The 1/2 equivalent point in a titration curve

[Saba]

TL;DR Summary

It is pretty challenging for me to understand how the 1/2 equivalent point in a titration curve (when either acid or base is weak) the pH = pKa.
I researched about the formula that is used to get this, but I couldn't quite understand that.

 

[Borek]

What are expected concentrations of the remaining, non-neutralized titrated acid and its conjugate base at half point?

What is ratio of these concentrations equal to?

What is log of that?

 

[Bruce_f]

From the equation above (the Henderson-Hasselbach equation if I remember correctly), the half equivalent point is when the concentrations of the acid and its conjugate base are equal. Any number divided by itself is 1 (one). The log of 1 is 0 (zero), so therefore pH = pKa