Titration-Curve Method

The information that is available in many chemical plants is a titration curve for each stream to be neutralized. The method outlined below can be used in this 

Let us assume that titration curves for the feed streams are known. These can be the typical sharp curves for strong acids or the gradual curves for weak acids, with or without buffering. The dynamie model keeps traek of the amount of each stream that is in the tank at any point in time. Let C be the concentration of the nth stream in the tank, F be the flow rate of that stream into the tank, and Fou, be the total flow rate of material leaving the tank. 

If the volume of the liquid in the tank is eonstant, the outflow is the sum of all the inflows. The flow rates of caustic and lime slurry are usually negligible. For three feed streams 

Fqh = total flow rate of OH- ion into the system in the caustic and lime slurry streams 

Rjij = rate of OH- ion generation due to the dissolving of the solid CaCOa particles 

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Bashford, D., Karplus, M. Multiple-site titration curves of proteins an analysis of exact and approximate methods for their calculation. J. Phys. Chem. 95 (1991) 9556-9561. 

Sketching an Acid—Base Titration Curve To evaluate the relationship between an equivalence point and an end point, we only need to construct a reasonable approximation to the titration curve. In this section we demonstrate a simple method for sketching any acid-base titration curve. Our goal is to sketch the titration curve quickly, using as few calculations as possible. 

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

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... 

Derivative methods are particularly well suited for locating end points in multi-protic and multicomponent systems, in which the use of separate visual indicators for each end point is impractical. The precision with which the end point may be located also makes derivative methods attractive for the analysis of samples with poorly defined normal titration curves. 

Derivative methods work well only when sufficient data are recorded during the sharp rise in plT occurring near the equivalence point. This is usually not a problem when the titration is conducted with an automatic titrator, particularly when operated under computer control. Manual titrations, however, often contain only a few data points in the equivalence point region, due to the limited range of volumes over which the transition in plT occurs. Manual titrations are, however, information-rich during the more gently rising portions of the titration curve before and after the equivalence point. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

This method provides a reasonable estimate of the piQ, provided that the weak acid is neither too strong nor too weak. These limitations are easily appreciated by considering two limiting cases. For the first case let s assume that the acid is strong enough that it is more than 50% dissociated before the titration begins. As a result the concentration of HA before the equivalence point is always less than the concentration of A , and there is no point along the titration curve where [HA] = [A ]. At the other extreme, if the acid is too weak, the equilibrium constant for the titration reaction... 

The precision of the end point signal depends on the method used to locate the end point and the shape of the titration curve. With a visual indicator, the precision of the end point signal is usually between +0.03 mb and 0.10 mb. End points determined by direct monitoring often can be determined with a greater precision. 

Finding the End Point Potentiometrically Another method for locating the end point of a redox titration is to use an appropriate electrode to monitor the change in electrochemical potential as titrant is added to a solution of analyte. The end point can then be found from a visual inspection of the titration curve. The simplest experimental design (Figure 9.38) consists of a Pt indicator electrode whose potential is governed by the analyte s or titrant s redox half-reaction, and a reference electrode that has a fixed potential. A further discussion of potentiometry is found in Chapter 11. 

The scale of operations, accuracy, precision, sensitivity, time, and cost of methods involving redox titrations are similar to those described earlier in the chapter for acid-base and complexometric titrimetric methods. As with acid-base titrations, redox titrations can be extended to the analysis of mixtures if there is a significant difference in the ease with which the analytes can be oxidized or reduced. Figure 9.40 shows an example of the titration curve for a mixture of Fe + and Sn +, using Ce + as the titrant. The titration of a mixture of analytes whose standard-state potentials or formal potentials differ by at least 200 mV will result in a separate equivalence point for each analyte. 

In a titrimetric method of analysis the volume of titrant reacting stoichiometrically with the analyte provides quantitative information about the amount of analyte in a sample. The volume of titrant required to achieve this stoichiometric reaction is called the equivalence point. Experimentally we determine the titration s end point using a visual indicator that changes color near the equivalence point. Alternatively, we can locate the end point by recording a titration curve showing the titration reaction s progress as a function of the titrant s volume. In either case, the end point must closely match the equivalence point if a titration is to be accurate. Knowing the shape of a titration... 

Gran plot a linearized form of a titration curve, (p. 293) graphite furnace an electrothermal atomizer that relies on resistive heating to atomize samples, (p. 414) gravimetry any method in which the signal is a mass or change in mass. (p. 233)... 

Chemical shifts of pyridine and the diazines have been measured as a function of pH in aqueous solution and generally protonation at nitrogen results in deshielding of the carbon resonances by up to 10 p.p.m. (73T1145). The pH dependence follows classic titration curves whose inflexions yield pK values in good agreement with those obtained by other methods. 

It was indicated that the original method can be extended on systems where two or three analytes can be determined from a single titration curve. The shifts DpH affected by j-th PT addition should be sufficiently high it depends on pH value, a kind and concentration of the buffer chosen and its properties. The criterion of choice of the related conditions of analysis has been proposed. A computer program (written in MATLAB and DELPHI languages), that enables the pH-static titration to be done automatically, has also been prepared. 

It was noted that the content of functional groups on the surface of studied A1,03 was 0,92-10 mol/g of acid character for (I), FOS-IO mol/g of basic character for (II). The total content of the groups of both types was 1,70-lO mol/g for (III). The absence of appreciable point deviations from a flat area of titration curves in all cases proves simultaneously charges neutralization character on the same adsoi ption centers and non-depending on their density. The isoelectric points of oxide surfaces have been detenuined from titration curves and have been confirmed by drift method. 

