Le Châtelier's Principle · High School Chemistry

Why make ammonia at high pressure?

Industrial ammonia plants run at hundreds of atmospheres and 400–500 °C, and they continually remove the ammonia as it forms. High-pressure equipment is expensive, so why use it? And if higher temperatures make reactions faster, why not run hotter? The answers come from how an equilibrium responds when conditions change.

Le Châtelier’s principle

An equilibrium holds only for a given set of conditions. Change the conditions and the system shifts until it reaches a new equilibrium.

In 1888, Henri Le Châtelier summed up the pattern: if a change is made to a system at equilibrium, the equilibrium shifts in the direction that partly counteracts the change. This is Le Châtelier’s principle勒夏特列原理.

Concentration

Adding a reactant or removing a product makes Q smaller than K, so the equilibrium shifts right, toward products. Adding a product or removing a reactant shifts it left. For example:

\ce{Fe^3+(aq) + SCN-(aq) <=> FeSCN^2+(aq)}

Adding more Fe³⁺ or SCN⁻ to this solution deepens its blood-red color as more FeSCN²⁺ forms.

Pressure and volume

For reactions involving gases with different numbers of moles of gas on each side, compressing the mixture (raising the pressure) shifts the equilibrium toward the side with fewer moles of gas. Expanding it shifts the equilibrium toward the side with more. If both sides have the same number of moles of gas, as in H₂ + I₂ ⇌ 2HI, changing the volume causes no shift.

Compressing a mixture raises every gas concentration by the same factor. Q changes only because the powers in the numerator and denominator add up to different totals.

Temperature

Heating shifts an equilibrium in the endothermic direction; cooling shifts it in the exothermic direction. Unlike concentration and pressure, temperature changes K itself: heating raises K for an endothermic reaction and lowers K for an exothermic one. For example:

\begin{aligned} &\ce{2NO2(g) <=> N2O4(g)} \\ &\Delta H^\circ = -57.2\ \text{kJ/mol}_\text{rxn} \end{aligned}

A flask of NO₂ and N₂O₄ turns darker red-brown in hot water, as the equilibrium shifts left in the endothermic direction to make more NO₂. In ice water the color fades.

Catalysts and inert gases

A catalyst speeds up the forward and reverse reactions equally. Equilibrium is reached sooner, but it doesn’t shift and K doesn’t change.
Adding an unreactive gas such as helium at constant volume raises the total pressure but changes no concentration. Q still equals K, so there is no shift.

Pick a reaction at equilibrium and apply a change. Compare the old equilibrium, the moment just after the change, and the new equilibrium. For N₂O₄ ⇌ 2NO₂ you can also see the color:

Try it: stress an equilibrium and watch it shift

old equilibriumjust after the changenew equilibrium

How Chinese textbooks differ

Chinese textbooks say an equilibrium shifts “in the forward direction” or “in the reverse direction” instead of right or left.
In the Chinese version of the iron(III) thiocyanate experiment, the equation is written Fe³⁺ + 3SCN⁻ ⇌ Fe(SCN)₃. Students also add iron powder, which reduces Fe³⁺ to Fe²⁺, so the red color fades.
Chinese classes also use potassium dichromate (orange Cr₂O₇²⁻ ⇌ yellow CrO₄²⁻) to show the effect of adding acid or base. US classes often use pink Co(H₂O)₆²⁺ and blue CoCl₄²⁻ to show the effect of temperature.

Example 1: compressing NO₂ and N₂O₄

A syringe holds an equilibrium mixture of NO₂ and N₂O₄. The plunger is quickly pushed in to halve the volume. How does the color change, seen from the side, and why?

Step-by-step solution

What sets the color. NO₂ is red-brown and N₂O₄ is colorless, so the color depends on [NO₂].
Just after compressing. Halving the volume instantly doubles every concentration, including [NO₂], so the color darkens.
Use Q to find the shift. For 2NO₂ ⇌ N₂O₄, Q = [N₂O₄]/[NO₂]². After both concentrations double:
$\begin{aligned} Q' &= \frac{2[\ce{N2O4}]}{(2[\ce{NO2}])^2} \\ &= \frac{1}{2} \cdot \frac{[\ce{N2O4}]}{[\ce{NO2}]^2} \\ &= \frac{1}{2}K \end{aligned}$
Q < K, so the equilibrium shifts right, toward fewer moles of gas. NO₂ is used up and the color slowly lightens.
In the end. The shift only partly counteracts the change. At the new equilibrium [NO₂] is still higher than before, so the gas is darker than at the start.
With numbers. Starting at 25 °C from [NO₂] = 0.0143 M (the table in 2.11.4), compression raises it to 0.0287 M, and the new equilibrium has about 0.0209 M: less than right after compression, but more than at the start.
A common mistake. Thinking “the equilibrium shifts right, so the gas ends up lighter than at the start.” The shift only takes back part of the jump in [NO₂].

