Ammonia synthesis

Why does squeezing a gas mixture harder produce more ammonia, when the reaction had already come to rest?

A sealed vessel of nitrogen and hydrogen sits at equilibrium. Nothing is changing. Squeeze it, and more ammonia appears. That is odd twice over: a system that had stopped starts again, and it starts in a particular direction, as though it knew which way to go.

The usual answer — "the equilibrium shifts to oppose the change" — restates the observation in a confident voice. It does not say what a molecule does differently when the walls come in. Let us find out what actually moves.

Start with the word "rest". At equilibrium, is anything happening? Take a vessel at equilibrium and swap some hydrogen for its heavy isotope. Wait, then look: the label turns up in the ammonia. Nothing stopped. Nitrogen and hydrogen are still combining and ammonia is still coming apart — at equal rates. Equilibrium is a standoff between two ongoing processes, not a halt. That already tells us where to look: not at a stopped thing being restarted, but at a balance being tipped.

So what breaks the tie? Count molecules. One nitrogen and three hydrogens make two ammonias: four gas molecules become two. Now compress. Every molecule is closer to every other, so both directions speed up — but not by the same factor. The forward direction needs four particular molecules to find each other; the reverse needs two. Concentrate everything and the harder-to-arrange event gains more, so the forward rate outruns the reverse and net ammonia accumulates until the rates match again at a higher ammonia fraction.

You can watch the same thing in the equilibrium constant, which is cleaner because it assumes nothing about mechanism. Write the reaction quotient in partial pressures: ammonia squared on top, nitrogen times hydrogen cubed underneath. Compress the vessel so every partial pressure is multiplied by the same factor k. The top scales by k squared and the bottom by k to the fourth, so the quotient falls by a factor of k squared. The equilibrium constant did not move — it depends only on temperature. So the quotient is now below it, and the reaction runs forward until they match. That is a derivation, not a slogan, and its content is entirely the exponents: 2 on top, 1 + 3 = 4 underneath. Change a reaction so both sides have equal moles of gas and pressure does nothing at all.

Which is exactly the check that saves us from the slogan. "Equilibrium opposes the change" predicts a shift for any squeeze; the mole count predicts none when the counts are equal, and none when you raise the pressure by pumping in an inert gas at fixed volume, because that leaves every partial pressure untouched. Both of those are what is observed. Le Chatelier's principle is a serviceable mnemonic with known counterexamples, better treated as a summary of results than as a reason for them.

Now the industrial twist, because it shows what pressure is really buying. The reaction gives out heat, so cooling the vessel raises the equilibrium yield — and yet the process runs hot. Why? Because the nitrogen triple bond is among the strongest in chemistry, and at any temperature where the yield is excellent, nothing happens on a human timescale. So an iron catalyst is used to break that bond on a surface, and the temperature is raised to a compromise where the rate is usable. From memory the plants run at something like 400 to 500 degrees Celsius and a few hundred atmospheres; treat those figures as approximate, and the bond energy of dinitrogen — roughly 940 kilojoules per mole — as the softest number here. That compromise is where pressure earns its keep: the heat needed for a workable rate costs equilibrium yield, and the pressure buys some of it back.

Two misconceptions are worth naming. The catalyst does not shift the equilibrium: it lowers the barrier for the forward and reverse steps by the same amount, so it changes when you arrive, never where. If you see a claim that a catalyst improves yield, what is meant is yield in the time available, which is a different quantity.

And the pressure is not squeezing ammonia into existence by force. Nothing is being crushed into a smaller molecule. The compression only changes the relative frequency of two kinds of event that were already both happening, and the direction of the shift is decided by an integer difference in mole counts, not by pressure acting on a bond.

One honest limit on the picture: everything above is written in partial pressures, which is the ideal-gas idealisation. At a few hundred atmospheres real gases deviate noticeably from it, and a design engineer works in fugacities instead. The direction of the argument survives — fewer moles of gas is still the favoured side — but the numerical yield the simple expression predicts is not the one the plant sees.

• Why the iron surface makes dissociating dinitrogen easier, and what the promoters actually promote.
• Whether an equilibrium can be pushed by continuously removing the product instead of squeezing the reactants.

Every term the collection defines is gathered in the glossary.