Gran plots

For volumes of titrant before the equivalence point, a plot of Vb X [H3O+] versus Vb is a straight line with an x-intercept equal to the volume of titrant at the end point and a slope equal to Results for the data in Table 9.5 are shown in Table 9.6 and plotted in Figure 9.13d. Plots such as this, which convert a portion of a titration curve into a straight line, are called Gran plots. 

A second approach for determining the piQ of an acid is to replot the titration curve in a linear form as a Gran plot. For example, earlier we learned that the titration of a weak acid with a strong base can be plotted in a linear form using the following equation... 

This short paper describes a modification to the traditional Gran plot for determining the concentration of a weak acid in the presence of a strong acid. 

Directions are provided in this experiment for determining the dissociation constant for a weak acid. Potentiometric titration data are analyzed by a modified Gran plot. The experiment is carried out at a variety of ionic strengths and the thermodynamic dissociation constant determined by extrapolating to zero ionic strength. 

The following data were collected with an automatic titrator during the titration of a monoprotic weak acid with a strong base. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for this data, and locate the equivalence point for each. 

Schwartz has published some hypothetical data for the titration of a 1.02 X ICr" M solution of a monoprotic weak acid (pXa = 8.16) with 1.004 X ICr M NaOH. " A 50-mL pipet is used to transfer a portion of the weak acid solution to the titration vessel. Calibration of the pipet, however, shows that it delivers a volume of only 49.94 ml. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for these data, and determine the equivalence point for each. How do these equivalence points compare with the expected equivalence point Comment on the utility of each titration curve for the analysis of very dilute solutions of very weak acids. 

Meloun, M. Havel, J. Hogfeldt, E. Computation of Solution Equilibria. Ellis Horwood Limited Chichester, England, 1988. The following paper provides additional information about the use of Gran plots. 

Schwartz, L. M. Advances in Acid-Base Gran Plot Methodology, /. Chem. Educ. 1987, 64, 947-950. 

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)... 

Gran-plot (multiple standard addition with 10iE/s vs. concentration) 0.1-3% 0-1-3% less accurate if interfering ions are present best results if many points between 30 and 80% of a titration curve are evaluated and discordant points are eliminated... 

Gran plot for titration of a strong acid with a strong base. If to V ml of a strong acid (concentration CA) V ml of a strong base (concentration Cb) have been added, CH + will be given by... 

Gran plots for other types of titrations. Gran64 gave the equations for dibasic acid titration and for precipication, complex-formation and redox titrations especially for the precipitation and complex-formation titrations the equations are complicated. 

A special advantage of the Gran plot is that it lends itself extremely well to computerized automation and data treatment. 

A computer program has been used to calculate the magnitude of systematic errors incurred in the evaluation of equivalence points in hydrochloric acid titrations of total alkalinity and carbonate in seawater by means of Gran plots. Hansson [13] devised a modification of the Gran procedure that gives improved accuracy and precision. The procedure requires approximate knowledge of all stability constants in the titration. 

To appreciate that an ISE must be selective if its measurements are to be useful, and how the Nernst equation can be adapted to take account of the ISE selectivity by using the concept of a selectivity coefficient (or ratio ). To leam how the problems of selectivity can be overcome by using a standard-addition method, such as drawing a Gran plot - one of the more useful of such methods. 

Errors Caused by Low Precision of Volume Determination Use of Gran Plots... 

We sometimes find that the end point is still elusive, even with due care and patience. In such cases, a Gran plot may help - a plot of log,o (emf) against volume will be linear (or at least, passably linear), and the volume at equivalence is then given by the intercept on the jc-axis. 

Figure 4.9 Gran plot of electrode potential E against volume of silver ion (O), used to determine the solubility constant of AgCl. E is obtained from the emf of the cell, reference electrode Ag ISE , where the ion-selective electrode is a solid-state ISE based on AgjS. The ISE is immersed in a stirred solution of KCl (of initial concentration 5 X 10 mol dm ) the volume values on the jc-axis relate to the aliquots of added AgN03 (of concentration 2 x 10 mol dm ). The antilog trace ( ) is clearly proportional to the volume of AgNOs added. From Christian, G.D., Analytical Chemistry, 5th Edn, Wiley, 1994. Reprinted by permission of John Wiley Sons, Inc.

Note how the Gran plot in Figure 4.9 is curved at intermediate and small addition levels, thus making adjustment quite difficult. Such curvature is best taken to indicate that a complication is present, e.g. that the precipitate has an appreciable solubility (when determining Kf) or that dissociation of a complex has occurred (when trying to measure Kcompiexation)-... 

Figure 4.10 shows a Gran plot which can be used for such a situation. In this figure, the addition values on the right-hand side of the abscissa represent the volumes (i.e. the known additions) of contaminant brought about by adding, e.g. small amounts of hydroxide to a solution in which a fluoride ISE is immersed. The intercept of the plot on the left-hand side represents the equivalent amount of hydroxide within the sample prior to the multiple standard addition process. This intercept tells us the concentration of hydroxide. Therefore, knowing [OH ], we... 

When the electrode is an ISE, poor selectivity can impair the final value of the concentration that is determined, in which case a Gran plot is constructed in order to correct for the way that the emf comprises various contributory components. 

Experimentally, an analyst will run several standards (at constant AEj to calibrate the analysis, and will then determine the amounts of analyte in solution. A standard additions method such as a Gran plot will further enhance the accuracy of measurement (e.g. see Section 4.3.2). 

At extreme overpotentials, the current is independent of potential. This maximum current is said to be limiting, that is, current a Cbuik- It is termed the diffusion current, /j. The dependence of la on concentration, drop speed, etc., is described by the Ilkovic equation (equation (6.5)), although calibration graphs or standard addition methods (Gran plots) are preferred for more accurate analyses. 

Gran plot A commonly employed multiple-addition method, used to correct for unknown amounts of contaminant and for dilution errors (see Section 4.3.2). 

Hence, the Gran plot is obtained by plotting against the volume (see fig. 5.2). To facilitate this procedure, a special semi-antilogarithmic paper is... 

A drawback of Gran plots is the fact that all deviations from the theoretical slope value cause an error and that side reactions are not considered. The method was modified by Ingman and Still [63], who considered side reactions to a certain degree, but the equilibrium constants and the concentrations of the components involved must be known. The Gran method is, however, advantageous for determinations in the vicinity of the determination limit The extrapolation of the linear dependence yields the sum + c, where c, is the residual concentration of the test component produced by impurities, dissolution of the ISE membrane, etc. 

The fluoride ion selective electrode is the most popular means of fluoride ion determination after sample destruction by any method but it does have limitations. It can be used either directly to measure the fluoride potential6 or as an end-point detector in a potentiometric titration with a lanthanum(l II) reagent as titrant.4,7 Problems can be experienced with potential drift in direct potentiometry, especially at low fluoride ion concentrations. Titration methods often yield sluggish end points unless water miscible solvents are used to decrease solubilities and increase potentia 1 breaks and sulfate and phosphate can interfere. End-point determination can be facilitated by using a computerized Gran plotting procedure.4... 

The first important documentation in the spreadsheet is the name of the file. A name such as Expt 9 Gran Plot" is much more meaningful than "Dan s Lab . The next important feature is a title at the top of the spreadsheet, which tells its purpose. To remind ourselves what formulas were used in the spreadsheet, we added text (labels) at the bottom. In cell A14, write "Formula and in cell A15 write C5 = A 6+ A 8 B5 + A 10 B5A2+ A 12 B5A3 . This documentation tells us how numbers in column C were calculated. 

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