Of titrants

Up to 5 mL solvent is usually added per titration. Near the end point the mixture is shaken vigorously after each addition of titrant, and the appearance or disappearance of the f color in the organic layer is observed. 

The accuracy of a standardization depends on the quality of the reagents and glassware used to prepare standards. For example, in an acid-base titration, the amount of analyte is related to the absolute amount of titrant used in the analysis by the stoichiometry of the chemical reaction between the analyte and the titrant. The amount of titrant used is the product of the signal (which is the volume of titrant) and the titrant s concentration. Thus, the accuracy of a titrimetric analysis can be no better than the accuracy to which the titrant s concentration is known. 

For a titration to be accurate we must add a stoichiometrically equivalent amount of titrant to a solution containing the analyte. We call this stoichiometric mixture the equivalence point. Unlike precipitation gravimetry, where the precipitant is added in excess, determining the exact volume of titrant needed to reach the equivalence point is essential. The product of the equivalence point volume, Veq> and the titrant s concentration, Cq, gives the moles of titrant reacting with the analyte. 

Almost any chemical reaction can serve as a titrimetric method provided that three conditions are met. The first condition is that all reactions involving the titrant and analyte must be of known stoichiometry. If this is not the case, then the moles of titrant used in reaching the end point cannot tell us how much analyte is in our sample. Second, the titration reaction must occur rapidly. If we add titrant at a rate that is faster than the reaction s rate, then the end point will exceed the equivalence point by a significant amount. Finally, a suitable method must be available for determining the end point with an acceptable level of accuracy. These are significant limitations and, for this reason, several titration strategies are commonly used. 

Instead of measuring the titrant s volume we also can measure its mass. Since the titrant s density is a measure of its mass per unit volume, the mass of titrant and volume of titrant are proportional. 

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

The titration curve in Figure 9.1 is not unique to an acid-base titration. Any titration curve that follows the change in concentration of a species in the titration reaction (plotted logarithmically) as a function of the volume of titrant has the same general sigmoidal shape. Several additional examples are shown in Figure 9.2. 

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. 

Table 9.1), with the choice of buret determined by the demands of the analysis. The accuracy obtainable with a buret can be improved by calibrating it over several intermediate ranges of volumes using the same method described in Chapter 5 for calibrating pipets. In this manner, the volume of titrant delivered can be corrected for any variations in the buret s internal diameter. 

Titrations may be automated using a pump to deliver the titrant at a constant flow rate, and a solenoid valve to control the flow (Figure 9.5). The volume of titrant delivered is determined by multiplying the flow rate by the elapsed time. Automated titrations offer the additional advantage of using a microcomputer for data storage and analysis. 

Finally, for volumes of NaOH greater than the equivalence point volume, the pH is determined by the concentration of excess OH-. For example, after adding 30.0 mb of titrant the concentration of OH- is... 

Figure 9.8b shows a titration curve for a mixture consisting of two weak acids HA and HB. Again, there are two equivalence points. In this case, however, the equivalence points do not require the same volume of titrant because the concentration of HA is greater than that for HB. Since HA is the stronger of the two weak acids, it reacts first thus, the pH before the first equivalence point is controlled by the HA/A buffer. Between the two equivalence points the pH reflects the titration of HB and is determined by the HB/B buffer. Finally, after the second equivalence point, the excess strong base titrant is responsible for the pH. 

Titration curve for 50.00 ml of 0.100 M CH3COOH with 0.100 M NaOH showing the range of pHs and volumes of titrant over which the indicators bromothymol blue and phenolphthalein are expected to change color. 

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

Another method for finding the end point is to plot the first or second derivative of the titration curve. The slope of a titration curve reaches its maximum value at the inflection point. The first derivative of a titration curve, therefore, shows a separate peak for each end point. The first derivative is approximated as ApH/AV, where ApH is the change in pH between successive additions of titrant. For example, the initial point in the first derivative titration curve for the data in Table 9.5 is... 

Before the equivalence point, and for volumes of titrant in the titration curve s buffer region, the concentrations of HA and A are given by the following equations. 

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. 

CH3COOH with strong base ROH is determined from the difference in the amount of titrant needed to react with a blank consisting only of acetic anhydride, and the amount reacting with the sample. 

Combining the two conservation equations gives a single equation relating the moles of analyte to the moles of titrant. 

Earlier we noted that an acid-base titration may be used to analyze a mixture of acids or bases by titrating to more than one equivalence point. The concentration of each analyte is determined by accounting for its contribution to the volume of titrant needed to reach the equivalence points. 

Since the volume of titrant needed to reach a pH of 4.5 is more than twice that needed to reach a pH of 8.3, we know, from Table 9.8, that the alkalinity of the sample is controlled by and HCOa. ... 

Equivalent Weights Acid-base titrations can be used to characterize the chemical and physical properties of matter. One simple example is the determination of the equivalent weighf of acids and bases. In this method, an accurately weighed sample of a pure acid or base is titrated to a well-defined equivalence point using a mono-protic strong acid or strong base. If we assume that the titration involves the transfer of n protons, then the moles of titrant needed to reach the equivalence point is given as... 

When the concentrations of HA and A are equal, equation 9.9 reduces to = [HaO ]) ot pH = pKa. Thus, the piweak acid can be determined by measuring the pH for a solution in which half of the weak acid has been neutralized. On a titration curve, the point of half-neutralization is approximated by the volume of titrant that is half of that needed to reach the equivalence point. As shown in Figure 9.20, an estimate of the weak acid s piQ can be obtained directly from the titration curve. 

Scale of Operation In an acid-base titration the volume of titrant needed to reach the equivalence point is proportional to the absolute amount of analyte present in the analytical solution. Nevertheless, the change in pH at the equivalence point, and thus the utility of an acid-base titration, is a function of the analyte s concentration in the solution being titrated. 

---