ABSTRACT
Thus, for sulfuric acid there is essentially one reaction along the way to the lone inflection point:
H
SO
+
2 OH
Æ
SO
+
2 H
O (5.3)
he volume of titrant added at the equivalence point of a titration can be accurately determined by plotting the first and second derivatives of the titration curve. A first derivative is a plot of the rate of change of the pH,
D
pH, vs. milliliters of titrant, and the second derivative is a plot of the rate of change of the first derivative,
D
(
D
pH), vs. milliliters of titrant. The plot in the center is the first derivative of the titration curve on the left, and the plot on the right is the second derivative. The rate of change of the curve on the left is a maximum at the midpoint of the inflection point, so the maximum on the first derivative coincides with this point, which is the equivalence point of the titration. Similarly, the rate of change is zero at the maximum of the curve in the center, so the equivalence point is also the point where the second derivative crosses zero. Thus, the equivalence point is the milliliters of titrant at the peak of the first derivative and the milliliters of titrant at the point where the line crosses zero for the second derivative. The second derivative provides the most precise measurement of the equivalence point.
