I was never fully satisfied by the usage of dimensions like m6mol-2s-1 (or worse) for rate constants in chemical kinetics. I used to think there should be a way to express this by a dimension free coefficient and use mole fractions (xi) instead.
After many pages of paper written I have to admit that this is not possible. It is due to the fact that kinetics and thermodynamics are not fully interchangeable and the concept of molar fractions shows to be rather useless in kinetics. An obvious example is given by a container filled with two gases to react. The rate is – assuming constant temperature – determined only by the chance of two molecules colliding in a certain amount of time. This probability is not affected whatsoever by adding a third gas to the container. In terms of molecular fractions this couldn’t be expressed because increasing the overall amount of substance will decrease the molar fraction of the components. Hence, there is no way beside using concentrations even if they are not as “nice” as fractions could be
A minute ago I mailed an article  to a professor of mine in which I discussed the topic in more detail. It is written in German but I’ll still attach it to this post. However, I just got aware that I didn’t mention the case of a second order reaction between molecules of the same substance in that work. I hope that it still might be useful to some of you somehow under certain kind of circumstances.