It depends upon the k. Ksp, Ka, Kb, Keq, Kc, Kp and the like have no units because activities are supposed to be used for the species and activities have no units. Some authors use units and some argue these Ks have units but they do not. The units used (and they vary) are called something like "temporary" units. k for rate constants, half lives, and that kind of thing do have units.
The word I was trying to think of when I wrote "temporary" was conditional. Many authors write conditional units; I suppose that's because they don't like to see numbers with no units. Technically, however, activities don't have units so neither do Kc, Kp, Keq, Ksp, etc.
No, a "k" constant generally does not have a unit. The letter "k" is commonly used to represent a proportionality constant in mathematical equations, such as the rate constant in chemical kinetics or the spring constant in Hooke's Law. These constants are dimensionless, meaning they do not have associated units. However, it is important to note that there are other variables and quantities in the equation that might have units, but "k" itself does not.
