Every reaction, whether we like it or not, will never progress to true completion. At best, we can have 99.99% of reactants converted into products before the reaction reaches an equilibrium. However, since this is awfully close to true completion, we assume the reaction goes to completion, since it effectively almost finishes.

The composition of a reaction mixture when it comes to chemical (dynamic) equilibrium is described by an equilibrium constant K. There are two types:

• K_c is the equilibrium constant in terms of concentrations. It is usually used for reactions in solution form, and sometimes for the gaseous form.
• K_p is the equilibrium constant in terms of pressures. It is usually used for reactions in gaseous form.

These constants are, well, constant when the thermodynamic temperature is constant. It will only vary if the temperature varies. Changes in the concentration of reactants/products, or the addition of a catalyst, will not affect this value. K_c is defined by the equation

K_c = ∏[products_eqm]^v_p / ∏[reactants_eqm]^v_r

where

• ∏ is the symbol for multiplication (analogous to Σ),
• [species_eqm] represents the concentration of that particular species at equilibrium, and
• v_p and v_r represent the stoichiometric coefficients of the species in the reaction equation.

Let’s illustrate this with an example. Say we have the reversible equation

aA + b(B) ⇌ cC + dD

where A, B, C, D are chemical species in aqueous medium and a, b, c, d are stochiometric coefficients (this just means the coefficients of the chemical equation). The equilibrium constant would be

K_c = ([C]^c[D]^d) / ([A]^a[B]^b)

which is exactly the form you learned in JC.

Similarly, we can define the equilibrium constant for pressure:

K_p = ∏(P_productseqm)^v_p / ∏(P_reactantseqm)^v_r

where P_specieseqm is the partial pressure of the species at equilibrium. Again, this is just JC stuff written differently.

Extent of Reaction

This notion of concentration and pressure at equilibrium can be summarised in one word – activity. The activity of any pure solid or liquid is defined to be 1. By consideration of the activities of each species, K can give us an indication of the extent of a reaction, i.e. how far a reaction proceeds until it reaches equilibrium. This is directly determined from the equations for K. Generally,

• if K is large, then the equilibrium lies to the right, favouring the product formation.
• Conversely if K is small, then the equilibrium lies to the left, favouring the reactant formation.

Reaction Quotient

Why stop at K, when we can calculate a value for every point in the reaction? This is known as the Reaction Quotient Q, and is given by the following equations:

Q_c = ∏[products]^v_p / ∏[reactants]^v_r

Q_p = ∏(P_products)^v_p / ∏(P_reactants)^v_r

and here we don’t need the concentrations or pressures to be at equilibrium.