Revision: Class 11 >> Equilibrium NEET (UG) Equilibrium

When the rate of formation of a product in a process is in competition with the rate of formation of the reactant, the state is then termed as "equilibrium state".

Chemical equilibrium refers to the state of a system in which the concentration of reactants and products does not change with time, and the system shows no further change in any property.

The equilibrium established between ions and unionised molecules in an aqueous solution is called ionic equilibrium.

The pOH of a solution can be defined as the negative logarithm to the base 10, of the molar concentration of OH⁻ ions in solution.

pOH = -log₁₀[OH^-]

The pH of a solution is defined as the negative logarithm to the base 10, of the concentration of H⁺ ions in solution in mol dm^–3.

pH is expressed mathematically as

pH = -log₁₀ [H⁺] or pH = -log₁₀ [H₃O⁺]

pH scale is a scale for measuring the hydrogen ion concentration in a solution.

A process in which a salt reacts with water to produce acidity or alkalinity is known as salt hydrolysis.

A buffer solution of pH less than 7 is called an acidic buffer. Weak acid with its salt of strong base gives acidic buffer.

e.g. CH₃COOH + CH₃COONa; HCN + NaCN

A buffer solution having a pH more than 7 is called a basic buffer. Weak base with its salt of strong acid gives basic buffer.

e.g. NH₄OH + NH₄Cl, C₆H₅NH₂ + C₆H₅NH₃Cl

A solution containing a weak acid and its salts with strong base is called an acidic buffer solution.

The ability of a buffer solution to resist changes in pH on the addition of acid or base is called buffer action.

A buffer solution is defined as a solution which resists drastic changes in pH when a small amount of strong acid, strong base, or water is added to it.

The solution maintains its pH constant or retains an acidic or basic nature even upon the addition of small amounts of acid or base.

The number of moles of a compound that dissolves to give one litre of saturated solution is called its molar solubility.

\[\text{Molar solubility (mol/L)}=\frac{\text{Solubility in g/L}}{\text{Molar mass in g/mol}}\]

It is defined as the product of molar concentration of its ions in a saturated solution each concentration terms raised to the power equal to the number of ions produced on dissociation of one molecule of an electrolyte.

\[A_{x}B_{y}\rightleftharpoons xA^{y+}+yB^{x-}\]

\[K_{\mathrm{sp}}=[A^{y^{+}}]^{x-}[B^{x^{-}}]^{y}\]

This law applies only to weak electrolytes, not to strong electrolytes.

This law is not applicable to strong electrolytes because strong electrolytes are almost completely.

Consider a binary electrolyte having a concentration. C and the degree of dissociation is α.

\[AB\longrightarrow A^++B^-\]

\[K=\frac{[A^+][B^-]}{[AB]}=\frac{C\alpha\times C\alpha}{C(1-\alpha)}=\frac{C\alpha^2}{1-\alpha},\] for a weak electrolyte 

\[1-\alpha\cong1\]

Where K_d is the dissociation constant.

• Equilibrium is possible only in a closed system at a given temperature.
• Equilibrium is dynamic in nature — forward and backward reactions continue but at equal rates.
• At chemical equilibrium: Rate of forward reaction = Rate of backward reaction
• Not all physical processes that stop at equilibrium are general characteristics of chemical equilibrium.

• Equilibrium is possible only in a closed system at a given temperature.
• Exists at the melting point where solid and liquid coexist.
• Rate of melting = Rate of freezing → dynamic equilibrium.
• Temperature and pressure remain constant as long as equilibrium is maintained.
• The addition of heat shifts the equilibrium towards melting (endothermic process).
• Removal of heat favours freezing (exothermic process).
• Example: Ice ⇌ Water at 0°C, 1 atm

• Established in a closed container when the rate of evaporation = the rate of condensation → dynamic equilibrium.
• Vapour pressure is the pressure exerted by vapour over the liquid surface at equilibrium at a given temperature.
• Vapour pressure increases with temperature because molecules have higher kinetic energy.
• Boiling point: Temperature at which vapour pressure = external (atmospheric) pressure.
• Lower external pressure → lower boiling point (e.g., water boils below 100°C at high altitudes).
• Strong intermolecular forces → lower vapour pressure → higher boiling point.
• At equilibrium, vapour pressure is independent of the amount of liquid or vapour present (as long as both phases exist).
• Example: Water ⇌ Vapour in a sealed container

• Direct transition: Solid ⇌ Vapour without passing through the liquid phase (sublimation ⇌ deposition).
• Requires a closed system for equilibrium to be established.
• Occurs in substances that have high vapour pressure at room/low temperatures.
• At equilibrium: Rate of sublimation = Rate of deposition
• Sublimation is endothermic (heat absorbed); Deposition is exothermic (heat released).
• Temperature determines the extent of sublimation — higher temperature → more vapour.
• Examples: Iodine (I₂), Camphor, Naphthalene, dry ice (CO₂)

