The first equivalence point

At the first equivalence point half of the stoichiometric amount of H2A(aq) initially present will have been neutralised, i.e. the H2A(aq) has been converted to an equal stoichiometric amount of NaHA(aq) which is fully ionised to Na+(aq) and HA Uaq). 

There are, however, two further equilibria which must be considered, since HA can act as a base or as an acid  

This is a quadratic equation in which ultimately involves four unknowns  

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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 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. 

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... 

It can be shown that the pH at the first equivalence point for a diprotic acid is given by... 

Within the first buffer region, both H2 A and RA are major species in solution, and we can apply the buffer equation to caicuiate the pH. Haifway to the first equivalence point of the titration [H2 A] — [H A ] and pH pTai = 1.82. 

To the first equivalence point NaOH + H3P04----- NaH2P04 + H20... 

We determine the molar concentration of H3P04 and then of HC1. Notice that only 10.0 mL of the NaOH needed to reach the first equivalence point reacts with the HCl(aq) the rest reacts with H3P04. 

This is the first equivalence point, a solution of 30.00 mL (= 10.00 mL originally + 20.00 mL titrant), containing 0.400 mmol H2P04 from the titration and the 0.150 mmol H2P042 originally present. This is a solution with... 

Figure 7-8 Experimental titration curves, (a) Titration curve for 40.00 mL of 0.050 2 M KI plus 0.050 0 M KCI titrated with 0.084 5 M AgN03. The inset is an expanded view of the region near the first equivalence point, (b) Titration curve for 20.00 mL of 0.100 4 M I titrated with 0.084 5 M Ag+.

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 ]. 

At any point between A (the initial point) and C (the first equivalence point), we have a buffer containing B and BH+. Point B is halfway to the equivalence point, so fB] = [BH+]. 

At the first equivalence point, B has been converted into BH+, the intermediate form of the diprotic acid, BH +. BH+ is both an acid and a base. From Section 10-1, we know that... 

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). 

The base Na+A. whose anion is dibasic, was titrated with HC1 to give curve b in Figure 11-4. Is point H, the first equivalence point, the isoelectric point or the isoionic point ... 

At 25.0 mL At the first equivalence point, H2M has been converted into HM. ... 

Halfway to the First Equivalence Point As NaOH is added, H2A+ is converted to HA because of the neutralization reaction... 

Halfway to the first equivalence point, we have an H2A+-HA buffer solution with [H2A+] = [HA]. The Henderson-Hasselbalch equation gives pH = PJCal = 2.34. 

At the First Equivalence Point At this point, we have added just enough NaOH to convert all the H2A+ to HA. The principal reaction at the first equivalence point is proton transfer between HA molecules ... 

When a typical diprotic acid H2A (Kal = 10-4 Ka2 = 10-10) is titrated with NaOH, the principal A-containing species at the first equivalence point is HA-. 

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. 

C is correct. The isoelectric point is where 100% of the amino add exists ns a zwittcrion. The isoelectric point occurs at the first equivalence point. 

Point A on the titration curve is half-way to the first equivalence point with 0.5 mol of base added per mole of phosphoric acid. If the pH at this point were between pH > 5 and pH < 9, die concentration of H3P04 and of H2P04 ion could be assumed to be equal. However, because the pH is approximately pH 3, the concentration of H3P04 at this point is less than that of the H2P04 ion by an amount equivalent to about twice the hydronium ion concentration. Thus, the correct expressions at the half-equivalence point for the equilibrium concentrations are... 

Assay (Note Use a combination pH-electrode for all titrations.) Accurately weigh between 0.100 and 0.150 g of sample, and dissolve it in 50 mL of ethanol. Perform the titration under a flow of nitrogen. Titrate with standardized 0.1 A tetrabutylammonium hydroxide in methanol or 2-propanol. Determine the volume of titrant needed to reach the first equivalence point (Vi mL) and the second equivalence point (V2 mL). 

This reaction occurs until the H3PO4 is consumed (to reach the first equivalence point). Therefore, at the first equivalence point the solution contains the major species Na+, H2P04 , and H 0. Then as more sodium hydroxide is added, the reaction... 

At the first equivalence point in the titration of the acid H3A with sodium hydroxide, the major species are H2A and H2O. What equilibrium will control the [H+] in such a solution ... 

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