The first buffer region

At point A, the system is in the first buffer region and pH = pKa). Once all the acid H,P04 molecules have lost their first acidic protons, the system is at B and the primary species in solution are the diprotic conjugate base and sodium ion—we have a solution of NaH2P04(aq). Point B is the first stoichiometric point, and to reach it we need to supply 1 mol NaOH for each mole of H P04. 

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. 

Additional points in the first buffer region can be computed in a similar way. Just Prior to First Equivalence Point... 

Moving beyond the first stoichiometric point, the titration enters the second buffer region. Here, the major species are H A and its conjugate base,. The pH in this region is given by the buffer equation, using the p of H j4.". At the second midpoint, [H j4" ] = [j4 " ], and pH = p. Ta 2 For the titration of maleic acid, pH = 6.59 at the second midpoint. 

In the effective buffer region the buffer capacity is determined almost exclusively by the first term in the brackets hence, neglecting the other terms, it follows that... 

A titration curve of a dibasic add is essentially a composite of the titration curves of an equimolar mixture of two weak acids with dissociation constants and Ki- In the two buffer regions, where Equation (3-30) applies, the shape can be calculated directly if Aj. The hydrogen ion concentration at the first end point is given approximately by Vj, and at the second end point it is nearly the same as that for the titration of a monobasic weak acid with = 2- If is much larger than K2, the above approximations are no longer valid then the precision of the intermediate end point is so low that it is no longer of analytical value. The titration curve is too shallow for quantitative use unless KJK2 exceeds about 10 or 10 . ... 

This implies that a subsystem density matrix element is utilized if Xn and Xv are located within the core of 9l , or if the basis functions couple the core region to the first buffer layer. The latter type of contribution is necessary in order to account for chemical bonding across subsystem boundaries. All other elements of P are considered to be edge contributions that contain undesirable truncation effects. 

Figure 11.14 shows the pH curve of a diprotic acid, such as oxalic acid, H2C204. There are two stoichiometric points (B and D) and two buffer regions (A and C). The major species present in solution at each point are indicated. Note that it takes twice as much base to reach the second stoichiometric point as it does to reach the first. 

Individual near-infrared absorption spectra are presented in Figure 13.3 for each of the mixture components. Figure 13.3 presents absorption spectra over the first-overtone and combination spectral regions, respectively. Each spectrum was collected from 100 mM solution of the selected solute dissolved in a pH 6.8 phosphate buffer solution and absorbance was calculated relative to a reference spectrum of the blank phosphate buffer. 

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