Example 2: conditions for making ammonia

N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH° = −92.2 kJ/mol. How could you increase the yield of NH₃ at equilibrium? Why do real plants run at 400–500 °C with a catalyst?

Step-by-step solution

What “yield” means here. The NH₃ obtained as a percent of the theoretical maximum (2.6.7). Because the reaction stops at equilibrium, the yield is well under 100% even with no losses. Shifting the equilibrium right raises it.
Pressure. The forward reaction reduces the moles of gas (4 → 2), so high pressure shifts the equilibrium right.
Temperature. The forward reaction is exothermic, so a lower temperature favors NH₃. But at low temperatures the reaction is far too slow.
Concentration. Removing NH₃ by liquefying it keeps the equilibrium shifting right, and the unreacted N₂ and H₂ are recycled.
The compromise. 400–500 °C balances a reasonable rate against a reasonable yield, and it is the range where the iron catalyst works best.
The catalyst. A catalyst speeds up the forward and reverse reactions equally, so it doesn’t shift the equilibrium or raise the equilibrium yield, but it lets the system reach equilibrium much sooner.
A common mistake. Thinking “hotter is always better” or “a catalyst increases the yield.” Heating speeds the reaction up, but for this exothermic reaction it shifts the equilibrium left.

Practice: which way does the equilibrium shift? (For N₂ + 3H₂ ⇌ 2NH₃, ΔH < 0.)

Ammonia: add N₂
Ammonia: remove NH₃ as it forms
Ammonia: raise the temperature
Ammonia: compress the container
Ammonia: add a catalyst
Ammonia: add helium at constant volume
H₂(g) + I₂(g) ⇌ 2HI(g): compress the container
Fe³⁺ + SCN⁻ ⇌ FeSCN²⁺: add a little solid KSCN
2NO₂ ⇌ N₂O₄ (ΔH < 0): put the flask in hot water

Common mistakes

Mistake 1: “The shift completely undoes the change.” It only partly counteracts it. After NO₂ is compressed, the color darkens, then lightens, but ends up darker than at the start.

Mistake 2: “A catalyst shifts the equilibrium toward products.” A catalyst speeds up both directions equally. The equilibrium doesn’t shift and the yield doesn’t change; equilibrium is simply reached sooner.

Mistake 3: “Heating speeds up the forward reaction and slows the reverse reaction.” Heating speeds up both. The endothermic direction speeds up more, so the equilibrium shifts that way.

Quick check

2SO₂(g) + O₂(g) ⇌ 2SO₃(g), ΔH < 0. Which change increases the amount of SO₃ at equilibrium?

The red equilibrium Fe³⁺ + SCN⁻ ⇌ FeSCN²⁺ has some Fe³⁺ removed (for example by adding iron powder, which reduces it to Fe²⁺). The color will:

Summary

Le Châtelier’s principle: when a change is made to a system at equilibrium, it shifts to partly counteract the change, never to cancel it completely.
Concentration and volume changes change Q: Q < K shifts right and Q > K shifts left. If both sides have equal moles of gas, volume changes don’t matter. Temperature changes K: heating shifts the equilibrium in the endothermic direction.
Catalysts and inert gases added at constant volume cause no shift.

On to AP (for later)

AP topic 7.9 asks you to predict shifts with Le Châtelier’s principle, and topic 7.10 asks you to justify them with Q and K: concentration and volume changes move Q away from K, while temperature changes K itself. Full-credit answers say whether Q or K changed, which is larger, and which way the equilibrium shifts.

Data sources: ΔH values in this lesson are calculated from this site’s table of enthalpies of formation (lesson 2.10.6).

Le Châtelier's Principle勒夏特列原理

Learning goals

Before you start

Why make ammonia at high pressure?