Calculations, Titration curves completeness

Dilute solutions of nominally 0.001 M NaOH and HGl are used to demonstrate the effect of an indicator s color transition range on titration error. Potentiometric titration curves are measured, and the indicator s color transition range is noted. Titration errors are calculated using the volume of titrant needed to effect the first color change and for a complete color change. 

Each leg of the titration curve is calculated separately. The first leg, from pH 1 to 6, corresponds to the dissociation of protonated alanine, H2A+. The second leg, from pH 6 to 11, corresponds to the dissociation of zwitterionic alanine, HA. It s as if we started with H2A+ at low pH and then titrated with NaOH. When 0.5 equivalent of NaOH is added, the deprotonation of H2A+ is 50% done when 1.0 equivalent of NaOH is added, the deprotonation of H2A+ is complete and HA predominates when 1.5 equivalent of NaOH is added, the deprotonation of H A is 50% done and when 2.0 equivalents of NaOH is added, the deprotonation of HA is complete. 

Calculate a pH value for each of the six regions of the titration, and then extrapolate to complete the titration curve. 

Titration curve of alanine By applying the Henderson-Hasselbalch equation to each dissociable acidic group, it is possi ble to calculate the complete titration curve of a weak acid. Figure 1.11 shows the change in pH that occurs during the addition of base to the fully protonated form of alanine (I) to produce the completely deprotonated form (III). Note the following ... 

The complete titration curve, showing the pW of the solution as a function of the amount of strong base added, can be calculated in essentially this way. Its course is shown in Figure 20-3 K = 10- ). V e see that the solution has pH 7 when there is about 1% excess of acid hence if litmus were used as the indicator an error of about 1% would be made in the titration. 

When constructing Table 1-3, we assumed that at the first equivalence point the a-carboxyl is completely ionized and that the /S-carboxyl is completely un-ionized. These assumptions, of course, are not entirely true the actual degree to which the a- and /S-carboxyls are ionized can be calculated using the Henderson-Hasselbalch equation. If we carry out the calculation, we find that the proportion of a-carboxyl that is still in the COOH form exactly equals the proportion of /3-carboxyl in the COO form. (At pH 2.98, we are just as far above the p/ a, for the a-carboxyl as we are below the for the /S-carboxyl.) Thus, to determine the net charge on the molecule, we are justified in tallying only the predominant ionic forms at each key point along the titration curve. 

The spreadsheet representation of the titration will now involve switching from one equation to another, as soon as the product [Ag+] [Br ] exceeds the value of soAgBr- In this case, then, the titration curve really consists of separate pieces, not for reasons of mathematical convenience but as the direct consequence of the formation of a new precipitant phase. In the spreadsheet we can accomplish this change-over between the two formalisms by using IF statements. Note that it is still a completely straightforward calculation, without any circular reasoning. 

At the various points in your titration curve, list the major species present after the strong base (NaOH, for example) reacts to completion with the weak acid, HA. What equilibrium problem would you solve at the various points in your titration curve to calculate the pH Why is pH > 7.0 at the equivalence point of a weak acid-strong base titration Does the pH at the halfway point to equivalence have to be less than 7.0 What does the pH at the halfway point equal Compare and contrast the titration curves for a strong acid-strong base titration and a weak acid-strong base titration. 

Of course, titration curves can be also completely (and exactly) calculated, and software packages are available for this (e.g., at http //www2.iq.usp.br/docente/ gutz/Curtipot. html). However, such calculations are beyond the scope of this book, which is focused on demonstrating how titration diagrams can be constructed in such a way that the most important features are displayed. 

The precise interpretation of potentiometric titration curves for base titrations in acetonitrile and the calculation of the pH changes near the equivalence point require only knowledge of the dissociation constants, J hb+5 of protonated bases to be titrated, because in solvents of relatively high relative permittivity (such as acetonitrile) perchloric acid and perchlorate salts can be considered to be completely dissociated. The well-known expression commonly used is... 

Oxide activities calculated using equation (32) with K- = 0 from the observed Eu(lll)/Eu(ll) ratios in the system CaAl2Si208 Mg2Si0i - Ca2Si0i. are shown in Fig. 11. The calculated activities define ciarves similar to the titration curves determined experimentally in silicate melts (Fig. 7) despite the assumption of the completely acidic behaviour of EU2O3 and differences between Si02 and anorthite as end member components. It should also be noted that (31) is only one of a number of reactions which can be written to represent the acidic behavioxir of EU2O3. 

The Masson and Toop and Samis mixing models assume complete dissociation of the basic oxide components. Thus, while these models may allow the calculation of oxide activities within any binary, activities in different binary systems cannot be compared since they relate to different standard states. The magnitude of the polymerization constant for a system is a measure of the shape of the titration curve not its absolute position. Thus with decreasing K the curves become steeper, or more sharply inflected, reflecting strong interactions between 02- and 0° or Si-O-Si. As pointed out by Hess (l97l) values of K decrease as Z/r decreases. So the activity curves for Ca2+ systems should be more steeply inflected than in the case of the equivalent Mg2+ compositions and these effects are shown in Fig. 11. 

Suppose we are titrating the triprotic acid H P04 with a solution of NaOH. The experimentally determined pH curve is shown in Fig. 11.13. Notice that there are three stoichiometric points (B, D, and F) and three buffer regions (A, C, and E). In pH calculations for these systems, we assume that, as we add the hydroxide solution, initially NaOH reacts completely with the acid to form the diprotic conjugate base... 

The above system of directly sensing a process stream without more is often not sufficiently accurate for process control so, robot titration is preferred in that case by means of for instance the microcomputerized (64K) Titro-Analyzer ADI 2015 (see Fig. 5.28) or its more flexible type ADI 2020 (handling even four sample streams) recently developed by Applikon Dependable Instruments20. These analyzers take a sample directly from process line(s), size it, run the complete analysis and transmit the calculated result(s) to process operation (or control) they allow for a wide range of analyses (potentiometric, amperometric and colorimetric) by means of titrations to a fixed end-point or to a full curve with either single or multiple equivalent points direct measurements with or without (standard) addition of auxiliary reagents can be presented in any units (pH, mV, temperature, etc.) required. 

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