Location of End Points:
In potentiometric titration the end-point is detected by determining the volume at which a selectively large change in potential occurs as the titrant is added. The method can be employed for all the reactions used for titrimetric purposes: acid -bases, redox, precipitation and complex formation. The titration might be performed manually or the procedure might be automatic.
In manual titrations, the potential is measured after the addition of each successive increment of titrant and the resulting readings are plotted on graph paper vs the volume of titrant to give the titration curve shown in Figure (a). You can see, this increase is not linear and a sigmoid shaped curve is obtained as shown the figure. The greater change in emf occurs around the equivalence point. In fact the equivalence point of maximum change in emf with volume added. This is formed the point of inflexion. The equivalence point is determined by dropping vertical line from this point. Figure (b) shows a plot of slope of a titration curve i.e. the rate of change of potential, with a change in volume ( Δ E/ Δ V) against volume of titrant, the resulting curve rises to maxima at equivalent point. The volume at equivalence point is determined by dropping a vertical line from the peak to volume axis. The more complete the reaction, the sharper the peak and hence more accurate the location of equivalence point.
Figure (c) shows a plot of the change in the slope of a titration curve ( Δ2 E/ Δ V2) against the volume of titrant. At the point where the slop Δ2 E/ ΔV2 is a maximum, the derivative of the slope is zero. The end-point is located by drawing a vertical line from the point at which Δ2 E/ Δ V2 is zero to the volume axis. Portion of the curve joining the maximum and minimum values of Δ2 E/ΔV2 is steeper, the more complete the titration reactions.
Figure: Titration curves: (a) typical plot of emf vs volume; (b) typical first derivative titration curve; and (c) typical second derivative titration curve