Temperature, pressure and composition changes

A response reduces the new mismatch

Changing composition at fixed temperature can change Q while leaving K° fixed under the same convention. The system’s subsequent net reaction tends to reduce that mismatch until the relevant equilibrium relation and constraints are met again. It does not necessarily restore every old concentration.

Le Châtelier’s principle summarizes many such responses qualitatively. A quotient calculation makes the assumptions visible and avoids treating the word oppose as a promise of complete cancellation. Retain the initial state and what was added, removed or mechanically changed.

Compression scales reacting partial pressures

Consider the written reaction 2 NO₂(g) ⇌ N₂O₄(g), initially at equilibrium in an ideal gas mixture at fixed temperature. If volume is halved before chemical readjustment, each reacting partial pressure doubles. Using a_i = p_i/p°, Q′ = (2a_N₂O₄)/(2a_NO₂)² = K°/2.

Thus net N₂O₄ formation is favoured. More generally, multiplying every reacting partial pressure by f makes Q′/Q = f^Δn_gas under this ideal fixed-temperature model, where Δn_gas is the gaseous product coefficient total minus the reactant total. Here Δn_gas = −1. Equal gas totals give no quotient change from this uniform scaling alone.

The mechanical constraint changes the answer

Adding an inert gas at fixed temperature and volume raises total pressure but leaves each reacting p_i = n_iRT/V unchanged in the ideal model. Hence the reacting quotient stays at K° and this addition alone causes no equilibrium shift.

If instead temperature and total pressure are held fixed, adding inert gas can expand the volume. In the particular model where volume doubles, reacting partial pressures halve, so Q′ = 2K° for 2 NO₂ ⇌ N₂O₄. Net dissociation is favoured. These are different constraints, not contradictory answers about one identical operation.

Temperature and catalysts play different roles

Changing temperature generally changes K°. For a reaction with positive reaction enthalpy over the relevant interval, warming tends to favour its endothermic direction; an exothermic forward direction has the opposite tendency. Retain phases and conditions, and do not insert a dimensional heat quantity into an activity product.

A catalyst changes kinetics and can speed approach to equilibrium without changing K° for the same reaction under the same thermodynamic conditions. Equilibrium yield, operating speed and any externally maintained flow are separate features of a process. A response prediction does not alone establish an optimized industrial operating point.

Worked examples

Try it yourself

1. Which direction is initially favoured in the stated halved-volume NO₂ model?

   Show the answer and reasoning

   Formation of N₂O₄.

   Uniform pressure doubling makes Q′ = K°/2.

2. At fixed ideal-gas T and V, does adding an inert gas change the reacting partial pressures?

   Show the answer and reasoning

   No.

   Their amounts, temperature and volume remain unchanged even though total pressure rises.

3. Can temperature change K° itself?

   Show the answer and reasoning

   Yes.

   The equilibrium thermodynamic relation depends on temperature.

4. Does a catalyst restore the old equilibrium composition after arbitrary conditions have changed?

   Show the answer and reasoning

   No.

   It changes approach kinetics, while the equilibrium relation is determined by the new thermodynamic conditions.

What to carry forward

• State which variables are fixed before predicting a response.
• Use reacting partial pressures in ideal-gas activity quotients.
• Keep immediate perturbation quotients distinct from final compositions.
• Temperature affects K°; a catalyst affects approach kinetics.