How Equilibrium Shifts Under Pressure: Le Chatelier's Principle

Imagine a sealed steel cylinder containing a mixture of nitrogen, hydrogen, and ammonia, sitting at equilibrium. Push the piston down, halving the volume, and something curious happens: the cylinder warms briefly, the pressure rises less than you would expect from the volume change alone, and a chemical analysis shows that the ratio of ammonia to its constituent gases has crept upward. The system has done something to itself. It has shifted.

This is the territory of Le Chatelier's principle, which says that a system at equilibrium, when disturbed, responds in a way that partially offsets the disturbance. The principle is qualitative — it tells you the direction of the shift but not the magnitude — and pressure is one of its most instructive applications, because pressure changes act selectively on gases and only when the reaction changes the total number of gas molecules.

Consider the synthesis of ammonia: N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g). On the left side there are four moles of gas; on the right, two. When you compress the mixture, you crowd all the gas molecules into a smaller volume, raising the partial pressure of each species. The system can relieve this crowding by converting four molecules into two — that is, by running the forward reaction. Compression therefore shifts this equilibrium toward ammonia. Expansion does the opposite: it favors the side with more moles of gas, dissociating ammonia back into its elements.

Now consider a contrasting case: H₂(g) + I₂(g) ⇌ 2 HI(g). Two moles of gas on each side. Compress this mixture and the partial pressures of all three species rise, but no shift occurs, because converting reactants to products would not reduce the total mole count. The reaction quotient Q changes in a way that exactly tracks the equilibrium constant K, and the system stays put. This is the most commonly missed feature of pressure effects: the principle applies only when Δn_gas, the change in moles of gas across the balanced equation, is nonzero.

The selectivity goes further. Adding an inert gas — say, argon — to a rigid container raises the total pressure but does not change the partial pressures of the reacting species, and so does not shift the equilibrium. The reacting molecules still collide at the same rates with each other; the argon is a bystander. If, however, you add argon while keeping total pressure constant by allowing the container to expand, the partial pressures of the reactants and products fall, and the equilibrium shifts toward the side with more moles of gas, exactly as if you had pulled the piston outward. The same additive produces opposite effects depending on whether volume or pressure is held fixed.

Liquids and solids, for their part, are nearly incompressible, and their activities are taken as constant. A reaction like CaCO₃(s) ⇌ CaO(s) + CO₂(g) responds to pressure only through the carbon dioxide term; the solids do not enter the calculation. Counting moles of gas, not moles of everything, is what matters.

Underlying all of this is a more fundamental fact: equilibrium is the condition where Q equals K, and K is fixed at a given temperature. Pressure changes do not alter K. They alter the concentrations or partial pressures that go into Q, and the system responds by adjusting composition until Q matches K once again. Le Chatelier's principle is a useful shorthand for predicting which way that adjustment runs, but the deeper account is bookkeeping: the equilibrium constant is sovereign, and the system rearranges its inventory to satisfy it.

This is why industrial ammonia synthesis runs at pressures of 150 to 300 atmospheres. The thermodynamics favor ammonia at high pressure because Δn_gas is negative; the engineering challenge is to build vessels that survive the conditions the chemistry demands. The principle does not tell the engineer how much pressure is enough — for that, one needs K itself — but it tells her, unambiguously, which direction is worth pushing.