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

Question

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.

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Answer 1 · 2016-05-16T21:06:48

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

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.