Titration curves analysis

Bashford, D., Karplus, M. Multiple-site titration curves of proteins an analysis of exact and approximate methods for their calculation. J. Phys. Chem. 95 (1991) 9556-9561. 

Derivative methods are particularly well suited for locating end points in multi-protic and multicomponent systems, in which the use of separate visual indicators for each end point is impractical. The precision with which the end point may be located also makes derivative methods attractive for the analysis of samples with poorly defined normal titration curves. 

Now that we know something about EDTA s chemical properties, we are ready to evaluate its utility as a titrant for the analysis of metal ions. To do so we need to know the shape of a complexometric EDTA titration curve. In Section 9B we saw that an acid-base titration curve shows the change in pH following the addition of titrant. The analogous result for a titration with EDTA shows the change in pM, where M is the metal ion, as a function of the volume of EDTA. In this section we learn how to calculate the titration curve. We then show how to quickly sketch the titration curve using a minimum number of calculations. 

The scale of operations, accuracy, precision, sensitivity, time, and cost of methods involving redox titrations are similar to those described earlier in the chapter for acid-base and complexometric titrimetric methods. As with acid-base titrations, redox titrations can be extended to the analysis of mixtures if there is a significant difference in the ease with which the analytes can be oxidized or reduced. Figure 9.40 shows an example of the titration curve for a mixture of Fe + and Sn +, using Ce + as the titrant. The titration of a mixture of analytes whose standard-state potentials or formal potentials differ by at least 200 mV will result in a separate equivalence point for each analyte. 

The titration curve for a precipitation titration follows the change in either the analyte s or titrant s concentration as a function of the volume of titrant. For example, in an analysis for V using Ag+ as a titrant... 

In a titrimetric method of analysis the volume of titrant reacting stoichiometrically with the analyte provides quantitative information about the amount of analyte in a sample. The volume of titrant required to achieve this stoichiometric reaction is called the equivalence point. Experimentally we determine the titration s end point using a visual indicator that changes color near the equivalence point. Alternatively, we can locate the end point by recording a titration curve showing the titration reaction s progress as a function of the titrant s volume. In either case, the end point must closely match the equivalence point if a titration is to be accurate. Knowing the shape of a titration... 

A quantitative analysis for NH3 in several household cleaning products is carried out by titrating with a standard solution of HGl. The titration s progress is followed thermometrically by monitoring the temperature of the titration mixture as a function of the volume of added titrant. Household cleaning products may contain other basic components, such as sodium citrate or sodium carbonate, that will also be titrated by HGl. By comparing titration curves for prepared samples of NH3 to titration curves for the samples, it is possible to determine that portion of the thermometric titration curve due to the neutralization of NH3. 

Potentiometric titration curves are used to determine the molecular weight and fQ or for weak acid or weak base analytes. The analysis is accomplished using a nonlinear least squares fit to the potentiometric curve. The appropriate master equation can be provided, or its derivation can be left as a challenge. 

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. 

Calculate or sketch (or both) titration curves for the following (unbalanced) redox titration reactions at 25 °C. Assume that the analyte is initially present at a concentration of 0.0100 M and that a 25.0-mL sample is taken for analysis. The titrant, which is the underlined species in each reaction, is 0.0100 M. 

It was indicated that the original method can be extended on systems where two or three analytes can be determined from a single titration curve. The shifts DpH affected by j-th PT addition should be sufficiently high it depends on pH value, a kind and concentration of the buffer chosen and its properties. The criterion of choice of the related conditions of analysis has been proposed. A computer program (written in MATLAB and DELPHI languages), that enables the pH-static titration to be done automatically, has also been prepared. 

The plot of pH against titrant volume added is called a potentiometric titration curve. The latter curve is usually transformed into a Bjerrum plot [8, 24, 27], for better visual indication of overlapping pKiS or for pffjS below 3 or above 10. The actual values of pKa are determined by weighted nonlinear regression analysis [25-27]. 

In routine analysis, often a one-dimensional so-called end-point titration can be automatically carried out up to a pre-set pH or potential value and with a previously chosen overall titration velocity in order to avoid overshoot, the inflection point should be sufficiently sharp and the titrant delivery must automatically diminish on the approach to that point in order to maintain equilibrium, and stop in time at the pre-set value. For instance, the Metrohm 526 end-point titrator changes both the dosing pulse length and its velocity by means of a pulse regulator in accordance with the course of the titration curve in fact, the instrument follows the titration two-dimensionally, but finally reports only a one-dimensional result. The Radiometer ETS 822 end-point titration system offers similar possibilities. However, automated titrations mostly represent examples of a two-dimensional so-called eqilibrium titration, where the titration velocity is inversely proportional to the steepness of the potentiometric titration curve hence the first derivative of the curve can usually also be recorded as a more accurate means of determining the inflection... 