Titration is the analytical method used to determine the amount of acid in a solution. A measured volume of the acid solution is titrated by slowly adding a solution of base, typically NaOH, of known concentration. As incremental amounts of NaOH are added, the pH of the solution is determined and a plot of the pH of the solution versus the amount of OH added yields a titration curve. The titration curve for acetic acid is shown in Figure 2.12. In considering the progress of this titration, keep in mind two important equilibria ... 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

The methods dependent upon measurement of an electrical property, and those based upon determination of the extent to which radiation is absorbed or upon assessment of the intensity of emitted radiation, all require the use of a suitable instrument, e.g. polarograph, spectrophotometer, etc., and in consequence such methods are referred to as instrumental methods . Instrumental methods are usually much faster than purely chemical procedures, they are normally applicable at concentrations far too small to be amenable to determination by classical methods, and they find wide application in industry. In most cases a microcomputer can be interfaced to the instrument so that absorption curves, polarograms, titration curves, etc., can be plotted automatically, and in fact, by the incorporation of appropriate servo-mechanisms, the whole analytical process may, in suitable cases, be completely automated. 

The method may be used to titrate a mixture of acids which differ greatly in their strengths, e.g. acetic (ethanoic) and hydrochloric acids the first break in the titration curve occurs when the stronger of the two acids is neutralised, and the second when neutralisation is complete. For this method to be successful, the two acids or bases should differ in strength by at least 10s to 1. 

The chromium in the substance is converted into chromate or dichromate by any of the usual methods. A platinum indicator electrode and a saturated calomel electrode are used. Place a known volume of the dichromate solution in the titration beaker, add 10 mL of 10 per cent sulphuric acid or hydrochloric acid per 100 mL of the final volume of the solution and also 2.5 mL of 10 per cent phosphorus) V) acid. Insert the electrodes, stir, and after adding 1 mL of a standard ammonium iron)II) sulphate solution, the e.m.f. is measured. Continue to add the iron solution, reading the e.m.f. after each addition, then plot the titration curve and determine the end point. 

As shown in Section 15.17, the location of the end point of a potentiometric titration can often be accomplished more exactly from the first or second derivative of the titration curve, than from the titration curve itself. Similarly, absorption observations will often yield more information from derivative plots than from the original absorption curve. This technique was used as long ago as 1955, but with the development of microcomputers which permit rapid generation of derivative curves, the method has acquired great impetus.9,10... 

Principle. By means of potentiometric titration (in nonaqueous media) of a blend of sulfonic and sulfuric acids, it is possible to split the neutralization points corresponding to the first proton of sulfuric acid plus that of sulfonic acid, and to the second proton of sulfuric acid. The first derivate of the titration curve allows identification of the second points the corresponding difference in the volume of titrating agent is used as a starting point in the calculation method (Fig. 4). 

For further discussion of experimental methods for determination of electrophoretic titration curves of proteins, see the recent study by Gianazza et al. [129], For discussion of the free solution mobility of DNA see Stellwagen et al. [368],... 

For a completely symmetrical curve, the end-point can be easily established as the inflection point through which a tangent can be drawn here for convenience the "rings method (Fig. 2.23) can be used, where the inflection point is obtained by intersection of the titration curve with the line joining centres of fitting circles (marked on a thin sheet of transparant plastic see ref. 61). 

Final remarks on end-point detection. In addition to our remarks above on the types of titration curves and the Henderson equation or more extended relationships, we can state that in Gran s method activity coefficients are taken into account however, these were assumed to be constant, which is incorrect, and therefore the addition of an ISA (ion strength adjuster) must be recommended (for errors of the Gran method see ref.66). 

Subsequently, Bos and Dahmen used in m-cresol65 (e = 12.29 at 25° C) a potentiometric titration method combined with conductometry. Essential precautions were the preparation of water-free m-cresol (<0.01% of water), the use of a genuine Bronsted base B, e.g., tetramethylguanidine (TMG), and the application of a glass electrode combined with an Ag-AgCl reference electrode filled with a saturated solution of Me4NCl in m-cresol. The ion product of the self-dissociation of m-cresol, Ks, was determined from the part beyond the equivalence point of the potentiometric titration curve of HBr with TMG comparison with titration curves calculated with various Ka values showed the best fit for Ks = 2 10 19... 

At first we determined, by means of the DVP method, ifTMAX of 2,4-dinitro-phenolate, 2,5-dinitrophenol picrate, acetate and benzoate, which lay between 10 3 and 10 5. Next, separate potentiometric titrations of 2,5-dinitrophenol and picric acid were carried out on the basis of the previously known (see above) ptfax = 6.5 and P hx2- = 100 for 2,5-dinitrophenol and p.fiTHX = 3.0 for picric acid, we calculated titration curves for estimated values of 0 and obtained, for the best fit between the experimental and calculated curves, K o = 10 21 for both 2,5-dinitrophenol and picric acid. In both instances changing fTMA0H for 1 to 10 6 did not alter the calculated titration curve. Finally, for potentiometric titrations of other acids with TMAOH while using / TMAX values from DVP results, in addition to Kn 0 = 10 21, we obtained the best fit between the experimental and calculated curves again when pifbenzoic acid = 1 (see Fig. 4.12)... 

In this automatic system, the authors preferably used coulometric generation of titrant (cf., microcoulometric determination of deviations in the above end-point titration ), e.g., H, OH, Ag, Hg2+, Br2,12, Fe(CN) (cf., Table 1 in ref. 63). The detection method may be potentiometric (logarithmic signal), amperometric (linear signal), biamperometric, conductometric, oscillometric, etc. Moreover, the authors evaluated triangle programmed titration curves by... 

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