Proof for Henderson - Hasselbalch formula
For the mathematicians - Ignore this if you don't like it
1) Write the reaction:
| HA(aq) | D | H+(aq) | + | A-(aq) |
2) Write the equilibrium expression, Ka
| Ka |
= |
[H+] x [A-] |
| [HA] |
3) Rearrange the equation
| [H+] |
= |
Ka x | [HA] |
| [A-] |
4) Take - logs of all species in the equation:
| -log[H+] |
= |
-logKa |
- log |
[HA] |
| [A-] |
5) Replace -log[H+] with pH and -logka with pKa:
| pH |
= |
pKa |
- log |
[HA] |
| [A-] |
6) Flip the concentrations over in order to have a '+' log function:
| pH |
= |
pKa |
+ log |
[A-] |
| [HA] |