K_"eq" is the so-called thermodynamic equilibrium constant....and thus for the reaction....
A+Brightleftharpoons C+D
K_"eq"=([C][D])/([A][B])....K_"eq" is properly dimensionless....
I grant that not all equilibria are set up like this, and conceivably we COULD have....
A+BrightleftharpoonsC
...the which, ostensibly, could have units. In these scenarios we use DIMENSIONLESS activities to report the concentration of [A], [B], and [C].
And why do we make all these specifications? Well, because of the "Gibbs Free Energy equation....", the which specifies that....
lnK_"eq"=-(DeltaG^@)/(RT)....and establishes the relationship of the thermodynamic equilibrium constant to the free energy, and of course we may only take "logs" of a dimensionless number....
