Equilibrium: NEET notes.

01 · NCERT § "Equilibrium in Physical Processes"

Equilibrium in physical processes

• At equilibrium the forward and reverse processes continue at equal rates, so measurable properties stay constant; the equilibrium is dynamic, not static.
• Solid-liquid equilibrium: ice and water coexist at 273 K at atmospheric pressure, and the rate of melting equals the rate of freezing; the normal melting point is the temperature at which this happens at 1 atm.
• Liquid-vapour equilibrium: in a closed vessel the vapour pressure becomes constant when evaporation and condensation rates match; the normal boiling point is the temperature at which vapour pressure equals 1.013 bar (1 atm).
• Solid-vapour equilibrium is seen with substances that sublime, such as iodine, camphor and ammonium chloride.
• A saturated solution is in equilibrium with undissolved solute: dissolution and crystallisation occur at the same rate.
• Henry's law links gas solubility to pressure: at fixed temperature, the amount of a gas that dissolves in a fixed amount of solvent rises in step with the gas pressure over it, and it falls as temperature rises. Opening a soda bottle drops the CO₂ pressure, so dissolved CO₂ escapes until a new equilibrium is reached.
• What all these cases share: a closed system held at one temperature, two opposite processes running at matching rates, and observable properties such as pressure or concentration that stop changing.

02 · NCERT § "Law of Chemical Equilibrium and Equilibrium Constant"

Law of chemical equilibrium and Kc

• Chemical equilibrium can be reached from either side: starting with reactants alone or with products alone leads to the same equilibrium mixture at a given temperature.
• Guldberg and Waage's law of mass action: for aA + bB ⇌ cC + dD, Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ at equilibrium, with concentrations in mol L⁻¹.
• Kc is constant at a fixed temperature, whatever the starting concentrations.
• The equilibrium constant of the reverse reaction is 1/Kc.
• Multiplying a balanced equation by n raises K to the power n; dividing by n gives the nth root of K.
• Adding two reactions multiplies their equilibrium constants.
• Units of Kc are (mol L⁻¹)^Δn; K is dimensionless when Δn = 0, and in thermodynamic treatments K is often taken as dimensionless using standard states.
• In calculations, convert equilibrium moles to mol L⁻¹ before substituting; the volume cancels out only when Δn = 0.

03 · NCERT § "Homogeneous Equilibria"; § "Heterogeneous Equilibria"

Homogeneous and heterogeneous equilibria; Kp

• In a homogeneous equilibrium all species are in the same phase, such as all gases or all in one solution.
• For gases, partial pressures can replace concentrations, giving Kp; the two are linked by Kp = Kc(RT)^Δn.
• Δn = (moles of gaseous products) − (moles of gaseous reactants) from the balanced equation.
• When pressure is in bar and concentration in mol L⁻¹, R = 0.0831 bar L mol⁻¹ K⁻¹.
• If Δn = 0 (e.g. H₂ + I₂ ⇌ 2HI), Kp = Kc; for PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), Δn = +1 and Kp = Kc(RT).
• In a heterogeneous equilibrium more than one phase is present, such as water in equilibrium with its vapour or CaCO₃(s) ⇌ CaO(s) + CO₂(g).
• The concentrations of pure solids and pure liquids are constant and are left out of the K expression; for the decomposition of CaCO₃, Kp = p(CO₂).
• Even though pure solids and liquids do not appear in K, they must be present for the heterogeneous equilibrium to exist.

04 · NCERT § "Applications of Equilibrium Constants"

Applications of K and the reaction quotient

• The size of K shows how far a reaction goes: K > 10³ means products dominate, K < 10⁻³ means reactants dominate, and values in between mean appreciable amounts of both.
• The reaction quotient Q has the same form as K but uses concentrations at any instant, not just at equilibrium.
• If Q < K the reaction moves forward; if Q > K it moves backward; if Q = K it is at equilibrium.
• To calculate equilibrium amounts, set up an initial-change-equilibrium table using the stoichiometry, substitute into K and solve.
• Equilibrium concentrations depend on starting conditions, but the ratio defined by K does not.

