Titration curves linear segment

Concentration is not the only property that may be used to construct a titration curve. Other parameters, such as temperature or the absorbance of light, may be used if they show a significant change in value at the equivalence point. Many titration reactions, for example, are exothermic. As the titrant and analyte react, the temperature of the system steadily increases. Once the titration is complete, further additions of titrant do not produce as exothermic a response, and the change in temperature levels off. A typical titration curve of temperature versus volume of titrant is shown in Figure 9.3. The titration curve contains two linear segments, the intersection of which marks the equivalence point. 

Carter, K. N., Scott, D. M., Salomon, J. K., and Zarcone, G. S., Confidence Limits for the Abscissa of Intersection of Two Least-Squares Lines Such as Linear Segmented Titration Curves, Anal. Chem. 63, 1991, 1270-1278. 

The identicalness of the ionization sites in a linear polyelectrolyte (Tanford, 1961) stimulated the interest of Walter and Jacon (1994) in a possible relationship between Kz and M of ionic polysaccharides displaying the characteristic titration curve of a weak, monobasic acid. Without any theoretical assumption, Eq. (S.4) was derived from simple algebra by combining elementary principles of the dissociation theory of weak acids with polymer segment theory ... 

Linear titration curve — A type of -> titration curve in which a variable that is directly proportional to the concentration of the titrand and/or -> titrant, and/or a product of their chemical reaction is plotted as a function of the volume of titrant added. Thus, a linear titration curve generally consists of two linear segments that have to be extrapolated to intersect at a point that is associated with the equivalence point. The measurements are performed below and above the zone of the equivalence point and preferably away from this last point where nonlinear behavior is commonly found [i]. Linear titration curves are typical for - amperometric titrations, and - conductometric titrations, whereas - poten-tiometrc titrations yield nonlinear curves (- logarithmic titration curve). 

The change in absorbance of a solution may be used to follow the change in concentration of a radiationabsorbing constituent during a titration. The absorbance is directly proportional to the concentration of the absorbing constituents. A plot of absorbance versus titrant consists, if the reaction is complete, of two straight lines that intersect at the endpoint. If the reaction is appreciably incomplete, extrapolation of the two linear segments of the titration curve establishes the intersection and endpoint volume. 

In this chapter and several that follow, we deal exclusively with sigmoidal titration curves. We explore linear-segment curves in Section 26A-5. 

The vertical axis of a linear-segment titration curve is an instrument signal that is proportional to the concentration of the analyte or reagent. 

Spreadsheet Summary Amperometric titrations are the subject of the final exercise in Chapter 11 of Applications of Microsoft Excel in Analytical Chemistry. An amperometric titration to determine gold in an ore sample is used as an example. Titration curves consisting of two linear segments are extrapolated to find the end point. 

Amperometric titration A method based on applying a constant potential to a working electrode and recording the resulting current a linear segment curve is obtained. 

Linear segment curve A titration curve in which the end point is obtained by extrapolating linear regions well before and after the equivalence point useful for reactions that do not strongly favor the formation of products. 

A titration in which measurement of the current flowing at a voltammetric indicator electrode is used for detection of the equivalence point is termed an amperometric titration. The current measured is almost always a limiting current which is proportional to concentration, and can be due to the substance titrated, to the titrant itself, to a product of the reaction, or to any two of these—depending on the potential of the electrode and the electrochemical characteristics of the chemical substances involved. The titration curve is a plot of the limiting current, corrected for dilution by the reagent and, if necessary, for any residual current, as a function of the volume of titrant. Ideally, the titration curve consists of two linear segments which intersect at the equivalence point. 

Kinetic titration curves are constructed by plotting the relative analytical signal (absorbance, fluorescence, potential, or temperature) as a function of the volume of titrant added. If the two parameters are linearly related, then the titration curve will consist of two linear segments that can be extrapolated to intersect at the endpoint, as shown in Figure 4. Current instrumentation permits the use of automatic or semiautomatic devices capable of delivering the titrant and continuously monitoring the signal obtained. The time elapsed between the start of the titration and the endpoint is known as the pseudoinduction period and is proportional to the inhibitor concentration. These automated procedures are quite rapid and reproducible. 

The volumes of the increments of the thiosulphate solution added are reduced near the equivalence point. The titration is continued after the endpoint until a group of consecutive data readings display no change. Linear regression lines are fitted to the linear segments of the absorbance curve immediately before and after the end point. The intersection of the two regression lines marks the endpoint. 

Logarithmic titration curve — A sigmoidal shaped -> titration curve in which the cell voltage or a p-function of the titrand or titrant is plotted as a function of the volume of titrant added. The most important measurements are confined near and surrounding the middle segment of the sigmoid in which the equivalence point is found [i]. See also linear titration curve. Ref [i] Harris D (2002) Quantitative chemical analysis. WH Freeman, New York... 

---