Equivalence point determining

It has been shown that for most acid-base titrations the inflection point, which corresponds to the greatest slope in the titration curve, very nearly coincides with the equivalence point. The inflection point actually precedes the equivalence point, with the error approaching 0.1% for weak acids or weak bases with dissociation constants smaller than 10 , or for very dilute solutions. Equivalence points determined in this fashion are indicated on the titration curves in figure 9.8. 

Bimetallic alkoxides ( Meerwein salts ) have been known for more than 70 years, since the report made by Meerwein and Bersin [1101] on the formation of alkoxosalts (analogs of hydroxosalts MM m(OH)n) on titration of alcohol or benzene solutions of acidic alkoxides by those of basic ones to the equivalence points determined using the acid-base indicators ... 

The Gran Method is particularly valuable because, like most based on linear titrations, it yields straight line segments susceptible to least squares method analysis, which leads to great accuracy in equivalence point determination. 

A 1.00 mL sample of a fairly concentrated nitric acid solution is diluted to 200.00 mL. A 10.00 mL sample of the diluted solution requires 23.94 mL of a 0.0177 M solution of Ba(OH)2 to be titrated to the equivalence point Determine the molarity of the original nitric acid solution. 

The problem in any quantitative volumetric analysis for ions in solution is to determine accurately the equivalence point. This is often found by using an indicator, but in redox reactions it can often... 

The determinate error in a titration due to the difference between the end point and the equivalence point. 

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. 

In the overview to this chapter we noted that the experimentally determined end point should coincide with the titration s equivalence point. For an acid-base titration, the equivalence point is characterized by a pH level that is a function of the acid-base strengths and concentrations of the analyte and titrant. The pH at the end point, however, may or may not correspond to the pH at the equivalence point. To understand the relationship between end points and equivalence points we must know how the pH changes during a titration. In this section we will learn how to construct titration curves for several important types of acid-base titrations. Our... 

Before the equivalence point, HCl is present in excess and the pH is determined by the concentration of excess HCl. Initially the solution is 0.100 M in HCl, which, since HCl is a strong acid, means that the pH is... 

At the equivalence point the moles of HCl and the moles of NaOH are equal. Since neither the acid nor the base is in excess, the pH is determined by the dissociation of water. 

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... 

At the equivalence point, the moles of acetic acid initially present and the moles of NaOH added are identical. Since their reaction effectively proceeds to completion, the predominate ion in solution is CH3COO-, which is a weak base. To calculate the pH we first determine the concentration of CH3COO-. 

After the equivalence point NaOH is present in excess, and the pH is determined in the same manner as in the titration of a strong acid with a strong base. For example, after adding 60.0 mb of NaOH, 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. 

An end point for a titration is determined experimentally and represents the analyst s best estimate of the corresponding equivalence point. Any difference between an equivalence point and its end point is a source of determinate error. As we shall see, it is even possible that an equivalence point will not have an associated end point. 

Perhaps the most obvious limitation imposed by Ks is the change in pH during a titration. To see why this is so, let s consider the titration of a 50 mb solution of 10 M strong acid with equimolar strong base. Before the equivalence point, the pH is determined by the untitrated strong acid, whereas after the equivalence point the concentration of excess strong base determines the pH. In an aqueous solution the concentration of H3O+ when the titration is 90% complete is... 

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. 

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... 

A 0.2521-g sample of an unknown weak acid is titrated with a 0.1005 M solution of NaOH, requiring 42.68 mL to reach the phenolphthalein end point. Determine the compound s equivalent weight. Which of the following compounds is most likely to be the unknown weak acid ... 

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. 

Consider, for example, the determination of sulfurous acid, 1+2503, by titrating with NaOlT to the first equivalence point. Using the conservation of protons, we write... 

In the second limiting situation the analyte is a weaker acid or base than the interferent. In this case the volume of titrant needed to reach the analyte s equivalence point is determined by the concentration of both the analyte and the interferent. To account for the contribution from the interferent, an equivalence point for the interferent must be present. Again, if the acid dissociation constants for the analyte and interferent are significantly different, the analyte s determination is possible. If, however, the acid dissociation constants are similar, only a single equivalence point is found, and the analyte s and interferent s contributions to the equivalence point volume cannot be separated. 

The first task in calculating the titration curve is to determine the volume of EDTA needed to reach the equivalence point. At the equivalence point we know that... 

Before the equivalence point, Cd + is in excess, and pCd is determined by the concentration of free Cd + remaining in solution. Not all the untitrated Cd + is free (some is complexed with NH3), so we will have to account for the presence of NH3. Eor example, after adding 5.0 mL of EDTA, the total concentration of Cd + is... 

At the equivalence point, all the Cd initially present is now present as CdY -. The concentration of Cd, therefore, is determined by the dissociation of the CdY -complex. To find pCd we must first calculate the concentration of the complex, initial moles Cd McdVcd... 

After the equivalence point, EDTA is in excess, and the concentration of Cd + is determined by the dissociation of the CdY complex. Examining the equation for the complex s conditional formation constant (equation 9.15), we see that to calculate Ccd we must first calculate [CdY ] and Cedxa- After adding 30.0 mb of EDTA, these concentrations are... 

Before the equivalence point, pCd is determined by the excess concentration of free Cd +. Using values from Table 9.15, we plot pCd for 5.0 mL and 10.0 mL of EDTA (figure 9.28c). 

Before the equivalence point, the solution s electrochemical potential is determined by the concentration of excess Fe + and the concentration of Fe + produced by the titration reaction. Using values from Table 9.17, we plot E for 5.0 mb and 45.0 mb of titrant (Figure 9.35c). 

The equivalence point of a redox titration occurs when stoichiometrically equivalent amounts of analyte and titrant react. As with other titrations, any difference between the equivalence point and the end point is a determinate source of error. 

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