05 · NCERT § "Relationship between Equilibrium Constant K, Reaction Quotient Q and Gibbs Energy G"

K, Q and Gibbs energy

• ΔG = ΔG° + RT ln Q for a reaction mixture of any composition.
• At equilibrium ΔG = 0 and Q = K, giving ΔG° = −RT ln K = −2.303 RT log K.
• K = e^(−ΔG°/RT); a negative ΔG° means K > 1 and a positive ΔG° means K < 1.
• When ΔG < 0 the forward reaction proceeds (Q < K); when ΔG > 0 the reverse is favoured (Q > K).
• Use R = 8.314 J K⁻¹ mol⁻¹ with ΔG° in J mol⁻¹, not kJ mol⁻¹.

06 · NCERT § "Factors Affecting Equilibria"

Factors affecting equilibria: Le Chatelier's principle

• Le Chatelier's principle: disturb an equilibrium by altering concentration, pressure or temperature, and the system responds by moving in whichever direction partly cancels that disturbance.
• Adding a reactant or removing a product shifts the equilibrium forward; the value of K does not change.
• Raising pressure by reducing volume shifts a gaseous equilibrium towards the side with fewer gas moles; if Δn = 0 pressure has no effect.
• Adding an inert gas at constant volume leaves the equilibrium unchanged, because the partial pressures and molar concentrations of the reacting gases stay the same.
• Temperature is the only factor that changes the value of K: for an exothermic reaction K falls as temperature rises; for an endothermic reaction K rises.
• For N₂O₄(g) ⇌ 2NO₂(g), which is endothermic, heating increases the brown NO₂ and cooling favours colourless N₂O₄.
• In the Haber process, N₂(g) + 3H₂(g) ⇌ 2NH₃(g) with ΔH = −92.38 kJ mol⁻¹, high pressure favours ammonia, and a moderate temperature with an iron catalyst balances yield against rate.
• A catalyst speeds up the forward and reverse reactions equally, so equilibrium is reached sooner but its composition and K do not change.

07 · NCERT § "Ionic Equilibrium in Solution"; § "Acids, Bases and Salts"

Ionic equilibrium and acid-base concepts

• Faraday classified substances as electrolytes (conduct in solution) and non-electrolytes; strong electrolytes ionise almost completely, while weak electrolytes ionise partly and set up an equilibrium with unionised molecules.
• Arrhenius: acids give H⁺ (present as H₃O⁺) and bases give OH⁻ in water; the definition is limited to aqueous solutions.
• A bare proton is too reactive to exist alone in water; it binds to water as the hydronium ion H₃O⁺, and larger clusters such as H₉O₄⁺ also form.
• Brønsted-Lowry: an acid is a proton donor and a base is a proton acceptor.
• An acid and the base formed when it loses a proton are a conjugate pair; a strong acid has a very weak conjugate base, and a weak acid a relatively strong one.
• Water is amphoteric: it acts as a base towards HCl and as an acid towards NH₃.
• Lewis: an acid accepts an electron pair and a base donates one; BF₃, AlCl₃ and cations like Co³⁺ and Mg²⁺ are Lewis acids, while NH₃, OH⁻ and F⁻ are Lewis bases.
• Lewis acids need not contain hydrogen, which is how the theory covers electron-deficient molecules like BF₃.

08 · NCERT § "Ionization of Acids and Bases"

Ionisation of water, pH, weak acids and weak bases

• Water self-ionises: its ionic product Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K, so pure water there has [H₃O⁺] = 1.0 × 10⁻⁷ M and pH 7.
• Kw increases with temperature, so neutral water has pH below 7 when hot; neutrality means [H₃O⁺] = [OH⁻], not pH = 7.
• pH = −log[H₃O⁺] and pH + pOH = pKw = 14 at 298 K.
• For strong acids and bases, take complete dissociation and count all H⁺ or OH⁻ released: 0.05 M Ba(OH)₂ gives [OH⁻] = 0.10 M, pOH 1 and pH 13.
• For a weak acid HA of concentration c and degree of ionisation α, Ka = cα²/(1 − α); when α is small, α ≈ √(Ka/c) and [H₃O⁺] ≈ √(Ka c).
• pKa = −log Ka; a larger Ka (smaller pKa) means a stronger acid. Weak bases are treated the same way with Kb.
• For a conjugate pair, Ka × Kb = Kw, so pKa + pKb = 14 at 298 K.
• Polyprotic acids ionise in steps with Ka₁ > Ka₂ > Ka₃, because removing a proton from a negative ion is harder.
• Acid strength of H–A: down a group, bond strength controls it (HF < HCl < HBr < HI); along a period, electronegativity of A controls it (CH₄ < NH₃ < H₂O < HF).

