I’m wondering why a value choose $K_ exteq = frac
I goofed up the first time I tried to answer this question, erroneously using dimensional analysis to your equilibrium expression.
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It turns out that Silberberg<1> offers an excellent explanation of why $K_ exteq$ is dimensionmuch less, which is often glossed over as the terms of the equilibrium expression are mainly taught as concentrations. In actual reality, the terms are ratios of the concentration or activity of each species with a reference concentration (1 $mathrmmolcdotL^-1$ for options.) For example, a concentration of 2 $mathrmmolcdotL^-1$ divided by a reference of 1 $mathrmmolcdotL^-1$ returns a ratio of 2, via no devices. As each term has no devices, so as well does $K_ exteq$.
<1> Silberberg, M.E.; lutz-heilmann.info – The Molecular Nature of Matter and Change 3e; 2003, p. 719
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edited Apr 20 "15 at 12:57
answered Sep 11 "12 at 6:24
Rictough TerrettRicdifficult Terrett
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This source describes it well. It looks choose component of class material, but it plainly explains the dimensionlessness of $K_eq$.
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The resolution of this obvious paradox is that the above equation, while perfectly satismanufacturing facility for everyday usage, is not technically correct. An even more correct version is:
$$K_eq = fracfraclvert B vert_eqlvert B vert_ss fraclvert C vert_eqlvert C vert_ssfraclvert A vert_eqlvert A vert_ss$$
wright here the "ss" subscripts refer to the concentration of that species in the conventional state. (By this meaning, Keq is constantly unitless.)
It then goes on to state:
Strictly speaking, department by the typical state concentrations is also necessary in every thermodynamics equation in which you take the log of a concentration product, otherwise the units don’t come out right.) We will NEVER use this "correct" variation of the equation in this class (well, never before other than in one difficulty on this week’s difficulty collection...), and also $K_eq$ for a reactivity via unequal numbers of reactants and also products is ALWAYS provided through units,also in publiburned records.