Equilibrium

Equilibrium is one of the highest-yielding chapters in NEET chemistry because it supplies both direct numerical questions (K, pH, solubility) and conceptual reasoning questions (Le Chatelier, buffer action). It also underpins later topics like electrochemistry, thermodynamics and qualitative analysis, so weakness here quietly damages several other chapters.

What "Equilibrium" Actually Means: The Dynamic Picture

Whenever a process is reversible and takes place in a closed container, it eventually reaches a state where the measurable properties — concentration, pressure, colour, density — stop changing with time. This is equilibrium. The crucial idea is that the process has not stopped: the forward and backward changes continue at equal rates, so nothing appears to happen. This is why we call it dynamic, not static.

Physical equilibria illustrate this cleanly:

• Solid ⇌ Liquid (ice ⇌ water at 273 K, 1 bar): both phases coexist, melting rate = freezing rate. Temperature stays fixed while both phases are present.
• Liquid ⇌ Vapour in a closed vessel: the vapour exerts a fixed saturated vapour pressure at a given temperature, independent of the amount of liquid. Boiling point is where this equals external pressure.
• Solid ⇌ Vapour (sublimation of iodine, camphor, naphthalene).
• Solute (solid) ⇌ Solute (solution): a saturated solution in contact with excess solid. Radioactive-tracer experiments prove exchange continues between solid and dissolved sugar even though the concentration is constant.
• Gas ⇌ Gas in solution: governed by Henry's law, mass of dissolved gas ∝ its partial pressure (the basis of fizz in sealed soft drinks).

Chemical equilibrium behaves identically. In N₂ + 3H₂ ⇌ 2NH₃, if you start with only N₂ and H₂, the forward rate is maximum initially and falls as reactants deplete; the reverse rate starts at zero and rises. When the two curves meet, equilibrium is attained. Starting instead from pure NH₃ under the same conditions gives the same equilibrium composition — a hallmark test that a true equilibrium can be approached from either side.

Key characteristics to memorise: equilibrium is attainable only in a closed system; it is dynamic; catalysts speed up the attainment of equilibrium but never change the equilibrium composition (they lower activation energy of forward and reverse steps equally); and at equilibrium ΔG = 0.

The Equilibrium Constant: K꜀, K_p and Q

For a general reaction aA + bB ⇌ cC + dD, the law of chemical equilibrium (law of mass action applied to equilibrium) gives

K꜀ = [C]^c [D]^d / ([A]^a [B]^b)

where square brackets denote equilibrium molar concentrations. For gaseous reactions we may instead use partial pressures:

K_p = (p_C^c · p_D^d) / (p_A^a · p_B^b)

Since p = (n/V)RT = CRT for an ideal gas,

K_p = K꜀ (RT)^Δn, where Δn = (moles of gaseous products) − (moles of gaseous reactants).

Therefore K_p = K꜀ only when Δn = 0 (e.g. H₂ + I₂ ⇌ 2HI). Both K꜀ and K_p are strictly dimensionless when expressed in terms of activities, but in NEET-level numericals units appear as (mol L⁻¹)^Δn or (bar)^Δn.

Manipulation rules you should be able to apply instantly:

1. Reversing a reaction: K′ = 1/K.
2. Multiplying all coefficients by n: K′ = Kⁿ.
3. Adding two reactions: K_overall = K₁ × K₂.
4. Dividing coefficients by 2: K′ = √K.

Homogeneous vs heterogeneous equilibria. In a heterogeneous equilibrium the concentration of a pure solid or pure liquid is essentially constant and is folded into K. Thus for CaCO₃(s) ⇌ CaO(s) + CO₂(g), K_p = p_CO₂. For C(s) + CO₂(g) ⇌ 2CO(g), K_p = p²_CO / p_CO₂.

Reaction quotient Q has the same algebraic form as K but uses concentrations at any instant. Comparing Q with K predicts direction:

• Q < K → net forward reaction (products must build up)
• Q = K → equilibrium
• Q > K → net reverse reaction

Magnitude of K tells us extent, not speed. K > 10³ means the equilibrium mixture is almost all products; K < 10⁻³ means the reaction barely proceeds; intermediate values give appreciable amounts of both.

