Chemical equilibrium
Chemical equilibrium is not a reaction that has stopped. It is a state in which forward and reverse processes continue at equal rates, so the macroscopic composition remains constant. The quantitative tools are the equilibrium constant K and the reaction quotient Q.
Writing an equilibrium constant
For aA + bB ⇌ cC + dD, an activity-based equilibrium constant is:
K = a(C)ca(D)d / [a(A)aa(B)b]
Pure solids and pure liquids have activity close to 1 and do not appear explicitly. Introductory concentration expressions use molar concentrations as approximations for activities in sufficiently dilute solutions.
K depends on temperature. A catalyst changes the rate of approach to equilibrium, not K.
Q predicts the direction of change
Q has the same algebraic form as K but uses the current composition. If Q < K, the reaction proceeds forward overall. If Q > K, the reverse reaction is favored. When Q = K, the composition is at equilibrium.
This is more precise than saying the system “tries to oppose change.” A disturbance changes Q; the reaction then moves until Q again equals K.
Q versus K explorer
Le Châtelier with a molecular explanation
Adding reactant or removing product usually makes Q smaller, so the forward reaction occurs until equilibrium is restored. Compressing a gas mixture changes partial pressures; the shift depends on the stoichiometric powers in Q, often favoring the side with fewer gas molecules.
Temperature is different: changing T changes K itself because reaction enthalpy changes the relative thermodynamic stability of reactants and products. A catalyst changes neither Q nor K; it accelerates both directions.
ICE tables and extent of reaction
When an equilibrium composition must be calculated, an ICE table records Initial, Change and Equilibrium amounts. The changes must follow reaction stoichiometry. For A ⇌ B, if x mol L⁻¹ of A reacts, A falls by x and B rises by x.
The physically meaningful root must keep all concentrations nonnegative. Approximations such as “x is small” should be checked afterward, not assumed blindly.
K magnitude and what it does not mean
K ≫ 1 means products dominate at equilibrium under the chosen standard-state convention; K ≪ 1 means reactants dominate. It does not tell us how quickly equilibrium is reached.
Equilibrium constants also change when a reaction equation is reversed or multiplied: reversing gives 1/K; multiplying all coefficients by n raises K to the power n.
Equilibrium calculations with physical meaning
Activities explain why K is dimensionless
Rigorous equilibrium constants are written with activities referenced to standard states, so K itself is dimensionless. Concentrations and partial pressures used in introductory formulas are convenient approximations to those activities.
At high ionic strength or high gas pressure, those approximations can fail. Activity coefficients or fugacities are then introduced so the same thermodynamic structure remains valid.
A Haber-process example
For N₂ + 3H₂ ⇌ 2NH₃, compressing the mixture favors ammonia because Q contains four powers of gas pressure in the denominator but only two in the numerator. Lowering volume initially makes Q smaller relative to K, so net forward reaction follows.
Lower temperature favors ammonia thermodynamically because ammonia formation is exothermic, but very low temperature slows the kinetics. Industrial conditions are therefore a compromise among equilibrium, rate, separation and catalyst performance.
Equilibrium is compatible with microscopic motion
Isotopic-label experiments can reveal exchange even when macroscopic concentrations are constant. Molecules continue reacting in both directions; equilibrium means equal statistical fluxes, not molecular stillness.
This distinction matters when interpreting a flat concentration graph. A horizontal line shows no net composition change, not the disappearance of collisions or reaction events.
Worked example: Q before any algebra
For H₂(g) + I₂(g) ⇌ 2HI(g), suppose K = 50 and the current partial pressures give Q = (PHI²)/(PH₂PI₂) = 8. The mixture is not at equilibrium because 8 ≠ 50.
Since Q < K, net forward reaction increases HI and consumes H₂ and I₂ until the quotient rises to 50. This conclusion needs no ICE table; the table is only needed if the final composition is requested.
Exercises
Direction
If Q = 0.05 and K = 20, which net direction occurs?
Solution
Forward, because Q < K.
Catalyst
Does adding a catalyst change K?
Solution
No. It speeds both forward and reverse pathways and shortens the time to reach equilibrium.
Reverse reaction
If K = 50 for A ⇌ B, what is K for B ⇌ A?
Solution
1/50 = 0.020.