Equivalence point, in titration

Find the pH and volume (mL) of 0.0372 M NaOH needed to reach the equivalence point in titrations of... 

Calculate the pH at the equivalence point in titrating 0.100 M solutions of each of the following with 0.080 M NaOH (a) hy-drobromic acid (HBr), (b) chlorous acid (HCIO2), (c) benzoic acid (CgHjCOOH). 

We have already discussed two methods of locating the equivalence points in titrations (1) as the center of the vertical portion (i.e., the most rapid change of pH with titrant volume) of the curve and (2) the steepest point in the plot of titration curve slope (ApH/AV vs. pH). Both of these methods require that very precise and closely spaced data be taken in the vicinity of the equivalence point. 

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. 

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. 

The need for the indicator s color transition to occur in the sharply rising portion of the titration curve justifies our earlier statement that not every equivalence point has an end point. For example, trying to use a visual indicator to find the first equivalence point in the titration of succinic acid (see Figure 9.10c) is pointless since any difference between the equivalence point and the end point leads to a large titration error. 

The end point for this titration is improved by titrating to the second equivalence point, boiling the solution to expel CO2, and retitrating to the second equivalence point. In this case the reaction is Na2C03 + 2H3O+ -> CO2 + 2Na+ + 3H2O TRIS stands for tr/s-(hydroxymethyl)aminomethane. 

Where Is the Equivalence Point In discussing acid-base titrations and com-plexometric titrations, we noted that the equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. If you look back at Figures 9.8 and 9.28, you will see that for acid-base and com-plexometric titrations the inflection point is also in the middle of the titration curve s sharp rise (we call this a symmetrical equivalence point). This makes it relatively easy to find the equivalence point when you sketch these titration curves. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve s sharp rise. In this case the equivalence point is said to be asymmetrical. Example 9.12 shows how to calculate the equivalence point potential in this situation. 

From Figure 14.7, it should be clear that the only suitable indicator listed is methyl red. The other two indicators would change color too early, before the equivalence point. In general, for the titration of a weak base with a strong acid, the indicator should change color on the acid side of pH 7. 

This expression enables us to calculate the exact concentration at the equivalence point in any redox reaction of the general type given above, and therefore the feasibility of a titration in quantitative analysis. 

Boric acid behaves as a weak monoprotic acid with a dissociation constant of 6.4 x 10-10. The pH at the equivalence point in the titration of 0.2M sodium tetraborate with 0.2 M hydrochloric acid is that due to 0.1 M boric acid, i.e. 5.6. Further addition of hydrochloric acid will cause a sharp decrease of pH and any indicator covering the pH range 3.7-5.1 (and slightly beyond this) may be used suitable indicators are bromocresol green, methyl orange, bromophenol blue, and methyl red. 

A. Internal oxidation-reduction indicators. As discussed in Sections 10.10-10.16, acid-base indicators are employed to mark the sudden change in pH during acid-base titrations. Similarly an oxidation-reduction indicator should mark the sudden change in the oxidation potential in the neighbourhood of the equivalence point in an oxidation-reduction titration. The ideal oxidation-reduction indicator will be one with an oxidation potential intermediate between... 

Solutions as dilute as 0.001 M with respect to sulphate may be titrated with 0.01 M lead nitrate solution in a medium containing 30 per cent ethanol with reasonable accuracy. For solutions 0.01 M or higher in sulphate the best results are obtained in a medium containing about 20 per cent ethanol. The object of the alcohol is to reduce the solubility of the lead sulphate and thus minimise the magnitude of the rounded portion of the titration curve in the vicinity of the equivalence point. The titration is performed in the absence of oxygen at a... 

In conductometric titration the reaction is followed by means of conductometry there is little interest in the complete titration curve, but rather in the portion around the equivalence point in order to establish the titration endpoint. 

Again for the titration of Ce(IV) with Fe(II) we shall now consider constant-potential amperometry at one Pt indicator electrode and do so on the basis of the voltammetric curves in Fig. 3.71. One can make a choice from three potentials eu e2 and e3, where the curves are virtually horizontal. Fig. 3.74 shows the current changes concerned during titration at e1 there is no deflection at all as it concerns Fe(III) and Fe(II) only at e2 and e3 there is a deflection at A = 1 but only to an extent determined by the ratio of the it values of the Ce and Fe redox couples. The establishment of the deflection point is easiest at e2 as it simply agrees with the intersection with the zero-current abscissa as being the equivalence point in fact, no deflection is needed in order to determine this intersection point, but if there is a deflection, the amperometric method is not useful compared with the non-faradaic potentiometric titration unless the concentration of analyte is too low. 

A computer program has been used to calculate the magnitude of systematic errors incurred in the evaluation of equivalence points in hydrochloric acid titrations of total alkalinity and carbonate in seawater by means of Gran plots. Hansson [13] devised a modification of the Gran procedure that gives improved accuracy and precision. The procedure requires approximate knowledge of all stability constants in the titration. 

L (a) The two curves cross the point at which half of the total acetate is present as acetic acid and half is present as acetate ion. This is the half equivalence point in a titration, where pH = pK3 = 4.74. 

