What are the units of equilibrium constants kc, kp kn and kx?

Now the equilibrium constant for the reaction...

#A+BrightleftharpoonsC+D# is given by....

#K_"eq"=([C][D])/([A][B])#....and CLEARLY this is dimensionless. Agreed?

However, not all equilibria are so constructed...we could have the reaction....

#A+BrightleftharpoonsC#...where #K_"eq"=([C])/([A][B])#...the which ostensibly has units #L*mol^-1#...and for this reaction we would assume standard state activities...where the concentration is referenced to a standard state under standard conditions...

i.e. #a_A=([A])/([A_0])#...and we speak of the #"activity of A"#...A DIMENSIONLESS QUANTITY...and certainly we can take logs of a unitless number.

Why the insistence on dimensionless activities, and equilibrium constants? Well, remember the old Gibbs' equation...and its relationship to the thermodynamic equilibrium constant...

#-DeltaG_"rxn"^@=DeltaH^@-TDeltaS^@=-RTlnK_"eq"#

Now we can take the logarithm of a dimensionless number, we CANNOT take the log of a number with dimensions....

And under certain circumstances we could conceivably measure #K_"eq"# at a range of temperatures...and plot the log of #K_"eq"# against inverse temperature....and use the slope and x-intercept of the line to extract the thermodynamic parameters of the reaction...i.e. #DeltaH^@#, and #DeltaS^@#....

As regards to the rate constants...these are usually in terms of inverse time, i.e. #s^-1#...

Anyway if there is a more specific issue, or something you want clarified, fire away, and someone will try to address your question.... It would help if you told us at which level you study. The spray here is probably 2nd year physical chemistry....