Acid-base titration curves defined

There are, of course, many studies of the composition of gelatins derived from mammalian sources and from fish skins. In Table III the relatively recently available results on the whole collagens have been cited. Mammalian collagen is represented largely by the analyses summarized by Bowes and Kenten (40), performed on a preparation of ox hide. The data account for nearly 100% of the total substance and have been found in reasonable agreement with acid-base titration curves. This set of values may be used to define a standard collagen with which other substances may be compared. 

The most efficient ojjerational design would be for the machine to operate over the range of the acid-base titration curve with the steepest An/Ap slope. Because the Hill coefficient, n, as defined in Equation (5.20) is a measure of the slope, it provides for ready comparison of efficiencies. The Hill coefficients for Model Proteins I through v are listed in Figure 5.34, and the slopes are plotted in the inset. Accordingly, the comparison of the efficiencies of Model Proteins i and v simply becomes iii/liy = 1.5/8.0 = 0.19. Thus, by increasing the hydropho-bicity by the replacement of five Val (V) residues by five Phe (F) residues, as indicated in Table 5.5, increases the efficiency of the protein-based machine by just over fivefold. 

Define monoprotic acid, polyprotic acid, monobasic base, polybasic base, titration curve, and inflection point. 

More recently, flow titrations have been implemented in multi-commuted flow systems. With these systems, the exact amounts of the solutions involved can be modified in real time according to a concentration-oriented feedback mechanism. The flow titration really mimics a true titration because an analytical curve is not needed. A flow system exploiting a binary search to define the end point of an acid—base titration [324] is a good example of this approach. Stream directing solenoid valves were used to modify the sample and titrant volumes after every measurement via a feedback mechanism. Samples with concentrations within a range of two orders of magnitude could be titrated without modifying the flow manifold. 

Monolayers at the surface of aqueous electrolyte solutions may be useful models for polyelectrolytes [11, 14] and for biological membranes [15]. The average distribution of the fixed charges, limited to a plane near the interface, is well defined and the variation of the interfacial potential may be measured. Thus the surface potential-pH plots resemble those of acid-base titrations of polyacids [16, 19]. From these curves the degree of dissociation of the fatty acid in the monolayer may be deduced [17, 18]. 

Although not commonly used, thermometric titrations have one distinct advantage over methods based on the direct or indirect monitoring of plT. As discussed earlier, visual indicators and potentiometric titration curves are limited by the magnitude of the relevant equilibrium constants. For example, the titration of boric acid, ITaBOa, for which is 5.8 X 10 °, yields a poorly defined equivalence point (Figure 9.15a). The enthalpy of neutralization for boric acid with NaOlT, however, is only 23% less than that for a strong acid (-42.7 kj/mol... 

When plotted on a graph of pH vs. volume of NaOH solution, these six points reveal the gross features of the titration curve. Adding additional calculated points helps define the pH curve. On the curve shown here, the red points A-D were calculated using the buffer equation with base/acid ratios of 1/3 and 3/1. Point E was generated from excess hydroxide ion concentration, 2.00 mL beyond the second stoichiometric point. You should verify these additional five calculations. 

In the process of a weak acid or weak base neutralization titration, a mixture of a conjugate acid-base pair exists in the reaction flask in the time period of the experiment leading up to the inflection point. For example, during the titration of acetic acid with sodium hydroxide, a mixture of acetic acid and acetate ion exists in the reaction flask prior to the inflection point. In that portion of the titration curve, the pH of the solution does not change appreciably, even upon the addition of more sodium hydroxide. Thus this solution is a buffer solution, as we defined it at the beginning of this section. 

Table 5.1 gives commonly used examples of conjugate acid-base pair combinations and the pH range for which each is useful. This range corresponds to the pH range defined by the buffer region in the titration curve for each, and the middle of the range corresponds to the midpoint of each titration. 

It is possible to compare the strengths of weak acids by the values of their acid dissociation constants Ka. Figure 3.1 shows the titration curves for acids (HA or BH+) of different Ka values. The ordinate shows poH, which is defined by paH = -loga(SI I)). paH corresponds to the pH in aqueous solutions (see Section 3.2). The poH of non-aqueous solutions can be measured with a glass pH electrode or some other pH sensors (see Sections 3.2.1 and 6.2). For the mixture of a weak acid A and its conjugate base B, poH can be expressed by the Henderson-Hassel-balch equation ... 

