Calculate the Ka of a weak acid?

Question

A sample of a certain monoprotic weak acid was dissolved in water and titrated with 16.00mL of 0.125M NaOH to reach the equivalence point. During the titration, the pH after adding 2.00mL of NaOH was 6.912. Calculate the Ka for the weak acid.

 

 

Answer 1

Let HA represent the weak acid.

NaOH + HA ==> H₂O + NaA or removing spectators...

HA + OH^- ==> H₂O + A^-

This forms a buffer, i.e. a weak acid (HA) and the conjugate base (A^-)

To find initial moles of HA, we can use the moles of NaOH to reach equivalence. Thus...

0.016 L x 0.125 moles/L = 0.002 moles HA initially present

To find moles HA and moles A^- after addition of 2 mls of NaOH, we have...

0.002 L x 0.125 moles/L = 0.00025 moles OH- added.  This reacts with 0.002 moles HA leaving 0.00175 moles HA and forming 0.00025 moles A^-. This is the buffer.

We can now use the Henderson Hasselbalch equation pH = pKa + log (conjugate base/weak acid).

6.912 = pKa + log (0.00025/0.00175) = pKa + log 0.11429

6.912 = pKa - 0.845

pKa = 7.757

Ka = 1.75x10^-8