09 · NCERT § "Common Ion Effect in the Ionization of Acids and Bases"; § "Hydrolysis of Salts and the pH of their Solutions"

Common ion effect and hydrolysis of salts

• Adding an ion already present in a weak electrolyte's equilibrium pushes the equilibrium back and suppresses ionisation; adding CH₃COONa to acetic acid lowers [H₃O⁺] and raises pH.
• The common ion effect is a direct application of Le Chatelier's principle.
• Salts of a strong acid and a strong base (NaCl) do not hydrolyse and give neutral solutions.
• Salts of a weak acid and a strong base (CH₃COONa) hydrolyse to give basic solutions.
• Salts of a strong acid and a weak base (NH₄Cl) hydrolyse to give acidic solutions.
• For a salt of a weak acid and a weak base (CH₃COONH₄), pH = 7 + ½(pKa − pKb); the solution is neutral only if pKa = pKb.
• Hydrolysis is the reaction of a salt's cation or anion (or both) with water, which changes the pH away from 7.

10 · NCERT § "Buffer Solutions"

Buffer solutions

• A buffer resists change in pH when small amounts of acid or base are added or when it is diluted.
• An acidic buffer is a weak acid with its salt of a strong base (acetic acid and sodium acetate); a basic buffer is a weak base with its salt of a strong acid (ammonia and ammonium chloride).
• pH of an acidic buffer: pH = pKa + log([conjugate base]/[acid]) (Henderson-Hasselbalch equation).
• pOH of a basic buffer: pOH = pKb + log([conjugate acid]/[base]), and pH = 14 − pOH at 298 K.
• When the acid and its conjugate base are present at equal concentrations, pH = pKa.
• A buffer can also be made by partly neutralising a weak base with a strong acid: mixing 3 mmol of NH₃ with 1 mmol of HCl leaves 2 mmol NH₃ and 1 mmol NH₄⁺, a basic buffer.
• Within a buffer only the ratio of amounts matters, so millimoles can be used directly without dividing by the total volume.

11 · NCERT § "Solubility Equilibria of Sparingly Soluble Salts"

Solubility equilibria of sparingly soluble salts

• For a sparingly soluble salt in contact with its saturated solution, the product of ion concentrations, each raised to its stoichiometric power, is the solubility product Ksp.
• For BaSO₄ ⇌ Ba²⁺ + SO₄²⁻, Ksp = S² where S is the molar solubility.
• For a general salt MₓXᵧ, Ksp = xˣ yʸ S^(x+y); for M₂X, Ksp = 4S³, and for MX₂ (like CaF₂), also 4S³.
• If the ionic product in a solution exceeds Ksp, precipitation occurs; if it is less, the solution is unsaturated and more solid can dissolve.
• A common ion lowers the solubility of a sparingly soluble salt; this is used to purify common salt by passing HCl gas through its saturated solution, which precipitates NaCl.
• Salts of weak acids become more soluble at lower pH, because the anion is removed by protonation.
• Compare the solubility of salts by comparing S, not Ksp directly, unless they have the same formula type.

