Question

How does pKa (or pKb) related to pH measured in the solution when the volume of the titrant added is exactly half of that required to reach the equivalence point?

Answer 1

In acid-base titrations, we use the concept of neutralization. As we add titrant to titre, the neutralization process starts and it completes at the actual endpoint or equivalence point. We perform acid-base titrations using indicators to recognize equivalence point. These titrations are also called pH titrations. in pH titrations, we use either an acid or base as titrant. As titrant is added, it forms the salt in the solution. So when the volume of the titrant added is exactly half of that required to reach the endpoint, the quantity of salt formed will be the same as that of the Acid or base left in the solution. So considering Acid HA dissociation as

Hence dissociation constant for this acid is

at half the equivalence point, [HA]=[A^-], hence  

hence

Hence at half equivalance point pH =pKa

Similarly, if we take the base, pOH at half equivalence will be same as pKb

For base,

from above, it follows that at half equivalence, pOH=pKb,

Or, pH=14-pKb