If the acid being titrated is a weak acid, then there are equilibria that will be established and accounted for in the calculations. (See the Utterly Confused section at the end of the chapter.) Typically, a plot of pH of the weak acid solution being titrated versus the volume of the strong base added (the titrant) starts at a low pH and gradually rises until close to the equivalence point in which the curve rises dramatically. After the equivalence point region, the curve returns to a gradual increase. We can see this in Figure 16-1. 

The final region of the titration curve is after the equivalence point. In this region, the material originally present in the container is limiting. The excess reagent, the material added, will affect the pH. If this excess reactant is a weak acid or a weak base, this will be a buffer solution. 

Before continuing with other examples, it is important to consider how the equivalence point in an acid-base titration is found and what relationship this has with titration curves. As we have said, the inflection point at the center of these curves occurs at the equivalence point, the point at which all of the substance titrated has been exactly consumed by the titrant. The exact position for this in the case... 

The BNC can be defined by a net proton balance with regard to a reference level -the sum of the concentrations of all the species containing protons in excess of the reference level, less the concentrations of the species containing protons in deficiency of the proton reference level. For natural waters, a convenient reference level (corresponding to an equivalence point in alkalimetric titrations) includes H20 and H2C03 ... 

The contents of the flask is cooled, filtered through cotton wool, washings done with DW and the filtrate diluted to about 350 ml with DW. This dilution is a must so as to avoid any interference caused by its inherent green colour with the estimation of the equivalence point in the titration as per the following chemical reaction ... 

The equivalence point in complexometric titrations is invariably observed by the help of pM indicators. The relationship amongst pM, concentrations of ligand, chelate complex and stability constant may be established by the following equations ... 

Titrations in non-aqueous solvents have been traditionally an important tool for the accurate determination of various pharmaceuticals, some acids in foods, use of some acids or bases in detergents, cosmetics and textile auxiharies, in the analysis of industrial process streams, the analysis of polymers [1-7]. The determination of the pK or pK values of organic compoimds with acidity or basicity constant less than 10 can only be reahsed in non-aqueous media. Although water has excellent solvent properties, it is not suitable for such organic compotmds since the pH jump at the equivalence point in aqueous solution carmot be evalrrated with reasonable accuracy, with this resrrlt, the end point carmot be found. Moreover, most of this compotmds ate not soluble in water. For these reasons, titration in non-aqueous media has recently acqttired great importance. It is now well known that non-aqueous titrations greatly depend on the solvents used [4, 8-13]. 

These titrations have pH values that are less than 7 at the equivalence point. The equivalence point in the titration shown in Figure 8.13, involving ammonia and hydrochloric acid, occurs at a pH of 5.27. Either methyl red or bromocresol green could be used as an indicator, but not phenolphthalein. 

In an acid-base titration, you carefully measure the volumes of acid and base that react. Then, knowing the concentration of either the acid or the base, and the stoichiometric relationship between them, you calculate the concentration of the other reactant. The equivalence point in the titration occurs when just enough acid and base have been mixed for a complete reaction to occur, with no excess of either reactant. As you learned in Chapter 8, you can find the equivalence point from a graph that shows pH versus volume of one solution added to the other solution. To determine the equivalence point experimentally, you need to measure the pH. Because pH meters are expensive, and the glass electrodes are fragile, titrations are often performed using an acid-base indicator. 

People often visualize the titration process using a graph that shows the concentration of base on one axis and the pH on the other, as in Figure 17-1. The interaction of the two concentrations traces out a titration curve, which has a characteristic s shape. At the equivalence point in Figure 17-1, the amount of base present is equal to the cunount of acid present in the solution. If you re using an indicator such as phenolphthalein, the equivalence point marks when the first permanent color change takes place. 

The text claims that precipitation of I is not complete before Cl- begins to precipitate in the titration in Figure 7-8. Calculate the concentration of Ag+ at the equivalence point in the titration of 1 alone. Show that this concentration of Ag+ will precipitate Cl... 

The pH at the equivalence point in the titration of any strong base (or acid) with strong acid (or base) will be 7.00 at 25°C. 

As we will soon discover, the pH is not 7.00 at the equivalence point in the titration of weak acids or bases. The pH is 7.00 only if the titrant and analyte are both strong. 

The pH at the equivalence point in this titration is 9.25. It is not 7.00. The equivalence-point pH will always be above 7 for the titration of a weak acid, because the acid is converted into its conjugate base at the equivalence point. 

The pH is always higher than 7 at the equivalence point In the titration of a weak acid with a strong base. 

Alkalinity is defined as the capacity of natural water to react with H+ to reach pH 4.5, which is the second equivalence point in the titration of carbonate (CO5 ) with H. To a good approximation, alkalinity is determined by OH-, CO j, and HCOf ... 

Acidity of natural waters refers to the total acid content that can be titrated to pH 8.3 with NaOH. This pH is the second equivalence point for titration of carbonic acid (H2C03) with OH-. Almost all weak acids in the water also will be titrated in this procedure. Acidity is expressed as millimoles of OH- needed to bring 1 L of water to pH 8.3. 

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