Henderson-Hasselbach Equation

Introduced to this in AP Chemistry

K${}_a$ = $\frac{[H^{+}][A^{-}]}{[HA]}$ = [H${}^{+}$]$\frac{[A^{-}]}{[HA]}$

Negative log both sides

-log K${}_a$ = -log[H${}^{+}$]-log$\frac{[A^{-}]}{[HA]}$

Final Equation §

pH = pK${}_a$ + log$\frac{[A^{-}]}{[HA]}$

pK${}_a$ = -logK${}_a$

pK${}_b$ = - logK${}_b$

Trends §

[HA] = [A${}^{-}$]

• log 1 = 0
• pH = pK${}_a$
• makes the best buffer solution

[HA] > [A${}^{-}$]

• log of a # < 1 = negative
• pH < pK${}_a$
• more acid than base = lower pH

[HA] < [A${}^{-}$]

• log of a # > 1 = positive
• pH > pK${}_a$
• more conjugate base than acid = higher pH

Buffering Capacity §

pH = pK${}_a$ + log$\frac{[A^{-}]}{[HA]}$

• pH of a buffered solution is determined by the K${}_a$ and the ratio $\frac{[A^{-}]}{[HA]}$
• Capacity of a buffered solution is determined by the magnitude of both [A${}^{-}$] and [HA]
  • greater concentration of [A${}^{-}$] and [HA] = greater amount of strong acid/base can be added with minimal pH change