Link with free energy: ΔG = ΔG° + RT ln Q, and at equilibrium ΔG = 0, Q = K, giving

ΔG° = −RT ln K

So a large negative ΔG° corresponds to K ≫ 1; a positive ΔG° gives K < 1.

Le Chatelier's Principle and Factors Affecting Equilibrium

Statement: if a system at equilibrium is disturbed by a change in concentration, pressure or temperature, the system shifts in the direction that partly counteracts the disturbance.

• Concentration: adding a reactant (or removing a product) shifts the equilibrium forward. This is why NH₃ is continuously condensed out in the Haber process and why removing steam favours forward reaction in the water-gas shift.
• Pressure (by changing volume): compression shifts equilibrium toward the side with fewer moles of gas. For N₂ + 3H₂ ⇌ 2NH₃ (4 mol → 2 mol), high pressure increases NH₃ yield. If Δn = 0, pressure has no effect on composition.
• Addition of inert gas at constant volume: no shift (partial pressures of the reacting gases are unchanged). At constant pressure, adding inert gas increases volume and behaves like dilution, shifting toward the side with more gaseous moles.
• Temperature: this is the only factor that changes the value of K. For an exothermic reaction, raising T shifts equilibrium backward and K decreases; for an endothermic reaction, raising T shifts it forward and K increases. Hence NH₃ synthesis (exothermic) is run at a moderate 700 K compromise — lower T gives better yield but unacceptably slow rate.
• Catalyst: no shift; equilibrium is reached faster. Iron with Mo promoter in Haber's process, V₂O₅ in the Contact process.

Two classic industrial applications worth remembering: Haber process (high pressure ~200 atm, ~700 K, Fe catalyst) and Contact process for 2SO₂ + O₂ ⇌ 2SO₃ (exothermic, Δn negative → favoured by high pressure and lower temperature, V₂O₅ catalyst at about 720 K).

Ionic Equilibrium: Acids, Bases and pH

Electrolytes in water set up their own equilibria. Strong electrolytes (HCl, NaOH, NaCl) are essentially fully ionised; weak electrolytes (CH₃COOH, NH₃, HF) ionise only partially and establish a genuine equilibrium.

Three definitions of acids and bases:

1. Arrhenius: acid gives H⁺, base gives OH⁻ in water.
2. Brønsted–Lowry: acid is a proton donor, base a proton acceptor. Every acid has a conjugate base differing by one H⁺ (HCl/Cl⁻, H₂O/OH⁻, NH₄⁺/NH₃). A strong acid has a weak conjugate base. Species like H₂O and HCO₃⁻ that act both ways are amphiprotic/amphoteric.
3. Lewis: acid is an electron-pair acceptor (BF₃, AlCl₃, H⁺, Cu²⁺), base an electron-pair donor (NH₃, H₂O, OH⁻, Cl⁻). Note that Lewis acids need not contain hydrogen.

Ionisation of water: H₂O + H₂O ⇌ H₃O⁺ + OH⁻, with K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 298 K. In pure water both are 10⁻⁷ M. K_w increases with temperature, so the pH of neutral water falls below 7 above 298 K (water remains neutral).

pH = −log[H₃O⁺], pOH = −log[OH⁻], and pH + pOH = 14 at 298 K. Acidic: pH < 7; basic: pH > 7.

For a weak monobasic acid HA of concentration c with degree of ionisation α:

K_a = cα²/(1 − α); when α ≪ 1, α ≈ √(K_a/c) and [H⁺] = √(K_a c)

This is Ostwald's dilution law — α increases on dilution. Also pK_a = −log K_a; smaller pK_a means stronger acid. For a conjugate acid–base pair, K_a × K_b = K_w, i.e. pK_a + pK_b = 14.

For polyprotic acids (H₂CO₃, H₃PO₄), K_a1 ≫ K_a2 ≫ K_a3, because removing a proton from an already negative ion is progressively harder; the first step dominates [H⁺].

