Gran’s method

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). 

In this chapter you ll learn how to calculate species distributions of polyprotic weak acid species, how to apply Gran s method for the estimation of end-points in titrations and a general method for the calculation of titration curves. 

The location of the end-point of a titration by using either the first or second derivative of the titration data was discussed in Chapter 9. These methods use only the data points near the end-point. Another approach. Gran s method, makes use of the complete data set. It is useful when either (i) the inflection at the end-point is poorly defined or (ii) data at the end-point is missing. 

Gran.xls illustrates the use of Gran s method to find the equivalence point of a titration. 

The acid-base equilibrium constants of the beta-blockers atenolol, oxprenolol, timolol, and labetalol were determined by automated potentiometric titrations. The pKg values were obtained in water-rich or water methanol medium (20% MeOH) to obviate the solubility problems associated with the compounds. The initial estimates of pKa values were obtained from Gran s method and then, were refined by the NYTIT and ZETA versions of the LETAGROP computer program. The resultant values were 9.4 (/ = 0.1 M KCI, 20% methanol) for atenolol, 9.6 (/ = 0.1 M KCI) for oxprenolol, 9.4 (/ = 0.1 M KCI, 20% methanol) for timolol and 7.4 and 9.4 (/ = 0.1 M KCI) for labetalol. The potentiometric method was found to be accurate and easily applicable. The operational criteria for applying the methodology are indicated. 

The acidity constants of streptomycin were determined at 25 °C by potentiometry with an automatic system in aqueous medium at a constant ionic strength of 0.1 M. The acidity constants were calculated by algoridrms based on material balance equations. Experimental data were analyzed using Gran s method. Values of 7.84 (pX i), 11.54 (pX ), and >12 (P-K33) were found."... 

Table 3. Application of Gran s method with successive iteration. Synthetic cobalt plating bath. 

MacDonald, T. J., B. J. Barker, and J. A. Caruso, J. Chem. Ed., 49, 200 (1972). This article and the one by Kozarek and Fernando describe applications of Gran s method using the approximate equations only. 

Unfortunately, the equivalence point of a titration reaction is the least quantitative one, as we demonstrated in the preceding section. This is why logarithmic titrations are the most sensitive to the extent of the titration reaction. This is not the case for linear titrations. Let s first recall that linear titrations are those in which the dependent variable (the registered one) is directly proportional to the fraction titrated or to the concentration of the independent variable (in no case to the logarithm of its concentration or of its activity). Of course, the independent variable may be the activity rather than the concentration. Examples of linear titrations are spectrophoto-metric, amperometric, thermometric titrations, and so forth. This is the reason why Gran s method is interesting. Indeed, its principle involves the linearization of the logarithmic titration curves. 

However, an inconsistency remains The ordinate is never null regardless of the titration stage, since [H3O+] never tends toward zero The reason for this is as follows Gran s method is based on the expression of ATa only. It does not take into... 

The main advantage of Gran s method is to limit the titration error that might be due to the use of a neutralization reaction that is too equilibrated. Indeed, the straight line involved in Gran s method is drawn from the first points of the titration, for which, as we have demonstrated, the neutralization reaction is the most quantitative. 

Gran s method is based on the idea that a linear titration curve is obtained if the concentration of the indicated ion is plotted rather than the corresponding electrode EMF. This is due to the simple relationship Titration with 10% of the equivalence volume = 10% less free ion in solution 50% equivalence volume titrated = 50% less 100% titrated = no free measured ion in solution. With titrations followed by conductance measurements a direct proportionality (not logarithmic, as with EMF measurements) is obtained between the measured ion concentration and the conductance, resulting in linear concentration curves which can be extrapolated. To get the concentration corresponding to a particular EMF one can either use a suitable calibration curve, or read the concentrations directly off of a logarithmically divided instrument scale. The empirical Nernst equation can also be mathematically manipulated into a suitable form ... 

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