Le Chatelier's principle

Remarks

In this qualitative form the principle is a rule of thumb; its precise content is the set of thermodynamic stability conditions. For example, positive heat capacity means that heat added to a system raises its temperature, which then reduces the further flow of heat into it. Positive compressibility means that a rise of external pressure reduces the volume, which raises the internal pressure.

For a chemical equilibrium of ideal gases it gives two standard predictions. At fixed temperature, raising the pressure shifts the equilibrium toward the side with fewer moles of gas; for $\mathrm{N_2} + 3\,\mathrm{H_2} \rightleftharpoons 2\,\mathrm{NH_3}$ the yield of ammonia increases. At fixed pressure, raising the temperature shifts the equilibrium toward the endothermic direction, because $d \ln K / dT = \Delta H^\circ / (R T^2)$ for the equilibrium constant $K$, the standard reaction enthalpy $\Delta H^\circ$ and the gas constant $R$.

The stability hypothesis is necessary: near an unstable state a small change can trigger a large change in the same direction. The naive reading can fail when the disturbance is not a single conjugate variable. For ammonia synthesis at fixed temperature and pressure, adding nitrogen shifts the equilibrium toward decomposition of ammonia when the mole fraction of nitrogen exceeds $1/2$.

Going deeper

For a student

The principle was formulated in chemistry, and in general it is too vague to be a theorem. Its sharp versions follow from the convexity of the internal energy, which gives $C_V > 0$ and $\kappa_T > 0$. For reactions, the van 't Hoff equation gives the temperature dependence of an equilibrium constant. A refined version, often called the Le Chatelier–Braun principle, compares responses. The response of a variable is largest when the other variables are free to adjust, and smaller when they are held fixed. Examples are $C_p \ge C_V$ and $\kappa_T \ge \kappa_S$.