A more rigorous theory of $pH$

Mixture of a weak acid with a weak base with neighbouring $pK_a$ values

Exercise 10

    

$100\; mL$ of $0.1\; M$ formic acid was mixed with $100 \;mL$ of $0.5\;M$ sodium acetate a) Find for this mixture 7 equations between molarities at equilibrium: $[HCOOH]$, $[H_3O^+]$, $[CH_3COO^-]$, $[Na^+]$, $[HCOO^-]$ $[CH_3COOH]$ and $[OH^-]$ (the electroneutrality condition, three conditions of conservation of matter, two equilibrium conditions and the ionic product of water) b) Look at what equation leads this system!

One finds (computer !): $pH = 5.36$