Uncertainty titration curves

You may wonder why we did not use the titration curve to determine the pH at the stoichiometric point of the ephedrine titration, as we did to find the pH at the midpoint. Notice from Figure 18-6 that near the stoichiometric point, the pH changes very rapidly with added H3 O. At the stoichiometric point, the curve is nearly vertical. Thus, there Is much uncertainty in reading a graph to determine the pH at the stoichiometric point. In contrast, a titration curve is nearly fiat in the vicinity of the midpoint, minimizing uncertainty caused by errors in graph reading. 

For preliminary design purposes, the estimate from Eq. (52) is an adequate predictor of achievable PI performance when all tanks are tightly controlled. If control on one tank of a multiple CSTR system is rendered ineffective—due to uncertainty, high delay compared to the minimum delay, or simply the absence of a controller—the predicted disturbance attenuation should be increased by 50%. An exception to this is the case of variation in the sensitivity of pH to concentration on the final CSTR. In this case, no degradation of performance from that obtained with the minimum buffering (maximum titration curve slope) will occur as the performance required in terms of concentration deviations relaxes along with the controller performance. 

The reaction of iodine with proteins is neither quantitative nor completely specific, and since it may be expected to result in chemical substitution or oxidation of a variety of groups the interpretation of the titration curve of an iodinated protein is subject to considerable uncertainty. At-... 

A procedure is presented for estimation of uncertainty in measurement of the pK(a> of a weak acid by potentiometric titration. The procedure is based on the ISO GUM. The core of the procedure is a mathematical model that involves 40 input parameters. A novel approach is used for taking into account the purity of the acid, the impurities are not treated as inert compounds only, and their possible acidic dissociation is also taken into account. Application to an example of practical pK(a> determination is presented. Altogether, 67 different sources of uncertainty are identified and quantified within the example. The relative importance of different uncertainty sources is discussed. The most important source of uncertainty (with the experimental set-up of the example) is the uncertainty of the pH measurement followed by the accuracy of the burette and the uncertainty of weighing. The procedure gives uncertainty separately for each point of the titration curve. The uncertainty depends on the amount of the titrant added, being lowest in the central part of the titration curve. The possibilities of reducing the uncertainty and interpreting the drift of the pKJa) values obtained from the same curve are discussed. 

In principle one could use the break points in the titration curve as approximations of the equivalence points, although these points do not quite coincide with the true equivalence points moreover, co-precipitation (if not suppressed) often leads to a blurring of those points. At any rate, it is usually a better practice to avoid reliance on single points in a titration curves for the precise determination of the equivalence volumes, because such single readings are inherently rather vulnerable to experimental uncertainty. 

The carboxyl ionization [pK]) is low and easily identified. However, the ammonium and thiol groups have similar pK values (compare methylamine with methyl mercaptan, Table 2.1) and so an uncertainty exists as to which group ionizes first. Ki, K2, and K3 represent macroscopic ionization constants determined experimentally from a titration curve. K2 and are the composite of four microscopic ionization constants. Once the proton is lost from the carboxyl group, one of two ionization pathways may be followed ... 

A very important point must be emphasized A result obtained by titrimetry (that described immediately above) depends on the determination of only one titration curve point—the equivalence point. That is, it depends on one piece of experimental information. However, the titration curve is composed by plenty of other points, each of which brings a new piece of information about the unknown concentration. This is the reason why the current trend is to treat all points of the curve in order to benefit from all the available information and, hence, to reduce the uncertainties and inaccuracies resulting from the determination of a sole point. This is done by mathematical processes with the help of informatics programs (easy to write ourselves). The general mathematical treatment of titration curves is given at the end of Chap. 9. 

The laboratory titration curve would be more accurate due to the uncertainty as to the activity coefficients from high ion interaction. 

Figure 1 shows a comparison of the model results with the experimental results. The three curves shown in the plot correspond to three different values of the rate constant for the HOSO + O2 reaction upper - 8 x 10-13, middle - 4 x IO13, and lower - 2 x 10"13 cm3/s. Similar comparisons between model and experimental results have been made for a wide variety of other experimental conditions. Based upon such comparisons, we have concluded that a rate constant of (4 )x lu-13 cm3/s gives the best match between the experimental and model results, in both an absolute sense and based upon the shape of the O2 titration results. Since there is greater uncertainty in the absolute concentrations of HO radicals than there is in the trend of the HO concentrations with increasing O2, the comparison of the shapes of the experimental and model O2 titration profiles may provide a reliable basis for comparison. 

If the titrant is a weak electrolyte (such as ammonia), the curve is essentially horizontal past the equivalence point, which causes less uncertainty to the extrapolation of a curve. In titration of a weak base, such as acetate ion, with a strong acid, a salt and undissociated acetic acid are formed. After the endpoint is passed, a sharp rise in conductance attends the addition of excess hydronium ions. Salts whose acidic or basic character is too weak to give satisfactory endpoints with indicator are conveniently titrated with the conductometric method. The conductometric titration of a mixture of two acids that differ in degree of dissociation is frequently more accurate than a potentiometric titration. 

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