Question

How do you calculate PKa using the Henderson-Hasselbalch equation?

PH=6.98. Mix 25ml of 0.1M `NaH_2PO_4` and 25ml of 0.1M `Na_2HPO_4` and dilute with water in a 250ml Volumetric flask.

Answer 1

`pK_a=6.98-log((0.05M)/(0.05M))=6.98`

Explanation:

The Henderson-Hasselbalch equation is:

`pH=pK_a+log(([Base])/([Acid]))`

Therefore, `pK_a=pH-log(([Base])/([Acid]))`

`pK_a=6.98-log((0.05M)/(0.05M))=6.98`

Note that the new concentrations are divided by `2` because the total volume doubles `V_(soln.)=25mL+25mL=50mL`

Notice that n this case the `pH=pK_a` because the `[Na_2HPO_4]=[NaH_2PO_4]` and the `log` of the ratio is equal to zero.

Here is a video that explains more this topic (topic starts at minute 9:02):
Acid - Base Equilibria | Buffer Solution.