• In a saturated solution: Rate of dissolution = Rate of crystallisation → dynamic equilibrium.
• The equilibrium is represented as: Solute(s) ⇌ Solute(aq)
• Dynamic equilibrium exists between dissolved and undissolved solute — both processes continue simultaneously.
• Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a specific temperature.
• Solubility depends mainly on temperature — for most solids, solubility increases with temperature.
• At a given temperature, solubility has a definite fixed value.
• The presence of a common ion can reduce solubility (Common Ion Effect).
• Examples: NaCl, sugar dissolving in water

Governed by Henry's Law: The solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

where p = partial pressure of gas, K_H = Henry's constant, x = mole fraction of gas in solution.

• Solubility of gas ∝ partial pressure of gas above the liquid.
• Increase in pressure → more gas dissolves (equilibrium shifts forward).
• Increase in temperature → decreases gas solubility (gas escapes — equilibrium shifts backwards).
• Henry's constant (K_H) increases with temperature → solubility decreases.
• At high altitude, the partial pressure of O₂ is low → less O₂ dissolves in blood → breathing difficulties (altitude sickness).
• Examples: CO₂ in soft drinks, O₂ dissolved in blood

• Occurs only in a closed system at a given temperature.
• It is dynamic in nature — forward and backward processes occur simultaneously at equal rates.
• All macroscopic properties (temperature, pressure, concentration, density) remain constant at equilibrium.
• Equilibrium can be attained from either direction (approaching from the reactant side or the product side gives the same equilibrium state).
• Both opposing processes occur at the same rate — there is no net observable change.
• Requires specific temperature and pressure conditions for establishment.
• A definite value of a measurable quantity (e.g., vapour pressure, solubility) is attained at equilibrium for a given temperature.

Dynamic equilibrium: The state where the forward reaction rate equals the backward reaction rate and there is no net change in composition.

For a reversible reaction: aA + bB ⇌ cC + dD

Rate of forward reaction \[R_1=k_1[A]^a[B]^b\]

Rate of backward reaction \[R_2=k_2[C]^c[D]^d\]

At equilibrium: R₁ = R₂

• ΔG determines spontaneity:
  ΔG < 0 → spontaneous (forward), ΔG > 0 → non-spontaneous, ΔG = 0 → equilibrium
• Key relation:
  ΔG = ΔG^∘ + RT ln⁡ Q
• Reaction quotient (Q):
  Compares the current state of reaction; calculated like K but for non-equilibrium conditions.
• At equilibrium:
  Q = K and ΔG = 0 → no net change in system
• Standard relation at equilibrium:
  ΔG^∘ = −RT ln ⁡K
• Direction prediction using Q and K:
  Q < K → forward reaction (spontaneous)
  Q > K → backward reaction (reverse spontaneous)
• K depends only on temperature, not on concentration or pressure; it indicates the extent of reaction.

Addition of inert gas at constant volume: No effect on equilibrium.

• Partial pressures of reacting gases remain unchanged.
• Total pressure increases, but the molar concentrations of reactants/products remain unchanged.

Addition of inert gas at constant pressure: Volume increases → effective partial pressures of reacting gases decrease.

• Equilibrium shifts towards the side with a greater number of moles of gas (Δn > 0 side).
• If Δn = 0 → no effect even at constant pressure.

Does not change the equilibrium constant K (K depends only on temperature).

Catalyst also does not affect the equilibrium position - a similar concept worth remembering together.

• Increase in reactant concentration → equilibrium shifts forward (more products form).
• Increase in product concentration → equilibrium shifts backward (more reactants form).
• Decrease in reactant concentration → equilibrium shifts backward.
• Decrease in product concentration → equilibrium shifts forward.
• System always opposes the change — Le Chatelier's Principle.
• Affects only the position of equilibrium, not the value of K.
• Equilibrium constant K remains unchanged (K depends only on temperature).

Reaction Quotient Q is used to predict the direction of shift:

• Applicable only to gaseous equilibria (no effect on reactions in solution).
• Increase in pressure (decrease in volume) → shifts to the side with fewer moles of gas (Δn < 0 side).
• Decrease in pressure (increase in volume) → shifts to the side with more moles of gas (Δn > 0 side).
• If Δn = 0 → no effect of pressure change on the equilibrium position.
• Based on Le Chatelier's Principle, the system opposes the stress.
• Does not change the equilibrium constant K (K depends only on temperature).

The only factor that changes the equilibrium constant K.

• An increase in temperature favours the endothermic direction (heat absorbed).
• A decrease in temperature favours an exothermic reaction (heat released).

Treat heat as:

• Reactant in endothermic reaction → adding heat shifts forward
• Product in an exothermic reaction → adding heat shifts backwards

Affects both the position of equilibrium and the value of K.

