The thermodynamic definition of the equilibrium constant K is
where Δr Go is the reaction Gibbs energy at standard conditions (a constant for a particular reaction), R is the gas constant, T is temperature.
Since logarithms only take pure numbers, K is a dimensionless number. However, when equilibrium constants are calculated as a quotient of concentrations or partial pressures, the practice is to quote them in units of concentration or pressure according to the quotient.
For example, the units of Kc for
is mol-4dm12.