Equilibrium constant of water

If $$\ce{H2O}$$ dissociates as follows: $$\ce{2H2O <=> H3O+ + OH-}$$ and not in this way: $$\ce{H2O <=> H+ + OH-}$$ why is the equilibrium constant: $$K_{eq}=\frac {\ce{[H+][OH-]}} {\ce{[H2O]}}$$ and not: $$K_{eq}=\frac {\ce{[H3O+][OH-]}} {\ce{[H2O]^2}}$$

• Pure substances are excluded from equilibrium expressions. The last two equations are equivalent. Apr 7, 2019 at 18:19
• There is a similar issue with $\ce{CO2(aq)}$ and $\ce{H2CO3(aq)}$. Think of $\ce{H3O+(aq)}$ and $\ce{H+(aq)}$ as a shorthand for $\ce{H+_\text{total}(aq)}$, all forms of hydrogen ions associated with water.
– Karsten
Apr 7, 2019 at 21:39
• I think it is quite clear what the question is asking.
– A.K.
Apr 8, 2019 at 0:17

In a strict sense, all quantities in the equilibrium constant are not molar concentrations but activities. Activity is a thermodynamic quantity which is proportional to concentration. Now by IUPAC definitions of standard states, the activity of pure liquids and solids is taken is unity (by convention and for reference purposes. Therefore in the following expressions, $$\{\ce{H2O}\}$$ or $$\{\ce{H2O}\}^2$$ are all unity, no matter what the power is (real number). Elementary textbooks tend to say a lot of wrong or oversimplified stuff.

$$K_\mathrm{eq} = \frac{\{\ce{H+}\}\{\ce{OH−}\}}{\{\ce{H2O}\}}$$

and

$$K_\mathrm{eq} = \frac{\{\ce{H3O+}\}\{\ce{OH−}\}}{\{\ce{H2O}\}^2}$$

Here the curly bracket indicate activities. The IUPAC notation is $$a$$ for activity. The species of interest is written as a subscript. A more detailed answer as to why activity is taken as unity is already provided: Why are activities of solids and liquids taken to be unity?

• Well that is assuming that $\ce{[H2O]}$ and $\ce{[H2O]^2}$ denote the activities of water and not its concentration. Usually the bracket notation is used to indicate concentrations.
– MaxW
Apr 7, 2019 at 20:29
• You are right, it should rather be a_H2O. Apr 7, 2019 at 20:34
• @M.Farooq If you like brackets, you may want to use the curly ones ({,}) for activities (see What do curly brackets {} mean?). Apr 7, 2019 at 21:18
• Interesting, I never saw curly brackets for activity. This must be rather recent. Is this common in European textbooks? Apr 7, 2019 at 21:29
• @M.Farooq Hmm, I never traced the statistics of usage of either notation for activity, I see both curly brackets and $a$ here and there occasionally — I'd say both are used fairly equally, suggesting I read mostly US/British, German and Soviet/Russian literature. Apr 7, 2019 at 23:48