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How do we detect equivalence point from a titration of an acid with a basic titrant from thу titration curve ($\mathrm{pH}$ vs. Volume of titrant added)?
Can we predict an equivalence point just by seeing the shape? Some people say that
when $$\frac{\mathrm{d(pH)}}{\mathrm{d}V} = 0,$$ equivalence point has been reached.
Is it correct? I doubt if it is correct. It is also written that there is a distinct "break" in the curve at equivalence point. What is this break?
You do not detect equivalence points. What you detect is the endpoint. This is a very critical distinction.
You have some feature you are explicitly measuring, be it pH or color or opacity.
Once this feature changes you have reached the endpoint. The endpoint is not the equivalence point because you will never have exactly the right amount. Frequently, you overshoot a bit.
Also, the reason that the endpoint is detectable is because the transition is very sharp and sudden. That is because near the equivalence point, the pH (and whatever pH derived feature you have) changes very rapidly. The derivative is definitely not zero. In fact, the derivative you've provided is never zero but monotonically increasing or decreasing depending on whether you're tritrating with acid or base. It has to. If you add more base, the pH is only going to increase in value.
