The Equilibrium constant expression involves the concentrations or partial pressures of the reactants and products. The units of Equilibrium constant K will depend on the number of moles of reactants and products.
There are following two cases:
Case1. When the total number of moles of products is equal to the total number of moles of reactants, then K has no units. For example:
N2 (g) + O2 (g) ⇌ 2NO (g)
K = [NO] 2 / [N2] [O2]
If the concentrations are expressed in terms of moles per litre, then
(mol litre-1)2 / (mol litre-1) (mol litre-1)
= no units
Hence Equilibrium constant K has no units when the total number of moles of products is equal to the total number of moles of reactants
Case2. When the total number of moles of products is different than the total number of moles of reactants, then K has units. For example:
N2 (g) + 3 H2 (g) ⇌ 2 NH3
Equilibrium constant K will be given as:
K = [NH3] 2 / [N2] [H2] 3
The units of K will be
K = [(mol litre-1) 2]/[ (mol litre-1) (mol litre-1)3]
= L2 mol-2
Hence, it is concluded that equilibrium constant K has no units i.e. dimensionless if the total number of moles of products is equal to the total number of moles of reactants. On the other hand if the total number of moles of products is different than the total number of moles of reactants then K has specific units.