• Increase in volume → pressure decreases → shifts to the side with more moles of gas.
• Decrease in volume → pressure increases → shifts to the side with fewer moles of gas.
• Applicable only to gaseous equilibria.
• If Δn = 0 → no effect of volume change on the equilibrium position.
• Concept is the inverse of pressure change (Volume ∝ 1/Pressure).
• Does not affect the equilibrium constant K (K depends only on temperature).

• Catalyst does NOT change the equilibrium position.
• Speeds up both forward and backward reactions equally.
• Helps the system reach equilibrium faster (shorter time, same endpoint).
• Does not affect the equilibrium constant K.
• Does not change ΔG or the thermodynamics of the reaction.
• Only lowers the activation energy (Ea) of both forward and backward reactions equally.
• No change in equilibrium composition or yield of products.

• Also known as the law of equilibrium, a central concept in chemical equilibria.
• If a system at equilibrium is disturbed, it shifts to oppose the change.
• Explains the qualitative effect of temperature, concentration, and pressure on gaseous equilibrium.
• Not applicable to solid reversible reactions (e.g., Fe(s) + S(s) → FeS(s)).
• Only temperature changes the equilibrium constant K.

Effect of Temperature on Solubility:

• Case I — Solubility decreases with temperature: CaSO₄, NaOH
• Case II — Solubility increases with temperature: most ionic salts (e.g., NaCl, KNO₃)

Effect of Pressure on Boiling & Freezing Point:

• The boiling point increases with an increase in pressure
• The freezing point increases with an increase in pressure (increased pressure → stronger molecular interaction → higher freezing point)

Acids and bases are classified based on the type of ions they produce in solution.

• Acid → produces H⁺ ions (or H₃O⁺) in aqueous medium.
• Base → produces OH⁻ ions in aqueous medium.

Salt is formed by neutralisation of acid and base:

Example: HCl + NaOH → NaCl + H₂O

Nature of salt solution depends on the relative strength of acid and base used:

Acid: Substance that produces H⁺ ions (or H₃O⁺) in aqueous solution.

• Example: HCl → H⁺ + Cl⁻ ; H₂SO₄ → 2H⁺ + SO₄²⁻

Base: Substance that produces OH⁻ ions in aqueous solution.

• Example: NaOH → Na⁺ + OH⁻ ; KOH → K⁺ + OH⁻

H⁺ ions don't exist freely — they combine with water to form the hydronium ion (H₃O⁺).

Applicable only in aqueous solutions.

• Does not explain NH₃ as a base (no OH⁻ group present).
• Does not explain gas-phase reactions (e.g., HCl + NH₃ → NH₄Cl in the gaseous state).
• Does not explain why CO₂ and SO₂ show acidic character.

Acid: Proton (H⁺) donor → gives H⁺ → forms conjugate base.

Base: Proton (H⁺) acceptor → accepts H⁺ → forms conjugate acid.

General reactions:

• Acid ⇌ H⁺ + Conjugate base
• Base + H⁺ ⇌ Conjugate acid

A conjugate acid-base pair differs by exactly one proton (H⁺).

• Strong acid → weak conjugate base (and vice versa).
• Strong base → weak conjugate acid (and vice versa).

Explains reactions without water (non-aqueous media) — advantage over Arrhenius.

Explains why NH₃ acts as a base (accepts H⁺ from water).

Key Example:

• HCl = acid (donates H⁺) → Cl⁻ = conjugate base
• NH₃ = base (accepts H⁺) → NH₄⁺ = conjugate acid

• Acids ionise in water to give H⁺/H₃O⁺ ions; bases give OH⁻ ions.
• The extent of ionisation depends on the strength + concentration.
• Strong → almost complete ionisation; weak → partial (equilibrium exists).
• Represented as: HA ⇌ H⁺ + A⁻
• The degree of ionisation, α, increases with dilution.
• Basis of pH and equilibrium calculations.

Classification Based on Extent of Dissociation

The product of molar concentrations of H⁺ and OH^- ions at a specified temperature.

The ionisation of water can be represented as K_w:

K = [H₂O⁺] [OH^-] 

= 1.0 × 10^-14 M² at 25°C

The ionic product of water depends on temperature. When acid and base are added to pure water, K_w does not change. Value K_w increases with temperature.

pH = negative logarithm of H₃O⁺ ion concentration (mol/L).

• The pH scale (0–14) measures the concentration of H⁺ ions in a solution; values < 7 indicate acids, > 7 indicate bases, and 7 is neutral.
• A universal indicator shows different colours at different pH levels, helping to determine the strength of an acid or base.
• Strong acids/bases produce more H⁺ or OH⁻ ions in solution, while weak acids/bases produce fewer ions at the same concentration.