Le Chatelier's principle

The principle

What happens if we disturb a mixture at equilibrium? The French chemist Le Chatelier gave a simple rule in 1884:

If a change is made to a system at equilibrium, the system shifts in the direction that undoes part of the change.

The reaction quotient shows why. A change makes $Q_c$ differ from $K_c$. The mixture then moves until $Q_c = K_c$ again.

Changing a concentration

Add more of a reactant. $Q_c$ falls below $K_c$, so the reaction goes forward, using up some of what was added. Removing a product has the same effect.

Take $\text{A} \rightleftharpoons \text{B}$ with $K_c = 4.0$, at equilibrium with $[\text{A}] = 0.20$ mol/L and $[\text{B}] = 0.80$ mol/L. Add 0.50 mol/L of A.

• Just after: $Q_c = \dfrac{0.80}{0.70} = 1.14$, less than 4.0.
• So the reaction goes forward. Let $x$ mol/L of A change to B: $\dfrac{0.80 + x}{0.70 - x} = 4.0$.
• This gives $x = 0.40$. The new mixture has $[\text{A}] = 0.30$ mol/L and $[\text{B}] = 1.20$ mol/L.

The ratio is back to 4.0, but both amounts are larger than before.

Add a little A, then a lot. Is the new ratio of [B] to [A] ever different from 3.00?

A colourful example is iron(III) ions with thiocyanate ions:

The product is blood red. Add more thiocyanate and the red deepens. Add oxalic acid, which takes $\text{Fe}^{3+}$ out of the solution, and the red fades.

Changing the pressure

Squeezing a gas mixture into a smaller volume raises every partial pressure. The system shifts to the side with fewer moles of gas, which lowers the pressure.

In $\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3$, four moles of gas become two. A higher pressure therefore favours ammonia. If both sides have the same number of moles of gas, as for hydrogen iodide, pressure has no effect.

Adding an inert gas

Add argon to a mixture at constant volume. The partial pressures and concentrations of the reacting gases do not change, so the equilibrium does not shift. (At constant pressure the volume grows, which is like lowering the pressure.)

Changing the temperature

Temperature is different: it changes the value of K itself.

• For an exothermic reaction, K falls as the temperature rises. Heating shifts it backward.
• For an endothermic reaction, K rises as the temperature rises. Heating shifts it forward.

Dinitrogen tetroxide splits into brown nitrogen dioxide, and the change is endothermic:

In hot water the gas turns deep brown. In ice water it turns almost colourless.

A catalyst

A catalyst speeds up the forward and backward reactions equally. The mixture reaches equilibrium sooner, but K and the equilibrium mixture do not change.

The Haber process

Ammonia is made from nitrogen and hydrogen:

• High pressure, about 200 atm, favours the side with fewer moles of gas.
• The reaction is exothermic, so a low temperature would give more ammonia. But it would be far too slow. A temperature of about 700 K is a compromise.
• An iron catalyst makes equilibrium come quickly.
• Ammonia is cooled out of the mixture as it forms. Removing a product pulls the reaction forward.

Practise with new numbers

Try it in Python

The program adds A to the equilibrium mixture of the example above. It finds $Q_c$, says which way the reaction goes, and finds the new mixture.

Common mistakes

• Thinking a shift changes K. Only temperature changes K. Other changes move the mixture until $Q_c = K_c$ again.
• Saying a catalyst gives more product. It only gives the same mixture sooner.
• Applying pressure to solids and liquids. Count only the moles of gas.
• Thinking an inert gas at constant volume shifts the equilibrium. The partial pressures of the reacting gases do not change.

Remember these

• A disturbed equilibrium shifts to undo part of the change.
• Add a reactant or remove a product: forward.
• Higher pressure: towards fewer moles of gas.
• Heating: towards the endothermic direction, and K changes.
• A catalyst: equilibrium sooner, no shift.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. In $\text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2$, which way does the equilibrium shift if the volume is halved?

2. Does adding an iron catalyst change the amount of ammonia at equilibrium?

3. The ammonia equilibrium is exothermic. What happens to K when the temperature rises?

4. Argon is added to the hydrogen iodide equilibrium at constant volume. What happens?