Note, that you will get different units for different reactions, depending on the set of coefficients used. Try
and you will see what I mean.
That's when you try to express K using pressures or concentrations, but - what is often omitted in an approximate treatment used when teaching beginners - K is expressed using activities. As a first approximation activity is equal to the concentration (or pressure), but it can differ. We express it with
aA = γA[A]
where aA is activity of A, γA is its activity coefficient (with units chosen so that the activity becomes unitles) and [A] is the A concentration (but it could be pA, partial pressure of A, as well). For diluted solutions γ equals 1, but the higher the concentration, the more it can differ.
Also note that having units on K is a sure way of getting into problems. In thermodynamics we often need to calculate log of K (as in ΔG=RTln(K)) , good luck doing that when K is not unitles.
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