The pH of a solution halfway to the equivalence point

To determine the pH of a solution halfway to the equivalence point, we need to understand a bit about acid-base titrations. In an acid-base titration, a measured volume of one solution (the titrant) is reacted with a solution of another substance (the analyte) until the reaction is complete.

The equivalence point is reached when the stoichiometrically equivalent quantities of acid and base have been reacted. At the equivalence point, the acid and base have completely neutralized each other, resulting in a solution that is neither acidic nor basic.

Halfway to the equivalence point means that we have used half of the amount of titrant necessary to reach the equivalence point. At this point, there is still an excess of one of the reactants, which affects the pH of the solution.

To determine the pH halfway to the equivalence point, we need to know the nature of the acid-base reaction and the initial concentrations of the acid and base. Once we know those details, we can use the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation is given as:

pH = pKa + log ([A-]/[HA])

where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.

In an acid-base titration, the halfway point corresponds to when the ratio of the acid to the conjugate base is 1:1. So, [A-] = [HA], and the equation simplifies to:

pH = pKa + log (1)

Since the log of 1 is 0, the equation becomes:

pH = pKa

Therefore, at the halfway point, the pH of the solution is equal to the pKa of the acid being titrated.

So, to determine the pH halfway to the equivalence point, you need to know the pKa value of the acid. From there, you can substitute the value of pKa into the Henderson-Hasselbalch equation and calculate the pH.