Analysis of equivalence volumes from titration curve minima. 

The same analysis can be conducted using a pH meter to detect the end point as shown in Figure 10.1, which illustrates a titration curve. A... 

The titrimetric determination of soil constituents is most commonly applied to a limited number of soil analyses, namely, organic carbon, nitrogen compounds, carbonates, and chlorides. Determination of acid content by titration is generally not done because the titration curves are not amenable to typical titration analysis. Because of the color of soil and the fact that it is a suspension when stirred, it is often necessary to remove the constituent of interest before titration. In other cases, it is possible to do a direct titration using an appropriate indicator. However, even in these cases, detection of the end point is difficult. 

Discuss the four typical amperometric titration curves obtained in amperometric method of analysis and examine them critically with appropriate examples. 

Under ideal conditions, the determination of the endpoint of a titration is simple. It can be accomplished by using an appropriate indicator or by straightforward analysis of a pH titration curve, e.g. through the detection of the inflection point of the pH vs. addition curve. Often the requirement of ideal conditions is not met, and so application of the above methods will result in approximations only. Proper numerical analysis of titration curves is possible and will result in significantly improved outcomes. 

Whatever the aim of a particular titration, the computation of the position of a chemical equilibrium for a set of initial conditions (e.g. total concentrations) and equilibrium constants, is the crucial part. The complexity ranges from simple 1 1 interactions to the analysis of solution equilibria between several components (usually Lewis acids and bases) to form any number of species (complexes). A titration is nothing but a preparation of a series of solutions with different total concentrations. This chapter covers all the requirements for the modelling of titrations of any complexity. Model-based analysis of titration curves is discussed in the next chapter. The equilibrium computations introduced here are the innermost functions required by the fitting algorithms. 

For the determination of the dissociation constant in the excited state, several methods have been used the Forster cycle,(109 m) the fluorescence titration curve/113 the triplet-triplet absorbance titration curve,014 but all involve the assumption that the acid-base equilibrium may be established during the lifetime of the excited state, which is by no means a common occurrence. A dynamic analysis using nanosecond or picosecond time-resolved spectroscopy is therefore often needed to obtain the correct pK a values.1(n5)... 

In [LJ-control maps the substitution of one ligand by another one results in a change of the range of existence of the manifold intermediates. This change can be expressed by the ligand-property imluced shift of the titration curves identified by the relative position of their inflection points Lq s on the log (lL o/[Ni)Q) scale. These characteristic shifts provide information on the thermodynamic selectivity governed by the association processes only. This type of analysis is designated by . 

In their applications of A.C. oscillopolarographic titration for pharmaceutical analysis, Huang et al. reported a method for the titration of procaine hydrochloride with sodium tetraphenylborate [62]. Procaine hydrochloride was mixed with sodium tetraphenylborate in acetate buffer (pH 4.6). The precipitate was filtered off, and the unconsumed tetraphenylborate titrated with thallium sulfate by A.C. oscillo-polarography. The recovery was found to be 99.9 to 100.0%, and the coefficient of variation (n = 10) was 0.19%. The method could also be used to identify outdated samples of procaine hydrochloride injection solution, as its loss of water solubility is indicated by an incision in the titration curve. 

If you already use a spreadsheet, you can skip this section. The computer spreadsheet is an essential tool for manipulating quantitative information. In analytical chemistry, spreadsheets can help us with calibration curves, statistical analysis, titration curves, and equilibrium problems. Spreadsheets allow us to conduct what if experiments such as investigating the effect of a stronger acid or a different ionic strength on a titration curve. We use Microsoft Excel in this book as a tool for solving problems in analytical chemistry. Although you can skip over spreadsheets with no loss of continuity, spreadsheets will enrich your understanding of chemistry and provide a valuable tool for use outside this course. 

R. de Levie, A General Simulator for Add-Base Titrations, J. Chem. Ed. 1999, 76, 987 R. de Levie, Explicit Expressions of the General Form of the Titration Curve in Terms of Concentration, J. Chem. Ed. 1993, 70, 209 R. de Levie, General Expressions for Add-Base Titrations of Arbitrary Mixtures, Anal. Chem. 1996, 68, 585 R. de Levie, Principles ctf Quantitative Chemical Analysis (New York McGraw-Hill, 1997). 

The Student Web Site, www.whfreeman.com/cica7e, has directions for experiments that may be reproduced for your use. At this Web site, you will also find lists of experiments from the Journal of Chemical Education, a few downloadable Excel spreadsheets, and a few Living Graph Java applets that allow students to manipulate graphs by altering data points and variables. Supplementary topics at the Web site include spreadsheets for precipitation titrations, microequilibrium constants, spreadsheets for redox titration curves, and analysis of variance. 

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