# Why do we take active mass of water 1 but while calculating pKa of water as 55.345? [duplicate]

First, I should mention that the question was already asked here:Why is active mass of a pure solid or liquid always taken as unity? But while calculating $$\mathrm{p}K_\mathrm{a}$$ of pure water we take active mass of pure at $$\pu{25 ^{\circ}C}$$ as 55.345 and therefore get the $$\mathrm{p}K_\mathrm{a} = 15.74$$.

$$K_\mathrm{a}=\frac{[\ce{OH−}][\ce{H+}]}{[\ce{H2O}]}=\frac{\pu{e−14}}{55.345}=\pu{1.807E−16}=10^{−15.74}$$

Shouldn't we take active mass of water as one the do the calculation as

$$\mathrm{p}K_\mathrm{a}=−\log{([\ce{H+}][\ce{OH−}])}$$

For $$\pu{25 ^{\circ}C}$$, $$[\ce{H+}][\ce{OH−}]=\pu{e−14}=𝐾_\mathrm{w}$$

Thus follows $$\mathrm{p}K_\mathrm{a}=14$$

Why do we use different active masses in the two situation?Any help would be appreciated.

A similar answer is given but why we take active mass of water as 55.345 is not discussed - What is the real pKa of water?

• but we consider active mass of pure liquids as 1 so here why don't we consider [H2O] = 1? Commented Nov 16, 2022 at 6:26
• Convenient reference for text/formula formatting: Notation basics / Formatting of math/chem expressions / upright vs italic // For more: Math SE MathJax tutorial. // Not to be applied in CH SE titles. Commented Nov 16, 2022 at 8:58
• Check also results of Google: site:chemistry.stackexchange.com pKa water Commented Nov 16, 2022 at 9:15
• What makes you think that pure water has one molecules of water per liter? Commented Nov 16, 2022 at 11:47
• 55 isn't any "active mass", just how many moles of water are in a liter. Commented Nov 17, 2022 at 22:04

• If the standard chemical potential is considered for the pure liquid then the activity of the pure liquid is 1. $\mu = \mu_0 +RT\ln{\frac{a}{a_0}}$ Commented Nov 17, 2022 at 7:51