Above pH 8 the titration curve shows uptake of a second equivalent of base corresponding to production of (en)Pd(OH)2. This second section of the titration curve is also flattened, owing to break up of oligomers by uptake of a second hydroxide at high pH. Though little reaction occurs directly by this route, we define the second acidity constant in the usual way. 

The typical plot of titration curves is presented in Fig. 6. By the comparison of H+ or OH- concentration changes, for defined volume of the acid or base, the surface charge can be calculated according to the equation ... 

Four types of hydrous antimony oxide (antimonic acid), the amorphous (A-SbA), the glassy (G-SbA), the cubic (C-SbA), and the monoclinic (M-SbA) are known so far [138]. Both the A-SbA and G-SbA affect the selectivity sequence Li" < Na" < K" " < Rb+ < Cs", while the selectivity sequence of C-SbA is unusual with Li" " K+ < Cs < Rb" Na" " for micro amounts in acid media (Fig. 19). The degree of crystallinity of a-ZrP strongly influences its ion-exchange behavior as mentioned earlier. The pH versus base added plots for a-ZrP with different crystallinity are shown in Fig. 13. It is seen that each increase in acid concentration at a fixed reflux time is reflected in the shape of the curves. The titration curves with the most well-defined plateaus were obtained with the most highly crystalline samples [126]. 

By analogy to pH titration curves of acids and bases, it is customary in precipitation titrations to plot the quantity pM (defined by either — log [M " ] or — log a m ) against titration volume. For certain metals that form reversible electrodes with their ions, the measured electrode potential is a linear function of the logarithm of ion activity, so the titration curve can be realized experimentally in a potentiometric titration. In any case, the curve gives a useful indication of the sharpness of an endpoint break. 

Obviously the buffer intensity can be expressed numerically by differentiating the equation defining the titration curve with respect to pH. For a monoprotic acid-base system (see equations 67 and 69). 

Firstly, ion exchange resins when hydrated generally dissociate to yield equivalent amounts of oppositely charged ions. Secondly, as with conventional aqueous acid or alkali solutions, resins in their acid or base forms may be neutralized to give the appropriate salt form. Finally, the degree of dissociation can be expressed in the form of an apparent equilibrium constant (or pK value) which defines the electrolyte strength of the exchanger and is usually derived from a theoretical treatment of pH titration curves. ... 

Plasma base excess is defined as the initial concentration of titratable base when titrating the plasma with strong acid or base to pH (Std) - 7.4 at PCO2 = 40 mm Hg and 37 °C. The equation for the CO2 equilibration curve of plasma and calculation of plasma base excess can be written ... 

The alkalinity is measured by titration with a standardized solution of a strong acid such as H2SO4, HNO3, or HCl. The titration curve is identical, but inverse to the acidity titration curve in Fig. 5.6. The caustic alkalinity titration endpoint near pH 11 measures free OH from strong bases. At this endpoint HCO3 = OH . At the carbonate alkalinity endpoint (pH = 8.3) conditions are identical to those defined above for C02-acidity. 

We will next derive an expression for the titration curve showing the change in pH with volume of added base (cf. Butler 1964 Pankow 1991). First, define and as the original volume of solution to be titrated and the volume of added titrant. Thus, is known and fixed, and the final volume, V, is P = Vo -I- Vg. The original concentration of strong acid, HCl, will equal Clo, the original... 

Potentiometric Titration Direct potentiometric titration has been used to study for years the carbon surface, but until the mid-1990s the curves obtained did not show discrete endpoints useful for meaningful interpretation [200,205,209], The derivatives obtained in some studies were difficult to characterize due to the many maxima revealed when no well-defined endpoints were present [210], A first meaningful deconvolution of titration curves with theoretical description of acid-based dissociation on the surface of carbons was proposed in the mid-1990s... 

Potentiometric titration curves of humic compounds against strong base are usually broad and ill-defined thus reflecting the diversity in acidic groups. The apparent acidity of these groups can be expressed as ... 

Experimental values are derived by defining the ratio of [A ]/[HA] (or [B]/[BH ] for the base) as a function of pH. For example, this can be accomplished in a titration when pH is monitored as a specified amount of acid is titrated with a solution of base of known concentration providing curves comparable to those shown in Figure 2.14. Stoichiometric relations provide the required estimates of [A ]/[HA]. With many aromatic and heterocyclic compounds it is possible to use a spectrophotometric... 

The potentiometric titration curves of HA are usually broad and ill-defined, reflecting the varying properties of acidic groups on HA [23,24]. Wilson and Kinney [25] investigated the acid-base properties of lake water and marine humic substances and determined a two-step dissociation process. Schnitzer and... 

---