A question about the equilibrium constant
Doing a research for a work to my classroom, going by the kinectics definition of K, which I'll explain shortly justo to get my point.
Considering an reaction: aA + bB ⇌ cC + dD
we have that the rate of equation (in portuguese we call it reaction velocity) for the forwards and backwards direction is:
vf = kf [A]a [B]b and v^(b)=k^(b)[C]^(c)[D]^(d)
We can use this to build the equilibrium constant, K=CD/AB, which does not have any units.
Now here is my question, K doesnt have any units because we consider the activity of the species (and because by the gibbs energy the argument is inside a logarithm so it needs to be dimensioneless). But if we need to consider activitys in K, so it must be that the concentration in the rate equations must be activity instead, which bugs me out because if that's is true, for the units of the velocity to be mols/L.s the entire rate constant should be mols/L.s, which dont seems right to me. If someone could clarify this to me I would be really happy, thanks!!