Now here, of course #K_"eq"=([A][B])/([C][D])#, which of course is unitless because the #mol*L^-1# cancels out. But of course not all equilibria are set up like that, we could conceive of, #A+BrightleftharpoonsC#, where the units would not cancel out.
Strict application of thermodynamic principles relies on activities, #a#, not concentrations, where the activity is dimensionless by reference to a standard concentration, i.e. #a_A=[[A]]/[[A_"standard"]]#.
Thus when we use the Nernst equation #DeltaG^@=-RTln(K_"eq")#, we can properly take the logarithm of a dimensionless quantity.
So in summary, we should use dimensionless #"activities"#, however, the #A_0# values should be near as dammit to the molar concentration.
