Chemical Equilibrium: Beyond Le Chatelier

Q against K

The reaction quotient has the same form as the equilibrium constant but uses current concentrations rather than equilibrium ones. Comparing them predicts the direction of change:

This is more reliable than qualitative reasoning because it is quantitative and never ambiguous. Where a Le Chatelier argument is unclear, computing Q settles it.

Kp and Kc

where Δn is the change in the number of moles of gas. When Δn is zero the two are numerically equal, which is worth noticing because it means pressure changes then have no effect on the position of equilibrium at all.

Only gases are counted in Δn. Pure solids and pure liquids do not appear in the expression, because their activities are one — a point that must be applied when writing any equilibrium expression involving them.

Temperature dependence

Temperature is the only factor that changes the value of K. Everything else shifts the position of equilibrium without changing the constant.

For an exothermic reaction K decreases as temperature rises; for an endothermic one it increases. The equation is the van't Hoff relation, and it has the same form as the Clausius–Clapeyron and Arrhenius equations — a similarity worth noticing, since all three come from a free energy or enthalpy divided by RT.

The inert gas trap

Adding an inert gas is the case where careless Le Chatelier reasoning fails, and it is asked precisely for that reason.

At constant volume, adding an inert gas raises the total pressure but leaves each reacting gas's partial pressure exactly as it was, so Q is unchanged and nothing happens. At constant pressure the mixture must expand, which dilutes the reacting gases and shifts equilibrium toward the side with more gas molecules.

Answering "adding a gas increases pressure so equilibrium shifts" without specifying the condition is the trap, and it is wrong half the time.

Degree of dissociation

For a dissociation equilibrium, expressing everything in terms of the degree of dissociation and the total pressure gives a relationship between K and that degree. Where the degree is small, useful approximations simplify the algebra considerably.

Checking afterwards that the approximation was justified — that the degree really is small compared with one — is part of a complete answer, and questions sometimes choose values where it is not.

Frequently asked questions

Why do solids not appear in the equilibrium expression?

Because their activity is defined as one. Adding more solid does not change the position of equilibrium, provided some is present.

Why does only temperature change K?

Because K is determined by the standard free energy change, which depends on temperature. Concentration and pressure changes move the system along its existing equilibrium relationship without altering the constant.

Does adding an inert gas always shift equilibrium?

No. At constant volume it has no effect at all. Only at constant pressure does it shift equilibrium, and then toward the side with more moles of gas.

Can a catalyst improve yield?

Not at equilibrium. It can improve practical yield by reaching equilibrium faster or by favouring one pathway over a competing one, but it cannot change where equilibrium lies.