Editing Acid dissociation constant (section)

===Dimensionality===
In the equation
:<math>K_\mathrm{a} = \mathrm{\frac{[A^-] [H^+]}{[HA]}},</math>

''K''<sub>a</sub> appears to have [[dimensional analysis|dimensions]] of concentration. However, since <math>\Delta G = -RT\ln K</math>, the equilibrium constant, {{tmath|K}}, ''cannot'' have a physical dimension. This apparent paradox can be resolved in various ways. 
# Assume that the quotient of activity coefficients has a numerical value of 1, so that {{tmath|K}} has the same numerical value as the thermodynamic equilibrium constant <math>K^\ominus</math>.
# Express each concentration value as the ratio c/c<sup>0</sup>, where c<sup>0</sup> is the concentration in a [hypothetical] standard state, with a numerical value of 1, by definition.<ref>{{cite book |last1 = Petrucci |first1 = Ralph H. |last2 = Harwood |first2 = William S. |last3 = Herring |first3 = F. Geoffrey |date=2002 |title = General chemistry: principles and modern applications |url = https://archive.org/details/generalchemistry00hill |url-access = registration |edition=8th |page=[https://archive.org/details/generalchemistry00hill/page/633 633] |quote=Are you wondering... How using activities makes the equilibrium constant dimensionless? |publisher=Prentice Hall |isbn = 0-13-014329-4}}</ref> 
# Express the concentrations on the [[mole fraction]] scale. Since mole fraction has no dimension, the quotient of concentrations will, by definition, be a pure number.

The procedures, (1) and (2), give identical numerical values for an equilibrium constant. Furthermore, since a concentration {{tmath|c_i}} is simply proportional to mole fraction {{tmath|x_i}} and density {{tmath|\rho}}:
:<math>c_i = \frac{x_i\rho}{M} </math>
and since the molar mass {{tmath|M}} is a constant in dilute solutions, an equilibrium constant value determined using (3) will be simply proportional to the values obtained with (1) and (2).

It is common practice in [[biochemistry]] to quote a value with a dimension as, for example, "''K''<sub>a</sub> = 30&nbsp;mM" in order to indicate the scale, millimolar (mM) or micromolar (μM) of the [[concentration]] values used for its calculation.