Titration derivatives

Another method for finding the end point is to plot the first or second derivative of the titration curve. The slope of a titration curve reaches its maximum value at the inflection point. The first derivative of a titration curve, therefore, shows a separate peak for each end point. The first derivative is approximated as ApH/AV, where ApH is the change in pH between successive additions of titrant. For example, the initial point in the first derivative titration curve for the data in Table 9.5 is... 

Titration curves for a weak acid with 0.100 M NaOH—(a) normal titration curve (b) first derivative titration curve ... 

The second derivative of a titration curve may be more useful than the first derivative, since the end point is indicated by its intersection with the volume axis. The second derivative is approximated as A(ApH/AV)/AV, or A pH/AV. For the titration data in Table 9.5, the initial point in the second derivative titration curve is... 

Second-derivative titrators have the advantage that no preknowledge of the equivalence point potential is required. The signal processor calculates the second derivative of the electrode potential of the indicator electrode. Change in the sign of the second derivative causes a switching device to turn off the flow of the titrant. 

The methods developed in the previous section for deriving titration curves can be extended to mixtures that form precipitates of different solubilities. To illustrate, consider the titration of 50.00 mL of a solution that is 0.0500 M in iodide ion and 0.0800 M in chloride ion with 0.1000 M silver nitrate. The curve for the initial stages of this titration is identical to the curve shown for iodide in Figure 13-5 because silver chloride, with its much larger solubility product, does not begin to precipitate until well into the titration. 

Derivative titration curve A plot of the change in the quantity measured per unit volume against the volume of titrant added a derivative curve displays a maximum where there is a point of inflection in a conventional titration curve. See also. second derivative curve. 

A Gran-type plot can also be obtained by plotting the reciprocal of a first derivative curve, that is, AEIAV versus V. Since in a derivative titration I VILe goes to infinity at the equivalence point, the reciprocal will go to zero where the intersection of the two fines occurs, and a V-shaped plot results. In this application, the average volume between the two increments is plotted, as in the first derivative plot. The AE/AF values must be corrected for volume changes to obtain straight lines (AE/AF is linearly dependent on volume changes). 

A first derivative titration can be used to prepare a Gran plot. 

Cr vs. AgNOs (Figure 11.1) Chapter 11, Problem 12 Fe " vs. Ce + (Figure 14.1) Chapter 14, Problem 21 First and Second Derivative Titration Plots (Figures... 

Compare the Gran titration and the derivative titration methods for precise location of equivalent point for the system H3PO4 NaOH. First generate the data set for the titration curve then add "noise" (see Chapter 12) to both the titration volume and pH values using +0.02 ( RAND- RAND) to add to the volumes and +0.01 ( RAND- RAND) to pH values. 

Potentiometry, Fig. 3 Potentiometric titration curves, (a) typical plot of E versus volume, (b) typical first derivative titration curve, (c) typical second derivative titration curve... 

Simulation Learn more about derivative titrations. 

Fig. 11.5 Structures and pK values of some derivatives titrated in hydroalcohoUc mixtures...

Dilute 69 cm of purest syrupy phosphoric acid to 1 dm to obtain 1 M solution and by 10-fold dilution, prepare 0.1 M solution. Pipette 20.0 cm of the acid into a 250 cm conical flask. Calibrate the pH meter with a combined glass electrode and two buffer solutions at pH 4 and at 7. Dip the rinsed electrode into the flask, introduce a magnetic bar and add from a burette 0.1 M KOH solution in 2 cm aliquots, reading the pH on the meter when it settles. When the pH change becomes more rapid as the titration proceeds, decrease the volume down to 0.5 cm and then to 0.1 cm. After noting the first inflection point, continue with 2 cm additions of KOH and eventually to 0.1 cm addition until the second inflection point is reached. If a facility is available record the titration curve and preferably the derivative titration curve. 

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