Chemical Equilibrium: Definition, the Constant K and the Reaction Quotient Q

What is chemical equilibrium? A definition

A reaction is at equilibrium when nothing pushes the amounts of reactants and products to shift any further. According to Chem1, the general chemistry textbook by Stephen Lower, the system looks still to the naked eye, while at the molecular level the forward and reverse reactions are both under way at the same rate, so no net change remains. Chemguide, Jim Clark’s site, names the starting point: a reversible reaction in a closed system, where matter neither comes in nor goes out. Given time, the two reactions end up running at equal rates, and every substance in the mixture holds a constant amount while both reactions carry on. What sets the speed of each of the two is covered in the Recap on reaction rate.

Practical example: for H₂ + I₂ ⇌ 2HI, Chem1’s composition curves show that the equilibrium mixture is the same whether you start from the reactants or from HI.

Reversible reactions and irreversible reactions

In a reversible reaction the direction depends on the conditions: it can run from reactants to products or back again. Once it reaches equilibrium, the vessel still contains an appreciable amount of each, reactants and products alike.

The opposite case exists too. Chem1 observes that when K is very large, the reaction can be regarded as one-way, complete or irreversible.

The chemical equilibrium constant K: Kc and Kp

K is simply the value of the reaction quotient Q once the system has reached equilibrium. It can be written with concentrations (Kc) or with pressures (Kp), and the two numbers generally differ. A value of K always comes with its temperature: In an exercise Chem1 gives Kp = 0.14 at 900 K for the oxidation of sulfur dioxide (2SO₂ + O₂ ⇌ 2SO₃).

According to Chemguide, at a given temperature Kc always has the same value.

Factor	Effect on Kc
Temperature	changes the value
Pressure	no effect
Catalyst	no effect

Writing the reaction backwards inverts the K expression (Chem1), as the esterification example from Chemguide shows.

Practical example: in Chemguide’s esterification example (an organic acid and an alcohol forming ester and water) Kc is about 4 at room temperature. For the reverse hydrolysis it is about 1/4, that is 0.25.

Homogeneous and heterogeneous equilibria

A homogeneous equilibrium involves a single phase, a heterogeneous one involves substances in more than one phase.

	Homogeneous	Heterogeneous
Phases	just one	more than one

In K expressions pure solids are left out, because concentration only makes sense within a phase (Chem1). For a hydrate losing water, in a solid-vapor equilibrium, K equals the partial pressure of the water vapor.

The reaction quotient Q: which way the reaction goes

Q is calculated from the amounts present at a given moment, and comparing it with K shows the direction of the net reaction. If Q equals K the system is at equilibrium and the composition no longer changes in a net way. How an equilibrium shifts when concentration, pressure or temperature change is the subject of Le Chatelier’s principle.

Comparison	Situation	Net reaction
Q = K	equilibrium	no change
Q > K	too many products	to the left, toward reactants
Q < K	too few products	to the right, toward products

Calculating equilibrium with an ICE table

Chem1’s calculation method starts from a table with three rows: initial, change and equilibrium, the so-called ICE table. It is used to find the composition at equilibrium from K and the starting conditions.

Practical example: for phosgene (COCl₂ ⇌ CO + Cl₂) the page starts from 0.124 atm of COCl₂, with Kp = 0.0041 at 600 K. Because K is small, the change x is small compared with the starting pressure, and the approximate solution is very close to the exact one. The final pressures are 0.104 atm of COCl₂ and 0.0206 atm each of CO and Cl₂, all at 600 K.