Progress of a titration

A graph showing the progress of a titration as a function of the volume of titrant added. 

PROBLEM 6.16.3. Sketch curves for the progress of a titration of 50 mL of 2 x 10 4 M acetic acid, a weak acid (Ka 1.75 x 10 4mol/L), with a strong base, 4 x 10-4 M NaOH. The equivalence point of the titration will be reached when 25 mL of NaOH will have been added. The following regions require different equations to be solved ... 

McGraw-Hill, 1997, and even some remnants of my Spreadsheet Workbook for Quantitative Chemical Analysis, McGraw-Hill, 1992. This is partially because I have retained some of the didactic innovations introduced in these earlier texts, such as an emphasis on the progress of a titration rather than on the traditional titration curve, the use of buffer strength rather than buffer value, and the use of the abbreviations h and A in the description of electrochemical equilibria. However, the present text exploits the power of Excel to go far beyond what was possible in those earlier books. 

The progress of a titration is represented by plotting the pH of the solution versus the volume of added titrant the resulting graph is called a pH curve or titration curve... 

Finding the End Point by Monitoring Temperature The reaction between an acid and a base is exothermic. Heat generated by the reaction increases the temperature of the titration mixture. The progress of the titration, therefore, can be followed by monitoring the change in temperature. 

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... 

Titration is the analytical method used to determine the amount of acid in a solution. A measured volume of the acid solution is titrated by slowly adding a solution of base, typically NaOH, of known concentration. As incremental amounts of NaOH are added, the pH of the solution is determined and a plot of the pH of the solution versus the amount of OH added yields a titration curve. The titration curve for acetic acid is shown in Figure 2.12. In considering the progress of this titration, keep in mind two important equilibria ... 

This method is primarily concerned with the phenomena that occur at electrode surfaces (electrodics) in a solution from which, as an absolute method, through previous calibration a component concentration can be derived. If desirable the technique can be used to follow the progress of a chemical reaction, e.g., in kinetic analysis. Mostly, however, potentiometry is applied to reactions that go to completion (e.g. a titration) merely in order to indicate the end-point (a potentiometric titration in this instance) and so do not need calibration. The overwhelming importance of potentiometry in general and of potentiometric titration in particular is due to the selectivity of its indication, the simplicity of the technique and the ample choice of electrodes. 

A solution of a weak base is titrated with a solution of a standard strong acid. The progress of the titration is followed with a pH meter. Which of the following observations would occur ... 

The progress of the titration is monitored by plotting the jj values versus the added volume of a known concentration in the solution. 

In a typical acid-base titration (Section 3.10), a solution containing a known concentration of base (or acid) is added slowly from a buret to a second solution containing an unknown concentration of acid (or base). The progress of the titration is monitored, either by using a pH meter (Figure 16.6a) or by observing the color of a suitable acid-base indicator. With a pH meter, you can record data to produce a pH titration curve, a plot of the pH of the solution as a function of the volume of added titrant (Figure 16.6b). 

Consider the redox titration of 120.0 mL of 0.100 M FeS04 with 0.120 M K Cr Oy at 25°C, assuming that the pH of the solution is maintained at 2.00 with a suitable buffer. The solution is in contact with a platinum electrode and constitutes one half-cell of an electrochemical cell. The other half-cell is a standard hydrogen electrode. The two half-cells are connected with a wire and a salt bridge, and the progress of the titration is monitored by measuring the cell potential with a voltmeter. 

End point (of a titration) — An experimental point in the progress of a titrimetric reaction located where the reaction between the -> analyte and reagent is considered as complete. Ideally, it should be coincident to the - equivalence point [i]. 

Fortunately, there is such a method, which is both simple and generally applicable, even to mixtures of polyprotic acids and bases. It is based on the fact that we have available a closed-form mathematical expression for the progress of the titration. We can simply compare the experimental data with an appropriate theoretical curve in which the unknown parameters (the sample concentration, and perhaps also the dissociation constant) are treated as variables. By trial and error we can then find values for those variables that will minimize the sum of the squares of the differences between the theoretical and the experimental curve. In other words, we use a least-squares criterion to fit a theoretical curve to the experimental data, using the entire data set. Here we will demonstrate this method for the same system that we have used so far the titration of a single monoprotic acid with a single, strong monoprotic base. 

The progress of the titration of a solution of volume 1/M and concentration CM of metal ions with a volume VL of titrant solution containing a concentration CL of free ligand L then follows as... 

In TT, temperature changes occur only when titration is in progress and when there is sample reactant present. As a consequence, the start and endpoint of a titration are readily observed, and the number of moles titrated is calculated as in regular titrimetry. By determining the heat capacity of the system under study, heats of reaction can be readily determined. In addition, equilibrium constants can be evaluated under the appropriate conditions. 

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