas at constant volume does not change partial pressures or shift the equilibrium.
Catalyst: Lowers activation energy for forward and backward reactions equally. It does NOT alter $K$ or the equilibrium composition, just the speed of attaining it.

Industrial Applications

Haber Process ( $NH_3$ synthesis): Exothermic ( $\Delta H = -92.38 \text{ kJ/mol}$ ). Favored by high pressure (200 atm), optimal moderate temperature (500°C), and an iron catalyst.
Contact Process ( $SO_3$ synthesis): Exothermic. Uses Platinum ( $Pt$ ) or Divanadium pentoxide ( $V_2O_5$ ) as a catalyst to speed up the sluggish oxidation of $SO_2$ .

Color Change Reactions (Equilibrium Shift Proofs)

$Fe^{3+} \text{(yellow)} + SCN^- \text{(colourless)} \rightleftharpoons [Fe(SCN)]^{2+} \text{(deep red)}$ . JEE Tip Adding oxalic acid removes $Fe^{3+}$ forming $[Fe(C_2O_4)_3]^{3-}$ , fading the red color. Adding $HgCl_2$ removes $SCN^-$ forming $[Hg(SCN)_4]^{2-}$ , also fading the red color.
$2NO_2 \text{(brown)} \rightleftharpoons N_2O_4 \text{(colourless)}$ . Exothermic. Immersing in ice turns it colourless; hot water turns it deep brown.
$[Co(H_2O)_6]^{3+} \text{(pink)} + 4Cl^- \rightleftharpoons [CoCl_4]^{2-} \text{(blue)} + 6H_2O$ . Endothermic. Freezing mixture turns it pink; room temp makes it blue.

08Ionic Equilibrium, Electrolytes & Acid-Base Theories

Michael Faraday classified substances as electrolytes (conduct electricity in aqueous solutions) and non-electrolytes.

Arrhenius Concept: Acids yield $H^+_{(aq)}$ in water; bases yield $OH^-_{(aq)}$ . (Limited to aqueous media).

Brönsted-Lowry Concept

Acids are proton ( $H^+$ ) donors; bases are proton acceptors.

Conjugate Pairs: Differ by one proton. A strong acid yields a very weak conjugate base ( $HCl \rightarrow Cl^-$ ), and a strong base yields a weak conjugate acid.

Lewis Concept: Acids are electron-pair acceptors (e.g., $BF_3, AlCl_3, Co^{3+}, Mg^{2+}, H^+$ ); bases are electron-pair donors (e.g., $H_2O, NH_3, OH^-, F^-$ ).

09pH, Water Auto-ionization (KwK_wKw) & Acid Strength

Auto-ionization of Water

$H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-$ .

$K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14} M^2$ at 298 K. $pK_w = pH + pOH = 14$ .
JEE Tip $K_w$ increases with temperature. However, pH variations with temperature are small and often ignored.
Molarity of pure water $\approx 55.55 M$ .

Weak Acids (

K_a

) and Bases (

K_b

)

$K_a = \frac{c\alpha^2}{1-\alpha}$ . For very weak acids, $\alpha = \sqrt{K_a/c}$ .

Conjugate Pair Relation: $K_a \times K_b = K_w \implies pK_a + pK_b = pK_w = 14$ (at 298K).

Factors Affecting Acid Strength

Down a group: H-A bond strength decreases (size increases), making cleavage easier. Acidity: $HF < HCl < HBr < HI$ .

Across a period: H-A electronegativity difference increases, marking easier charge separation. Acidity: $CH_4 < NH_3 < H_2O < HF$ .

Polyprotic Acids: Have successive constants. $K_{a1} \gg K_{a2} \gg K_{a3}$ .
Indicators: Compounds like phenolphthalein and bromothymol blue are weak acids ( $HIn \rightleftharpoons H^+ + In^-$ ) where the unionized form and conjugate base form display different colors.

10Salt Hydrolysis & Buffer Solutions

Salt Hydrolysis

Salts from strong acids + strong bases ( $NaCl$ ) do not hydrolyse (pH = 7).

Weak Acid + Strong Base ( $CH_3COONa$ ): Hydrolyses to give $OH^-$ . Alkaline, pH > 7.
Strong Acid + Weak Base ( $NH_4Cl$ ): Hydrolyses to give $H^+$ . Acidic, pH < 7.
Weak Acid + Weak Base ( $CH_3COONH_4$ ): Both ions hydrolyse. $pH = 7 + \frac{1}{2}(pK_a - pK_b)$ .

Buffer Solutions

Solutions resisting pH change upon addition of small amounts of acid/alkali or upon dilution.

Acidic Buffer (Weak Acid + Conjugate Base Salt): e.g., $CH_3COOH + CH_3COONa$ . Henderson-Hasselbalch: $pH = pK_a + \log \frac{[\text{Salt}]}{[\text{Acid}]}$ .
Basic Buffer (Weak Base + Conjugate Acid Salt): e.g., $NH_4OH + NH_4Cl$ . $pOH = pK_b + \log \frac{[\text{Conjugate Acid}]}{[\text{Base}]}$ .

