What are the units for Ksp and why are they not always included in calculations?

[Zoey Brown]

Homework Statement

I have found, through experimentation, the ksp of calcium hydroxide to be 3.0 x10^-7 (which i know has a pretty large percent error). However, i am conflicted as to what the units should be because logically, plugging the units into the ksp equation should give you units of M^3 (ksp= [ca][oh-]^2. However, after research online, i found that ksp doesn't have units. Why does Ksp have no units if it is seemingly so easy to calulate it?

Homework Equations

The Attempt at a Solution

One idea i was thinking about was that the ksp units are unique to each equation which may be why they are omitted?

 

[mjc123]

The units for the solubility product should indeed be M³. I have not found that "Ksp doesn't have units" online. However, insofar as a solubility product is an equilibrium constant, strictly speaking equilibrium constants should be dimensionless, as ΔG^o = -RTlnK, and the argument of a logarithm must be dimensionless. This is achieved by dividing each concentration by the concentration of the standard state, i.e. 1M. So
Ksp = ([Ca²⁺]/1M)([OH^-]/1M)²
which has numerically the same value as your Ksp.
However, I like to keep the units, as it's a useful check on whether you're getting the powers right.