Revise

Must-know facts

1. 01Equilibrium is dynamic: forward and backward rates are equal, not zero.
2. 02Normal boiling point: vapour pressure = 1.013 bar (1 atm).
3. 03Reverse reaction: K' = 1/K; equation multiplied by n: K' = Kⁿ.
4. 04Kp = Kc(RT)^Δn with Δn = gaseous products − gaseous reactants; R = 0.0831 bar L mol⁻¹ K⁻¹.
5. 05Pure solids and liquids are omitted from K; CaCO₃ ⇌ CaO + CO₂ has Kp = p(CO₂).
6. 06Q < K forward; Q > K backward; Q = K equilibrium.
7. 07ΔG° = −RT ln K = −2.303 RT log K.
8. 08Only temperature changes K; a catalyst changes neither K nor composition.
9. 09Inert gas added at constant volume: no shift.
10. 10Haber process: N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92.38 kJ mol⁻¹.
11. 11Kw = 1.0 × 10⁻¹⁴ at 298 K; it rises with temperature.
12. 12pH + pOH = 14 at 298 K.
13. 13Ka × Kb = Kw; pKa + pKb = 14.
14. 14Weak acid (small α): [H⁺] = √(Ka c).
15. 15Lewis acids: BF₃, AlCl₃, Co³⁺, Mg²⁺; Lewis bases: NH₃, OH⁻, F⁻.
16. 16Acid strength: HF < HCl < HBr < HI (bond strength); CH₄ < NH₃ < H₂O < HF (electronegativity).
17. 17Salt of weak acid + weak base: pH = 7 + ½(pKa − pKb).
18. 18Buffer: pH = pKa + log([salt]/[acid]); pH = pKa when they are equal.
19. 19Ksp for M₂X or MX₂ = 4S³; for MX = S².
20. 20Common ion lowers solubility; NaCl is purified by HCl gas.

Where marks go

Common traps

Reference

Formulas

Equilibrium constant (concentrations)

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

For aA + bB ⇌ cC + dD; pure solids and liquids omitted.

Kp and Kc

Kp = Kc(RT)^Δn

Δn = gaseous product moles − gaseous reactant moles; R = 0.0831 bar L mol⁻¹ K⁻¹ with p in bar.

Gibbs energy and Q

ΔG = ΔG° + RT ln Q

At equilibrium ΔG = 0 and Q = K.

Gibbs energy and K

ΔG° = −RT ln K = −2.303 RT log K

K = e^(−ΔG°/RT).

Ionic product of water

Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ (298 K)

pKw = 14 at 298 K.

pH

pH = −log[H₃O⁺] ; pH + pOH = 14

The sum is 14 only at 298 K.

Weak acid ionisation

Ka = cα² / (1 − α) ≈ cα² ; [H₃O⁺] = cα ≈ √(Ka c)

Approximation valid when α is small.

Conjugate pair

Ka × Kb = Kw ; pKa + pKb = pKw

Applies to an acid and its own conjugate base.

Salt of weak acid and weak base

pH = 7 + ½(pKa − pKb)

At 298 K; independent of salt concentration.

Acidic buffer

pH = pKa + log([A⁻]/[HA])

Henderson-Hasselbalch equation.

Basic buffer

pOH = pKb + log([BH⁺]/[B])

Then pH = 14 − pOH at 298 K.

Solubility product

Ksp = xˣ yʸ S^(x+y) for MₓXᵧ

MX: S²; M₂X or MX₂: 4S³; S in mol L⁻¹.

Glossary

Key terms

Dynamic equilibrium

State where opposing processes run at equal rates so the composition stays constant.

Law of mass action

Reaction rate is proportional to the product of reactant active masses, leading to the K expression.

Reaction quotient (Q)

The K-type ratio evaluated at any moment, used to predict the direction of change.

Heterogeneous equilibrium

An equilibrium involving species in more than one phase.

Le Chatelier's principle

A disturbed equilibrium shifts to partly undo the disturbance.

Conjugate acid-base pair

Two species differing by one proton.

Lewis acid

A species that accepts an electron pair.

Amphoteric

Able to act as either an acid or a base, as water does.

Degree of ionisation (α)

Fraction of a weak electrolyte present as ions at equilibrium.

Common ion effect

Suppression of a weak electrolyte's ionisation, or of a salt's solubility, by an added shared ion.

Hydrolysis

Reaction of a salt's ions with water that makes the solution acidic or basic.

Buffer solution

A solution that resists pH change on adding small amounts of acid or base.

Solubility product (Ksp)

Equilibrium constant for a sparingly soluble salt dissolving into its ions.