11Solubility Product (KspK_{sp}Ksp) & Common Ion Effect

Solubility Categories: Soluble ( $>0.1M$ ), Slightly Soluble ( $0.01M - 0.1M$ ), Sparingly Soluble ( $<0.01M$ ).

Solubility Product (

K_{sp}

)

For a sparingly soluble salt $M_xX_y \rightleftharpoons xM^{p+} + yX^{q-}$ with molar solubility $S$ : $K_{sp} = [M^{p+}]^x[X^{q-}]^y = (xS)^x(yS)^y = x^x y^y S^{(x+y)}$ .

JEE Tip Example: Zirconium phosphate $(Zr^{4+})_3(PO_4^{3-})_4 \implies K_{sp} = 3^3 \cdot 4^4 \cdot S^7 = 6912 S^7$ .

Ionic Product ( $Q_{sp}$ ): If $Q_{sp} > K_{sp}$ , precipitation occurs.
Common Ion Effect: Decreases solubility.

Effect of pH on Solubility

Salts of weak acids (like phosphates, cyanides) show increased solubility at lower pH (more acidic). The $H^+$ ions protonate the weak acid anion, actively removing it from the solubility equilibrium.

$S = \left[ K_{sp} \frac{([H^+] + K_a)}{K_a} \right]^{1/2}$ .

12Important Rules, Laws & Principles

Law of Mass Action: Equilibrium constant is the product of product concentrations divided by reactant concentrations, each raised to their stoichiometric coefficients.
Henry’s Law: The mass of a gas dissolved in a solvent is directly proportional to the partial pressure of the gas above the solvent.
Le Chatelier’s Principle: When an equilibrium system is subjected to a change in concentration, pressure, or temperature, it shifts in a direction that minimizes or counteracts the change.

13Formulae & Equations

$K_p = K_c(RT)^{\Delta n}$
$\Delta G = \Delta G^\circ + RT \ln Q$
$\Delta G^\circ = -RT \ln K$ $\implies K = e^{-\Delta G^\circ/RT}$
$K_w = [H^+][OH^-] = 10^{-14} M^2$ (at 298K)
$pK_a + pK_b = pK_w = 14$ (for conjugate pairs)
$pH = 7 + \frac{1}{2}(pK_a - pK_b)$ (Salt of Weak Acid & Weak Base)
$pH = pK_a + \log \frac{[\text{Salt}]}{[\text{Acid}]}$ (Henderson-Hasselbalch, Acidic Buffer)
$K_{sp} = x^x y^y S^{(x+y)}$ (General formula for $M_xX_y$ salt solubility)

14EXCEPTIONS & ANOMALIES

Pure Solids and Liquids in $K_{eq}$ : Normally, concentration terms are included in $K$ , BUT the molar concentrations of pure solids and pure liquids are absolutely constant regardless of their amount. They are mathematically folded into the $K$ value and conventionally assigned an active mass of exactly 1.
Dimensionless Units of $K$ : $K_c$ and $K_p$ are frequently written with units like $mol/L$ or $bar$ , BUT strictly thermodynamically, if referenced against standard states (1 bar, 1 M), they are completely dimensionless quantities.
Inert Gas Addition: Adding an inert gas typically changes total pressure, BUT if added at constant volume, it exerts zero shift on the equilibrium because the partial pressures/molarities of the reacting species are totally undisturbed.
The Bare Proton Anomaly: $H^+$ is often written in equations, BUT its extremely small size radius ( $\sim 10^{-15} m$ ) generates an intense electric field making it impossible to exist freely. It is uniquely heavily hydrated into $H_3O^+$ , $H_5O_2^+$ , $H_7O_3^+$ , and $H_9O_4^+$ .
Solubility and pH: Normally, adding ions decreases solubility via the common ion effect, BUT adding $H^+$ (lowering pH) to a salt containing a weak acid anion actually increases its solubility by protonating the anion and dragging the equilibrium forward.
Polyprotic Acid Dissociation: One might assume multiple protons leave a molecule with similar energy, BUT $K_{a1}$ is always vastly greater than $K_{a2}$ . Once the first proton leaves, electrostatic forces fiercely hold onto the remaining protons in the now-negatively charged anion.
Water's Unique Dual Role: Most substances are strictly acidic or basic, BUT water is anomalous as an amphoteric solvent, seamlessly acting as an acid in the presence of $NH_3$ and a base in the presence of $HCl$ , and even simultaneously reacting with itself (auto-ionization).
Temperature and pH: $K_w$ strictly depends on temperature (increases as T increases), BUT the variation in the pH scale with temperature is so mathematically slight that it is practically ignored in general calculations.

