Derive Henderson – Hasselbalch equation?

We can derive a general equation for calculating the pH of any buffer solution. Consider a mixture of weak acid (HX) and its conjugate base.
HX + H2O ⇌ H3O+ + X
Ka = [H3O+] [X] / [HX]
Taking log on both the sides, we will get:
Log Ka = log [H3O+] + log ([X] / [HX])
-log Ka = – log [H3O+] – log ([X] / [HX])
pKa = pH – log ([X] / [HX])
pH = pKa + log ([X] / [HX])

The quantity [X] / [HX] is the ratio of concentration of salt or conjugate base of acid and acid present in the mixture.
Therefore, pH = pKa + log ([salt]/ [base])
This equation is called Henderson – Hasselbalch equation. Similarly, for a basic buffer,
pOH = pKb + log ([salt]/ [base])
pH = 14 – pKb – log ([salt]/ [base])

Category: Ionic Equilibria

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