Hydrolysis of salts of weak acid-weak base

[Rishavutkarsh]

I just came across the hydrolysis of the salts and the formula
pH=7+1/2(pKa-pKb)
What's bugging me about this is how can this be independent of Concentration?
I mean if we dilute it why won't it affect the pH? That means that even a negligible amount of such a salt can affect the pH of a bucket of water? Also there is no assumption involved so please explain how exactly is this plausible, thanks.

 

[Borek]

It is only approximate, and works reasonable well as well as the salt concentration is reasonably high.

See the derivation and discussion on these pages:

http://www.chembuddy.com/?left=pH-calculation&right=pH-salt-simplified

http://www.chembuddy.com/?left=pH-calculation&right=pH-amphiprotic-salt

(the latter is about slightly different case, but the conclusions about concentrations are very similar).