Equilibria

Le Chatelier, Kc and Kp

Le Chatelier's principle

• Position shifts to oppose a change. Raise T → shifts in the endothermic direction. Raise p → shifts to fewer gas moles. Catalyst → no shift, equilibrium reached faster.
• Haber process (N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹): compromise 400–450 °C, ~200 atm, iron catalyst — low T favours yield but is too slow.

Equilibrium constant

• K changes only with temperature. For an exothermic reaction, raising T decreases K.
• Concentration/pressure changes move the position but K is unchanged.
• Kp uses partial pressures: p(X) = mole fraction × total pressure.

3.1.6.2Kc from equilibrium data — the ICE routine

3.1.10Kp — the same idea with pressures

• Mole fraction x = moles of gas ÷ total moles; partial pressure p = x × P(total); Kp built exactly like Kc but with partial pressures of gases only.
• Solids and pure liquids never appear in Kp expressions.
• Like Kc, Kp changes with temperature only — pressure shifts the position, not the constant.

3.1.6.3The three industrial equilibria

Extended🎓 Beyond the standard course

• The reaction quotient Q is Kc's expression evaluated with current concentrations. Q < K → forward shift; Q > K → reverse; Q = K → equilibrium. This single comparison replaces all hand-waving about "position".
• van 't Hoff: a plot of ln K against 1/T is linear with gradient −ΔH°/R — the quantitative version of "heating an exothermic equilibrium lowers K", and the exact mirror of Arrhenius for kinetics.
• Why solids never appear in K: their concentration (density ÷ molar mass) is fixed — formally, their activity is 1. CaCO₃(s) ⇌ CaO(s) + CO₂(g) reduces to Kp = p(CO₂): one gas controls the whole equilibrium.
• Small-K approximation: when K is tiny, "x is negligible against c" turns quadratics into one-liners — the same 5% rule you use for weak acids.

Deep dive📚 The rest of the chapter, in full

Kc from scratch: the ICE method

Kc units: build them from the expression each time. For N₂ + 3H₂ ⇌ 2NH₃, Kc = [NH₃]²/([N₂][H₂]³) has units (mol dm⁻³)² ÷ (mol dm⁻³)⁴ = mol⁻² dm⁶.

The golden rule of K

Only temperature changes K. Concentration, pressure and catalysts shift the position of equilibrium (or just the speed of reaching it) while K stays fixed. For an exothermic forward reaction, raising T decreases K; for endothermic, K increases. This one sentence — "Kc is unchanged because temperature is constant" — earns a mark in almost every equilibrium question about adding reagent or compressing the mixture.

Le Chatelier, systematically

Industrial compromises

Haber (N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹): low T favours yield but is slow; high P favours yield but is expensive and hazardous. Compromise: ~450 °C, ~200 atm, iron catalyst, and ammonia is liquefied out to pull the equilibrium right. Contact (2SO₂ + O₂ ⇌ 2SO₃, exothermic): ~450 °C, ~2 atm (already 99%+ conversion, so high pressure is not worth paying for), V₂O₅ catalyst. Arguments about conditions = rate vs yield vs cost, always all three.

Kp (Year 2)

For gases use partial pressures: p(X) = mole fraction × total pressure. Kp for N₂O₄ ⇌ 2NO₂ is p(NO₂)²/p(N₂O₄), units built the same way (here: kPa). Solids and pure liquids never appear in Kp or heterogeneous Kc expressions — their "concentration" is constant. Only temperature changes Kp; compressing the mixture shifts position until the same Kp is restored.

Mastery vault🏛 Every remaining spec point, banked

Kc when the volume refuses to cancel

Kp from first principles

• Partial pressure = mole fraction × total pressure; the partial pressures must sum to the total (use this as a check).
• Raising total pressure does not change Kp — the system shifts (here toward PCl₅) until the same Kp is restored with new partial pressures.
• Heterogeneous equilibria omit solids and pure liquids: for CaCO₃(s) ⇌ CaO(s) + CO₂(g), Kp = p(CO₂) alone — at a given temperature the CO₂ pressure above limestone is fixed no matter how much solid is present.

Interpreting K values

K ≫ 1: products dominate; K ≪ 1: barely reacts; K ≈ 1: comparable amounts. K says nothing about SPEED — H₂ + O₂ has a colossal K at 298 K yet a match is needed (kinetic barrier). Comparing K at two temperatures identifies ΔH's sign: K falling as T rises → forward reaction exothermic.

Ethanol two ways — the industrial comparison

Unreacted ethene is recycled over the catalyst — the standard fix when a compromise position leaves conversion low (same trick as the Haber loop). "Carbon-neutral" claims for fermentation ethanol fail once farming, transport and distillation energy are counted — a routine evaluation point.