Spreadsheet weak acid titration curve

The approach that we have worked out for the titration of a monoprotic weak acid with a strong base can be extended to reactions involving multiprotic acids or bases and mixtures of acids or bases. As the complexity of the titration increases, however, the necessary calculations become more time-consuming. Not surprisingly, a variety of algebraic and computer spreadsheet approaches have been described to aid in constructing titration curves. 

Figure 11-11 Spreadsheet that uses Equation 11-9 to calculate the titration curve for 50 mL of the weak acid 0.02 M MES (pKa = 6.27) treated with 0.1 M NaOH. We provide pH as input in column B and the spreadsheet tells us what volume of base is required to generate that pH. 

O Effect of pKa in the titration of weak acid with strong base. Use Equation 11-9 with a spreadsheet such as the one shown in Figure 11-11 to compute and plot the family of curves at the left side of Figure 11-3. For a strong acid, choose a large A"a, such as Ka = 102 or pKa = -2. 

Figure 20-11 illustrates a portion of a spreadsheet for the calculation of the titration curve of 2.500 mmol of a weak acid (pXa = 5) with 0.1000 M strong base. The volume required to obtain a given pH value was calculated for pH values from 3 to 12 in increments of 0.20. The formula used to calculate V in cell C9 is... 

Figure 20-11. Spreadsheet for weak acid-strong base titration curve.

T Spreadsheet Summary In the final three exercises in Chapter 7 of —I Applications of Microsoft Excel in Analytical Chemistry, we first use Excel to plot a simple distribution of species diagram (a plot) for a weak acid. Then, the first and second derivatives of the titration curve are plotted to better determine the titration end point. A combination plot is produced that simultaneously displays the pH versus volume curve and the second-derivative curve. Finally, a Gran plot is explored for locating the end point by a linear regression procedure. 

Fig. 4.6 Four successive stages in the automatic curve fitting of a very noisy progress curve (na= 0.1) for the titration of 0.1M weak acid (Ca = 0.1 M, Ka = 2 X lO M) with O.lMNaOH. The initial guess values used in the fitting were Ca= 0.25M, Ktt= 1 X10 7M. The spreadsheet parameters are shown to the left of the graphs.

We should note that the pH calculated from the relatively simple equations presented here break down near the equivalence point for weak acids and bases because the assumptions used in deriving them no longer apply. Even for strong acid-base titrations, we reach a point very near the equivalence point where the ionization of water becomes appreciable compared to the acid or excess base concentration, and the calculations are in error. You can satisfy yourself of these limitations by inserting in the spreadsheet examples titrant values that are, say, 99.99% or 99.999% and see where the calculated pH falls off the otherwise smooth titration curve. 

We will hot constract a diprotic titration curve here, but if you want a good mental exercise, try it You just can t make the simplifying assumptions that we can usually use with monoprotic acids that are sufficiently weak or not too dilute. See your CD, Chapter 8, for auxiliary data for the spreadsheet calculation of the titration curve for 50.00 mL 0.1000 M H2C1O4 versus 0.1000 M NaOH. You can download that and enter the Kai and Kai values for other diprotic acids and see what their titration curves look like. Try, for example, maleic acid. For the calculations, we used the more exact equations mentioned above for the initial pH, the first buffet zone, and the first equivalence point. We did not use the quadratic equation for the second equivalence point since Cr04 is a quite weak base (Kbi = 3.12 X 10 ). See Ref. 8 for other examples of calculated titration curves. 

Calculating acid-base titration curves Strong acids, strong bases (Table 8.1), p. 266 Spreadsheet calculations, p. 269 Weak acids, weak bases (Table 8.2), p. 272 Spreadsheet calculations, p. 277 Indicators (key equations 8.4, 8.5), p. 270 Titration of Na2C03, p. 280 Titration of polyprotic acids (Table 8.3), p. 281 Titration of amino acids, p. 286... 

An Excel spreadsheet can be constructed with appropriate formulas (to include the effects of dilution of the sample by titrant) to simulate the titration of weak and strong acids and bases (Figure 18.21). Some simulations use a master equation to calculate all points on the titration others use separate equations for different regions of the curve, for example before the equivalence point, at the equivalence point and after the equivalence point. The concentration of different species at a particular pH is calculated from [H (aq)l, and the volume of titrant required to produce that amount of each species is calculated. 

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