# Why does pKw first decrease but eventually increase when temperature rises?

I understand the initial decrease in pKw.

$\ce{Heat + H2O (l) <=> H+ (aq) + OH- (aq)}$

Temperature increases, reaction shifts to the right, so $\ce{H+} \text{ and } \ce{OH}$ concentration increases.

Higher $\ce{H+} \text{ and } \ce{OH}$ concentration results in lower $\ce{pK_w}$, as $\ce{pK_w = - log ([H+][OH-])}$

But why then does the $\ce{pK_w}$ start to increase beyond $250$ degrees C?

• I'm afraid your logic behind the decrease isn't exactly OK, or maybe it's just lacking details. – Mithoron Nov 19 '17 at 1:25
• I think there is a lot you're missing. 25 mPa is about 24.7 atmospheres. At that pressure water boils at 224 C. There is a semi-empirical formula. See maplesoft.com/applications/view.aspx?SID=154073&view=html – MaxW Nov 19 '17 at 6:46
• The closer you come to the boiling point, the less energy the ions gain from hydratisation. – Karl Nov 19 '17 at 10:34