Gran function

The beauty of a Gran plot is that it enables us to use data taken before the end point to find the end point. The slope of the Gran plot enables us to find Ka. Although we derived the Gran function for a monoprotic acid, the same plot (VbIO-PH versus Vb) applies to polyprotic acids (such as H6A in Figure 11-6). 

The Gran function. Vb10 PH, does not actually go to 0. because 10 ph is never 0. The curve must be extrapolated to find Ve. The reason the function does not reach 0 is that we have used the approximation that every mole of OH generates 1 mol of A, which is not true as Vb approaches Ve. Only the linear portion of the Gran plot is used. 

Figure 11-8 Gran plot for the first Challenge Show that when weak base. B. is titrated with a strong acid, the Gran function is...

Figure 3. E.m.f. titration curve for 154 grams sea water with v ml. (0.1000M HCl 4- 0.4483M NaCl). E (mv.) for the cell reference elec-trode solution glass electrode vs. v (ml). Fl9 F2, and are Gran functions for finding the equivalence points vl9 v2 (corresponding to Pt and 2 in Figure 2) (7)...

Barnard T. E. and Bisogni J. J. (1985) Errors in Gran function analysis of titration data for dilute acidified waters. Water Res. 19, 393-399. 

Figure 20-4 shows the titration data V and column C contains the formula =10 (-(E-offset)/slope). Figure 20-5 shows the linear relationship between the Gran function (column C in Figure 20-4) and the volume. 

Figure 4.13. Emf titration curve for 154 g of seawater with v milliliters (0.1000 M HCl plus 0.4483 M NaCl) characterization of equivalence points by the Gran method. F, Fj, and F3 are Gran functions, and n, is an arbitrary scale factor. For finding the equivalence points Vx and corresponding to / = 1 and/= 0, respectively. (From Dryssen and Sillen, 1%7.)...

Fig. 5.9-2 The Gran plots for the titration curve of Fig. 5.9-1. The Gran functions are hV,/ksIZ, (o r G ra n I,and lctlhiorGran2.

This system was also used to Implement the photometric titration of calcium in the presence of a higher concentration of magnesium reported by Jagner [78]. Calcium was titrated with EGTA at pH 8.6. A small amount of Zn-EGTA was also used and the decrease In the calcium concentration was followed by the simultaneous titration of zinc with Zincon as Indicator. The experimental data for absorbance vs. titrant volume added (v) were linearized by the Gran function [64]... 

The unknown copper concentration was calculated using the modified Gran function with iteration procedure. 

Because the equation describing the electrode potential in the presence of thiosulphate ions is more complicated than the simple Nernst equation the usual Gran method must be modified. The Gran function has the form ... 

At constant ionic strength, we can define the weak acid Gran function... 

Figure 7-2. Calculated titration curve and its Gran plot for 0.100 M NH4 with NaOH, 0.100 M. Here F is the acid, or the base Gran function.

Figure 7-5. Titration of 100.0 ml of hydroxide-carbonate mixture with 0.2062 HCl. (a) pH vs. ml titration curve, (b) Gran function plots revealing three equivalence points 18.7 ml, and two further segments of 10.3 ml each.

Total dissolved inorganic carbon can also be evaluated from the potentiometric titration method described in Section 8.4.1, if it is performed in a closed cell. However, this technique does not give the highest precision possible and thus the coulometiic method first described by Johnson et al. (1985) and outlined here is nowadays the method of choice. Nevertheless, Ct can be evaluated from the potentiomettic titration curve, either Gran function linearization (Section 8.4.2.3 Gran evaliiation ) or by a curve fitting procedure (Section 8.4.2.3 Non-linear curve-fitting ). 

Instead of the 10 ml of water in the blank determination described above, the sample solution to be investigated is used here. Otherwise, the procedure is exactly the same as before. Silver nitrate solution is added to the sample solution until the same potential as that found in the blank determination is attained. Here also the Gran function is plotted to an excess of about 0.5 ml silver nitrate solution. The chloride content of the solution can then be read directly off the graph from the point where the curve intersects the volume axis (in ppm for a titer of 1.00 ppm/ml). The previously determined blank value is then subtracted from this number. 

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