Chemical equilibrium

What it is

Many reactions run in both directions. In N₂O₄ ⇌ 2 NO₂, brown NO₂ gas forms from colourless N₂O₄, and NO₂ turns back into N₂O₄. Start with pure N₂O₄ in a closed container: the forward reaction slows as N₂O₄ is used up, while the reverse reaction speeds up as NO₂ builds. Eventually the two rates are equal and no concentration changes any more. That is chemical equilibrium.

Equilibrium is dynamic: molecules keep reacting in both directions, but equally many each way per second. The concentrations do not have to be equal; they are just constant.

Examples of equilibrium

• A + B ⇌ C + D with Kc = 4, starting at 1.0 mol/dm³ of A and B. If x has reacted, x²/(1 − x)² = 4, so x/(1 − x) = 2 and x = 2/3. At equilibrium [C] = [D] ≈ 0.667 and [A] = [B] ≈ 0.333 mol/dm³. Check: 0.667²/0.333² = 4.
• Acetic acid in water. CH₃COOH ⇌ CH₃COO⁻ + H⁺. With pKa = 4.756, Ka ≈ 1.8 · 10⁻⁵, and in 0.10 mol/dm³ about 1.3 % of the acid has donated a hydrogen ion. The rest remains as molecules.
• A sparingly soluble salt. AgCl(s) ⇌ Ag⁺ + Cl⁻: solid salt and dissolved ions are in equilibrium in a saturated solution, see the solubility product.

Not equilibrium

• A burning candle. The products, carbon dioxide and water vapour, leave the system, so the reaction keeps going until the candle is gone; it is effectively one-way.
• A bath with the tap running and the drain open. The level may hold still, but water flows through all the time. That is a steady flow in an open system, not an equilibrium.

Why it matters

Equilibrium says how much product you can get. Its position is described by the equilibrium constant: a K far above 1 means mostly products at equilibrium, far below 1 mostly reactants. K changes with temperature but not with a catalyst. The link to energy is in Gibbs energy and the equilibrium constant, and the general form covers reactions with coefficients.

Le Chatelier. When an equilibrium is disturbed it shifts so as to oppose the disturbance. In the example above, add A until [A] is 1.333 mol/dm³: the reaction quotient is Q = (0.667 · 0.667)/(1.333 · 0.333) = 1, smaller than K = 4, so the reaction runs to the right until a new equilibrium: [A] ≈ 1.155, [B] ≈ 0.155, [C] = [D] ≈ 0.845 mol/dm³.

The same idea carries the acid dissociation constant, the solubility product and, from the other side, the reaction rate: equilibrium is where the rates meet.

Common misconceptions

• “At equilibrium the reaction has stopped.” Both reactions are going, at the same rate.
• “At equilibrium the concentrations are equal.” No, they are constant. In the example [A] = 0.333 and [C] = 0.667.
• “A catalyst shifts the equilibrium.” It speeds up both directions equally, so equilibrium is reached sooner but ends up in the same place.
• “Equilibrium can be reached in any system.” In practice only in a closed one: an open system where substances leave or are fed in reaches at best a steady state, not equilibrium.

Common questions