Second Equivalence Point

This is the potential value of a solution of the ampholyte VO +. Between the first and second equivalence points, the general equation of the curve (17.22) can be reduced to 

From the chemical standpoint, these results mean that the sole reaction evolving is 

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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 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. 

Thus, if we titrate a monoprotic weak acid with a strong base, the EW and FW are identical. If the weak acid is diprotic, however, and we titrate to its second equivalence point, the FW will be twice as large as the EW. 

If the weak acid is monoprotic, then the FW must be 58.78 g/mol, eliminating ascorbic acid as a possibility. If the weak acid is diprotic, then the FW may be either 58.78 g/mol or 117.6 g/mol, depending on whether the titration was to the first or second equivalence point. Succinic acid, with a formula weight of 118.1 g/mol is a possibility, but malonic acid is not. If the analyte is a triprotic weak acid, then its FW must be 58.78 g/mol, 117.6 g/mol, or 176.3 g/mol. None of these values is close to the formula weight for citric acid, eliminating it as a possibility. Only succinic acid provides a possible match. 

There are two ways in which the sensitivity can be increased. The first, and most obvious, is to decrease the concentration of the titrant, since it is inversely proportional to the sensitivity, k. The second method, which only applies if the analyte is multiprotic, is to titrate to a later equivalence point. When H2SO3 is titrated to the second equivalence point, for instance, equation 9.10 becomes... 

To the second equivalence point NaOH + NaH2P04------> Na2HP04 + H20... 

To reach the second equivalence point means titrating 0.550 mmol H2P04, which requires an additional volume of titrant given by... 

Why does the titration curve of sodium carbonate have two inflection points Why does this titration require that the solution be boiled as you approach the second equivalence point Why can bromcresol green be used as the indicator and not phenolphthalein ... 

Describe the chemistry that occurs in each of the following regions in curve (a) in Figure 7-8 (i) before the first equivalence point (ii) at the first equivalence point (iii) between the first and second equivalence points (iv) at the second equivalence point and (v) past the second equivalence point. For each region except (ii), write the equation that you would use to calculate [Ag4 ]. 

The volume at the second equivalence point must be 2Ve, because the second reaction requires the same number of moles of HCI as the first reaction. 

At the second equivalence point, we have made BH which can be treated as a monoprotic weak acid. 

Point E is the second equivalence point, at which the solution is formally the same as one prepared by dissolving BH2C12 in water. The formal concentration of BHj4 is... 

There is no perceptible break at the second equivalence point (J), because BH 4 is too strong an acid (or, equivalently, BH is too weak a base). As the titration approaches low pH (S3), ... 

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. 

Table 11-6 gives useful equations derived by writing a charge balance and substituting fractional compositions for various concentrations. For titration of the diprotic acid, H2A, ct> is the fraction of the way to the first equivalence point. When = 2, we are at the second equivalence point. It should not surprise you that, when cj> = 0.5, pH = pAj and, when = 1.5, pH pAT2. When = 1, we have the intermediate HA " and pH j(pAj -I- pA j). 

Halfway Between the First and Second Equivalence Points At this point, half the HA has been converted to A- because of the neutralization reaction... 

At the Second Equivalence Point At this point, we have added enough NaOH to convert all the HA to A-, and we have a 1.00 M solution of a basic salt (Section 15.14). The principal reaction is... 

Since the initial solution of H2A+ contained 1.00 mol of H2A+, the amount of NaOH required to reach the second equivalence point is 2.00 mol. Beyond the second equivalence point, the pH is determined by [OH-] from the excess NaOH. 

A 25.0 mL sample of a diprotic acid is titrated with 0.240 M KOH. If 60.0 mL of base is required to reach the second equivalence point, what is the concentration of the acid ... 

A 40.0 mL sample of a mixture of HC1 and H3PO4 was titrated with 0.100 M NaOH. The first equivalence point was reached after 88.0 mL of base, and the second equivalence point was reached after 126.4 mL of base. 

At point E on the titration curve, 2.5 of base per mole of phosphoric acid have been added. Again, it is erroneous to assume that the P04- ion concentration equals the HP04- ion concentration at this half-equivalence point because a significant fraction of the base added beyond the second equivalence point (D in Figure 2.4) has not reacted with the HP04- ion. Thus, the proper expression for the third dissociation constant for phosphoric acid is given by the relations... 

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