Equivalence Point Endpoint Location

This section will cover the location of the equivalence point or endpoint by modern microprocessor- or computer-controUed potentiometric titrators. 

Equipment manufacturers may differ slightly as to the method of location. Only the most popular form will be covered here, and this involves endpoint location from first-derivative data. 

Hardcopy printout of titration data for the titration of a dibasic acid with a standard base. Metrohm 636 Titroprocessor 

Calculations similar to these are carried out by the integral microprocessor or computer. The calculations for the monotonous titrations carried out with a constant volume addition made after a preselected time in seconds are not identical but very much the same. It should be pointed out for clarification, that the volumes to the right in the last column are the average values between the actual volumes recorded for each of the two points examined. 

Where potentiometric titrations, other than those involving pH measurement are concerned, such as precipitation, complexation, oxidation-reduction, nonaqueous media, etc., the data obtained will be in the form of E versus V. All of the titration theory, and that of titration curves, will apply to such titrations, as will the general methods of endpoint location. 

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The stoichiometric equivalence point should be immediately detectable. This usually requires a large change in some physical or chemical property of the solution. This point in the reaction is often located by means of a secondary system, which provides an observable endpoint. This secondary system must be reproducible, clearly identifiable, and ideally coincident with the stoichiometric equivalence point. Because coincidence is not always achieved, the difference between the endpoint and the equivalence point should be easily measurable. Often, so-called blank solution is used for this correction. A chemical indicator... 

The electromotoric force (emf) of a cell depends on the ionic concentration of the solutions. To locate the equivalence point, the variation in emf is monitored as the concentration of the analyte changes. When the measured emf is plotted against the total volume of titrant added, the curve produced is similar to that of a titration curve Fig. 4. This technique has all the advantages of the conductometric method and gives an experimental curve from which the endpoint can be detected accurately. 

Instrumental systems involving an automatic burette drive linked to a recorder to which is also hnked the electrode couple potential output. A continuous rate of volume addition is selected, with a provision for slowdown near the titration equivalence point. The recorder plots the course of E versus V or pH versus V during the titration. For such plots, the equivalence point or endpoint is located manually with the use of various forms of curve-analysis plastic template overlays. Potentiographic titrators of this type often have a derivative circuit, so that the plot of AE/AV versus V can also be drawn by the recorder. The peak of this curve provides a somewhat simpler means of locating the equivalence-point volume. 

As we have already seen, titration curves exhibit a large pH change in the vicinity of the equivalence point. By the addition of a small quantity of properly selected indicator we can observe a color change close to the equivalence point and thereby locate the endpoint To the extent that the indicator endpoint and the true equivalence point differ, a titration error occurs, measured either in titrant volume or, as relative error, in percent... 

How far apart must successive pK values be in order to have clearly distinguishable endpoints for titration curves of polyprotic acids Consider as examples H3PO4 and citric acid. What about equivalence points at very high or low pH How easy are they to locate ... 

Examination of the titration curve visually can locate the endpoint as the midpoint of the nearly vertical portion in the vicinity of the equivalence point. Additionally, if the difference curve in which ApM/AVl is plotted against Vl, is constructed, the maximum is located at the endpoint. 

As we found with acid-base titrations in the last chapter, however, the most precise method for locating the endpoint is the Gran method. This method results in a linear plot which intercepts the equivalence point at the X axis. Not only can we easily find the best line through linear regression but, as mentioned earlier, the necessary points can be taken at a distance from the equivalence point making this method rapid and convenient. 

Exercise 2 Calculate the titration error obtained for the titration of 50 cm of a 10 mol/L acetic acid solution (pATa=4.75). Thetifrant is a solution of 10 moI/L sodium hydroxide. The endpoint is detected at pH = 8.00, whereas the equivalence point, theoretically, is located at pH=8.72. 

From a practical standpoint, we can infer from these considerations that there are two ways to titrate phosphoric acid We base it on either the first or second sharp endpoint. In the first case, only the first acidity is neutralized and the color-change interval is located near pH=4.8 Congo red is suitable. In the second case, the first two acidities are neutralized and the color-change interval is located near pH=9.8 thymolphthalein and phenolphthalein are suitable. The volumes at the equivalence point, which must be taken into account to calculate the titer, vary, of course, from simple to double according to the chosen strategy. 

The conduction band is characterized by eight equivalent minima at the endpoints L of the [111] axes of the Brillouin zone (symmetry Le). The surfaces of constant energy are elUpsoids of revolution with their major axes along [111]. Higher energy minima of the conduction band are located at the P point and (above these) on the [100] axes. 

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