◄ WORLD II · THE FOLDTHE OCHO · blue builds │ the machine │ red breaks

THE LE CHATELIER PRINCIPLE

Disturb an equilibrium and it pushes back. For A + B ⇌ C, add reactant and the mixture is thrown off balance — then the reaction runs toward products to swallow the surplus, and settles at a new position. But the equilibrium constant never moved: at fixed temperature Q climbs right back to the same K. Down the center, data flows: the disturbance goes in, the mass-action ODE re-equilibrates, the new position and the unchanged K come out. The blue team builds and defends; the red team tries to break it.

source Le Chatelier, Sur un énoncé général des lois des équilibres chimiques, Comptes Rendus 99, 786–789 (1884) — English translation at web.lemoyne.edu/giunta/lechat.html (Classic Chemistry). Rendered, not quoted.

◧ blue team · builds & defends
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THE MODEL — mass action pushes back

The reaction obeys one law: rate = kf[A][B] − kr[C]. Equilibrium is where that rate is zero, so K = kf/kr = [C]/([A][B]).

Add reactant: the forward term jumps, rate goes positive, C is made until the rate falls back to zero. The position moved; K did not. Live state of the current disturbance:

speciesat eq.after re-eq.

Q = [C]/([A][B]) — returns to K to <1e-9 whenever T is held fixed.

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THE LINEAGE — the qualitative face of mass action AVAN

Le Chatelier (1884) is the words; the mass-action law (Guldberg & Waage, 1864) is the equation beneath them. "The equilibrium shifts to oppose the change" is exactly what falls out of setting kf[A][B] = kr[C].

The one deep fact the principle hides: at constant T the ratio K = kf/kr is a constant of the rate laws, not of the current mixture — so no concentration push can move it. Temperature is the sole lever that touches K, through van’t Hoff. Each sphere is the next one’s premise.

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THE WITNESS live

The blue team’s live check: re-integrate the ODE after a push and confirm K is invariant, that raising T lowers K (exothermic), and that inert gas moves nothing. If red tampers, this badge is where it shows.

▼ the machine ▼
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DATA IN — the disturbance in ↓

The system starts at equilibrium for A + B ⇌ C with K = 4.00 at 298 K: [A] = [B] = 0.390, [C] = 0.610, Q = 4.000. You feed it one disturbance:

disturbancetouches K?predicted shift
add reactant Ano→ products
add product Cno← reactants
raise T (exothermic)K falls← reactants
add inert gas (const. V)nono shift

"Const. V" matters: at constant volume an inert gas changes total pressure but no partial pressure or concentration — so Q is untouched. That is what you feed the panel below.

▼   feed the disturbance into the engine   ▼
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▣ THE PANEL — the engine LIT

0.50

Add reactant A: the forward rate jumps, so C is produced until Q falls back to K. The position moves toward products; K is unchanged.

Every number is integrated live from rate = kf[A][B] − kr[C] by RK4 to steady state — nothing is looked up.

▼   the engine emits the new position   ▼
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DATA OUT — the result out ↓

What the machine proves: at fixed T a concentration push moves the position (here [C] rises 0.610 → 0.750 when 0.5 mol/L of A is added) while Q returns to K = 4.000000000 to <1e-9. Only temperature moves K — an exothermic reaction’s K falls as T rises (van’t Hoff, d ln K / d(1/T) = −ΔH/R). Inert gas at constant volume moves nothing.

The blue team’s witness (left) confirms these live; the red team (right) tries to make K appear to move.

red team · attacks & breaks ◨
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THE ADVERSARY

WALL The principle is a heuristic, not a theorem. Le Chatelier himself stated it too broadly; there are documented systems where adding a reactant shifts equilibrium away from consuming it (e.g. adding N2 to an ammonia synthesis already rich in N2 can lower the mole fraction of NH3). "Opposes the change" must be read as a shift in position, not a guarantee about any single mole fraction.

The rigorous statement lives in the Gibbs energy and the reaction quotient, not in the slogan. This engine restricts to the case where the slogan is exact — a single push on one dilute species at constant T and V — and shows the invariant that actually holds: K.

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THE GRAVEYARD

"Adding reactant increases K." Cut. K is fixed by kf/kr at constant T; adding reactant changes only Q, which then relaxes back to the same K. The engine proves Q → K to <1e-9.

"A catalyst shifts the equilibrium." Cut. A catalyst raises kf and kr together, leaving K = kf/kr unchanged. It reaches the same position faster; it does not move it.

"Inert gas shifts things because pressure rose." Kept, corrected. Only at constant pressure (which forces volume up and dilutes) — at constant volume the partial pressures are untouched and nothing shifts.

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THE TAMPER — break it

The red team’s move: read K off the disturbed, non-equilibrium mixture the instant reactant is added — so K appears to change. The blue team’s witness (window 7) is watching.

This is the classic error: compute [C]/([A][B]) at the moment of the push, before re-equilibration. Q there is 1.75, not 4 — so "K changed." It never did; you measured the wrong instant. The witness recomputes, disagrees, and turns red.