15Previous Year JEE Topics

Calculation of $K_p$ from $K_c$ and vice versa (especially ensuring proper R values and units, calculating $\Delta n$ for gaseous species only).
Gibbs Free Energy & $K_{eq}$ : Applying $\Delta G^\circ = -RT \ln K$ and identifying spontaneous vs non-spontaneous conditions.
Le Chatelier's Principle: Predicting direction of shift based on Temperature, Pressure/Volume, and inert gas addition at constant $V$ vs constant $P$ .
Reaction Colors: Recalling deep red $[Fe(SCN)]^{2+}$ , brown $NO_2$ , and pink/blue cobalt complexes to predict shift direction based on observation.
Conjugate Acid-Base Pairs: Identifying formulas differing by exactly one proton.
Buffer Solutions: Calculating pH using Henderson-Hasselbalch equations, particularly identifying when a half-neutralization creates a buffer naturally.
Solubility Product ( $K_{sp}$ ): Calculating molar solubility for asymmetric salts (like $A_2B_3$ , or $Zr_3(PO_4)_4$ ) and determining simultaneous solubility in presence of a common ion.

16JEE Traps

Pure Solids and Liquids in Equilibrium Expressions

✕Misconception

The concentrations of pure solids and pure liquids change during a reaction and must be included in the calculation of $K_c$ or $K_p$ .

✓Reality

The molar concentration of a pure solid or liquid remains constant. They are conventionally assigned an active mass of 1 and are ignored in the expression.

Addition of an Inert Gas

✕Misconception

Adding an inert gas to an equilibrium mixture will always shift the reaction direction.

✓Reality

Adding an inert gas at constant volume does not change the partial pressures or molar concentrations of reacting substances. Equilibrium remains completely undisturbed.

The Role of a Catalyst

✕Misconception

Adding a catalyst alters the equilibrium constant ( $K_c$ ) and increases product yield.

✓Reality

A catalyst does not affect the equilibrium composition or the value of $K$ . It only lowers activation energy, allowing the system to achieve the exact same equilibrium state faster.

Conjugate Acid-Base Strength

✕Misconception

A strong acid will dissociate to form a strong conjugate base.

✓Reality

The relationship is inverse. Strong acids have very weak conjugate bases and vice versa.

The Dynamic Nature of Chemical Equilibrium

✕Misconception

When a system reaches equilibrium, all microscopic chemical activity statically ceases.

✓Reality

Chemical equilibrium is strictly dynamic, meaning forward and reverse reactions continue to occur simultaneously at the exact same rate (proven by isotopic scrambling).

Predicting Temperature Shifts

✕Misconception

Increasing the temperature will always shift the reaction forward.

✓Reality

The shift depends entirely on enthalpy change ( $\Delta H$ ). For exothermic reactions ( $\Delta H < 0$ ), $K$ decreases as $T$ increases. For endothermic reactions ( $\Delta H > 0$ ), $K$ increases as $T$ increases.

pH of Weak Acid and Weak Base Salts

✕Misconception

The degree of hydrolysis and the final pH of a WA-WB salt depend on the initial concentration of the salt solution.

✓Reality

The degree of hydrolysis for this specific type of salt is independent of the concentration. The pH is determined solely by $pK_a$ and $pK_b$ : $pH = 7 + \frac{1}{2}(pK_a - pK_b)$ .

Effect of pH on the Solubility of Weak Acid Salts

✕Misconception

Lowering the pH will suppress the solubility of all sparingly soluble salts.

✓Reality

For salts of weak acids (like phosphates or carbonates), lowering the pH actually increases their solubility by protonating the weak acid anion and pulling the dissolution equilibrium forward.

Successive Ionization of Polyprotic Acids

✕Misconception

Polyprotic acids lose all their protons with roughly the same ease.

✓Reality

Higher-order ionization constants are vastly smaller than the primary one ( $K_{a1} \gg K_{a2} \gg K_{a3}$ ).

Units of Equilibrium Constants (

K_c

and

K_p

)

✕Misconception

Equilibrium constants strictly carry physical units like $mol/L$ or $atm$ .

✓Reality

Thermodynamically, if standard states are specified (e.g., 1 bar for gases, 1 M for solutes), $K_p$ and $K_c$ are actually dimensionless quantities.

Equilibrium revision notes

01Key Concepts & Definitions

02Physical Equilibrium

03Chemical Equilibrium & Reaction Extent

04Homogeneous and Heterogeneous Equilibria

05Equilibrium Constants (KcK_cKc​, KpK_pKp​) & Reaction Quotient (QQQ)

06Thermodynamics of Equilibrium

07Le Chatelier’s Principle & Industrial Factors

08Ionic Equilibrium, Electrolytes & Acid-Base Theories

09pH, Water Auto-ionization (KwK_wKw​) & Acid Strength

10Salt Hydrolysis & Buffer Solutions

Salt Hydrolysis

Buffer Solutions

11Solubility Product (KspK_{sp}Ksp​) & Common Ion Effect

12Important Rules, Laws & Principles

13Formulae & Equations

14EXCEPTIONS & ANOMALIES

15Previous Year JEE Topics

16JEE Traps

05Equilibrium Constants (KcK_cKc, KpK_pKp) & Reaction Quotient (QQQ)

09pH, Water Auto-ionization (KwK_wKw) & Acid Strength

11Solubility Product (KspK_{sp}Ksp) & Common Ion Effect