# Molar concentration of water and pKa value

By defintion, $\mathrm pK_\mathrm a$ value is defined as $$\mathrm pK_\mathrm a = -\lg ([\ce{H2O}] K_\mathrm{eq})$$

Consider the reaction: $$\ce{HCl + H2O <=> H3O+ + Cl-}$$

The Eq constant of $\ce{HCl}$ is defined as

$$K_\mathrm{eq} = \frac{[\ce{H3O+}][\ce{Cl-}]}{[\ce{H2O}][\ce{HCl}]}$$

Why is molar concentration of water fixed at 55.5? Wouldn't it depend on the extent of ionization?

• What does HCl have to do with the pKa of water? – jerepierre Mar 23 '16 at 17:08
• @jerepierre edited to be more specific. – doodle1234 Mar 23 '16 at 18:49

For most practical purposes, we assume that the aqueous solution is dilute and that the concentration of water is constant, that is, $[\ce{H2O}] \approx 55~\mathrm{M}$. This is the standard that is used to define the ionization constant of water, $K_\mathrm{w}$.
If the equation $1\times 10^{-14}~\mathrm{M^2} = [\ce{H3O+}][\ce{OH-}]$ didn't hold (at $25~\mathrm{^\circ C}$) then we would have to come up with other equations for acid-base equilibrium. Even for strong acid/base dissociations we approximate the equilibrium equation with full dissociation (i.e. one forward arrow).
• Please use \ce{} for chemical formulae. (See edit) – orthocresol Mar 23 '16 at 18:41