Factors governing acid strength in binary hydrides: down a group, bond dissociation enthalpy falls, so acidity increases (HF < HCl < HBr < HI); across a period, electronegativity rises, so acidity increases (CH₄ < NH₃ < H₂O < HF).

Common Ion Effect, Buffers, Salt Hydrolysis and K_sp

Common ion effect is Le Chatelier applied to ionic equilibria: adding an ion already present suppresses the ionisation of a weak electrolyte. Adding CH₃COONa to acetic acid lowers its α and raises the pH; adding NH₄Cl to NH₄OH suppresses OH⁻ (used in group-III qualitative analysis).

Buffer solutions resist pH change on addition of small amounts of acid or base. They contain a weak acid with its salt (acidic buffer, e.g. CH₃COOH + CH₃COONa) or a weak base with its salt (basic buffer, e.g. NH₃ + NH₄Cl). The Henderson–Hasselbalch equation:

pH = pK_a + log([salt]/[acid]) and pOH = pK_b + log([salt]/[base])

Maximum buffer capacity occurs when [salt] = [acid], where pH = pK_a. Blood is buffered near 7.4 by the carbonic acid–bicarbonate pair (H₂CO₃/HCO₃⁻); breathing adjusts dissolved CO₂ (and hence H₂CO₃) while the kidneys adjust HCO₃⁻, keeping pH within its narrow survivable range even though metabolism constantly generates acidic products.

Salt hydrolysis. A salt formed from a strong acid and a strong base (NaCl) does not hydrolyse, and its solution is neutral. A salt of a strong base and weak acid (CH₃COONa) hydrolyses to give a basic solution, since the anion is a moderately strong conjugate base: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. A salt of a weak base and strong acid (NH₄Cl) hydrolyses to give an acidic solution via NH₄⁺ + H₂O ⇌ NH₄OH + H⁺. When both acid and base are weak (CH₃COONH₄), the solution's pH depends on whether K_a or K_b is larger and is close to 7 only when they are comparable. The degree of hydrolysis rises on dilution, exactly as Ostwald's law predicts for any equilibrium being pulled apart by added water.

Solubility product (K_sp). For a sparingly soluble salt such as AgCl ⇌ Ag⁺ + Cl⁻, K_sp = [Ag⁺][Cl⁻] at saturation, and for a salt M_xN_y, K_sp = [M]^x[N]^y. Comparing the ionic product with K_sp predicts behaviour exactly like Q vs K: ionic product < K_sp means the solution is unsaturated and more solid can dissolve; ionic product = K_sp means saturation; ionic product > K_sp means precipitation occurs until the product falls back to K_sp. This is the basis of the common ion effect on solubility — adding NaCl to a saturated AgCl solution forces some Ag⁺ to precipitate out as AgCl, since [Cl⁻] has been pushed up and the ionic product must be restored to K_sp. Selective precipitation in qualitative inorganic analysis (separating group II sulphides from group IV) relies on exactly this comparison of ionic product against K_sp for different metal sulphides at a controlled [S²⁻].

Common Mistakes and Exam Traps

• Forgetting that K depends only on temperature. Adding more reactant, changing pressure, or adding a catalyst shifts the position of equilibrium or the rate of reaching it, but the numerical value of K stays fixed unless temperature changes — a very common wrong-option trap.
• Misapplying Le Chatelier to inert gas addition. At constant volume, adding an inert gas changes total pressure but not the partial pressures of the reacting species, so there is no shift at all — students who reflexively say "pressure increased, so equilibrium shifts toward fewer moles" get this one wrong.
• Using α ≈ √(K_a/c) when α is not actually small. Ostwald's dilution law approximation is only valid for weak electrolytes with α ≪ 1; for moderately strong weak acids or dilute enough solutions this approximation breaks down and the quadratic cα²/(1−α) = K_a must be solved exactly.
• Confusing pK_a strength direction. A smaller pK_a means a stronger acid (larger K_a), the same inverse relationship as pH — a frequent sign error under exam pressure.