Respuesta :
For the reaction of weak acid:
[tex] HA\rightleftharpoons H^{+}+A^{-} [/tex]
The Henderson-hasselbalch equation is:
[tex] pH = pk_a+ log \frac{[A^{-}]}{[HA]} [/tex]
The concentration ratio at [tex] pk_1 [/tex] is:
[tex] pH = pk_1+ log \frac{[A^{-}]}{[HA]} [/tex]
Substituting the values:
[tex] 3.2 = 4.1 + log \frac{[A^{-}]}{[HA]} [/tex]
[tex] log \frac{[A^{-}]}{[HA]} = - 0.9 [/tex]
[tex] \frac{[A^{-}]}{[HA]} = 0.126 [/tex]
Now, for calculating the pk_2 value:
[tex] pH = pk_2+ log \frac{[A^{-}]}{[HA]} [/tex]
[tex] 8 = pk_2+ log(0.126) [/tex]
[tex] pk_2 = 8.9 [/tex]
Thus, [tex] pk_2 = 8.9 [/tex].
