Dynamic equilibrium

A change that seems to stop

Pour some water into a flask and close it. At first the water level drops a little as water evaporates. After a while the level stops falling. The pressure of the vapour above the water stays steady.

Has evaporation stopped? No. Molecules still leave the liquid. But molecules of vapour also return to it, and now they return just as fast as they leave. The two changes cancel out.

This is equilibrium: a state in which the amounts in a closed system no longer change, because opposing processes run at the same rate.

Liquid and vapour

When the flask is first closed, there is little vapour, so condensation is slow. Evaporation wins and the vapour builds up. As it builds up, condensation speeds up. In the end:

The double arrow means both changes go on at once. The steady pressure of the vapour at a given temperature is the vapour pressure of the liquid.

Solid and liquid

Ice and water kept together at 273 K and 1 atm in a perfectly insulated flask show no change. Ice keeps melting and water keeps freezing, at equal rates. This temperature is the normal melting point of ice.

Solids and gases in liquids

Stir sugar into water at room temperature. At first it dissolves. Then some sugar stays at the bottom however long you stir. The solution is saturated. Sugar still dissolves, but sugar also comes out of solution just as fast.

A sealed bottle of soda holds carbon dioxide under pressure. There is an equilibrium between the gas in the space above and the gas dissolved in the drink. Open the bottle and the pressure above falls. Less gas can stay dissolved, so it fizzes out. The amount of gas dissolved goes up with the pressure of that gas above the liquid. This is Henry's law.

What all physical equilibria share

• They happen only in a closed system at a fixed temperature.
• Both opposing processes go on, at equal rates.
• Some measurable property stays constant, such as vapour pressure or concentration.
• The size of that property tells us how far the change went when equilibrium was reached.

Equilibrium in chemical reactions

Many reactions do not go to completion in a closed vessel. Take a reversible reaction:

At the start only A and B are present. The forward reaction is fast and the backward one cannot happen yet. As C and D build up, the backward reaction speeds up, while the forward one slows down. When the two rates become equal, the concentrations stop changing. The reaction has reached chemical equilibrium.

Start with all A, then switch to all B. Does the reaction settle at the same mixture? Now make the forward rate constant larger. Which way does the final mixture move?

The same mixture from either side

Hydrogen and iodine react to form hydrogen iodide:

Start at 700 K with 0.100 mol/L each of hydrogen and iodine. Or start with 0.200 mol/L of hydrogen iodide alone, which holds the same atoms. Both runs end with the same mixture.

So equilibrium can be reached from either direction.

Equilibrium is dynamic

How do we know the reactions do not simply stop? Chemists showed it with isotopes. They made ammonia from nitrogen and hydrogen until equilibrium was reached. They ran a second, identical mixture with deuterium, D, the heavy isotope of hydrogen, in place of hydrogen.

Then they mixed the two equilibrium mixtures. The total amounts of ammonia and of nitrogen stayed the same. Yet soon molecules such as $\text{NH}_2\text{D}$ and $\text{NHD}_2$ appeared. Atoms were still being swapped between molecules. Both reactions were still running.

Practise with new numbers

Try it in Python

The program runs a reaction A ⇌ B in small steps of time, starting once with A and once with B. It prints the mixture after 30 minutes.

Common mistakes

• Thinking the reactions stop at equilibrium. Both keep going, at equal rates.
• Thinking the amounts are equal at equilibrium. The rates are equal. The amounts can be very different.
• Forgetting the closed system. In an open dish the vapour escapes, and the water simply dries up.
• Thinking equilibrium can be reached only from the reactant side. It can be reached from either side.

Remember these

• Equilibrium needs a closed system at a fixed temperature.
• At equilibrium the forward and backward rates are equal, so the concentrations stay constant.
• Equilibrium is dynamic: both processes go on, as isotopes show.
• The same equilibrium mixture can be reached from the reactants or from the products.

Check yourself

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

1. A bottle of perfume is sealed and left in a cupboard at constant temperature. What is equal once the vapour above the liquid stops building up?

2. A beaker of salt water has some undissolved salt at the bottom that never gets smaller. Has dissolving stopped?

3. Why does a bottle of soda fizz when you open it?

4. At equilibrium, must the concentrations of reactants and products be equal?