Titration general equation

Tanford, C., Kirkwood, J. G. Theory of protein titration curves. I. General equations for impenetrable spheres. J. Am. Chem. Soc. 79 (1957) 5333-5339. 6. Garrett, A. J. M., Poladian, L. Refined derivation, exact solutions, and singular limits of the Poisson-Boltzmann equation. Ann. Phys. 188 (1988) 386-435. Sharp, K. A., Honig, B. Electrostatic interactions in macromolecules. Theory and applications. Ann. Rev. Biophys. Chem. 19 (1990) 301-332. 

Derive a general equation for the electrochemical potential at the equivalence point for the titration of Fe + with Mn04 the reaction is... 

Tanford, C Kirkwood, JG, Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres, Journal of the American Chemical Society 79, 5333, 1957. 

Tanford C, Kirkwood JG (1957) Theory of protein titration curves. I. general equations for impenetrable spheres. J Am Chem Soc 79 5333—5339. 

These titrations arc used in the estimation of metal salts. Ethylenediamine tetracetic acid (EDTA) shown in Figure 3.10 is the usual titrant used. It forms stable 1 1 complexes with all metals except alkali metals such as sodium and potassium. The alkaline earth metals such as calcium and magnesium form complexes which are unstable at low pH values and are titrated in ammonium chloride buffer at pH 10. The general equation for the titration is ... 

For these extreme cases the general equations (39) to (41) are still applicable, and suitable approximations can be made in order to simplify the calculations. At the very beginning of the titration, i.e., when the weak acid is alone present, 6 is zero and since the solution is relatively acid coH may be neglected the quantity B is then equal to Ch+, and equation (39) becomes... 

K. Linderstrom-Lang, Compt. Rend. Trav. Lab. Carlsberg, 15, 1 (1924). The Ionization of Proteins. C. Tanford and J. G. Kirkwood, /. Am. Chem. Soc., 79, 5333 (1957). Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres. 

A. J. Bard and S. H. Simpsonsen, The General Equation for the Equivalence Point Potential in Oxidation-Reduction Titrations, J. Chem. Educ., 37 (1960) 364. 

Eqs. (4.183) and (4.184) are, therefore, not based on the electroneutrality equation (4.181) because they also include weak acids and bases which are not protolyzed in solution at the given pH (that means in non-ionic form), but contribute to acid or base titration. The first attempt to determine airborne acidity was done by careful titration inserting microliter quantities of a NaOH solution (Brosset 1976) using Gran s titration method (Gran 1950). The reference points, however, are not objective criteria. Zobrist (1987) extended this definition to the general equations ... 

A general titration curve equation can be derived from the mass balance equation for the ligand, i.e., to state that the total ligand concentration is the sum of the bound and free ligand concentrations. By the bound ligand is meant the ligand incorporated into the metal complex(es). Thus, for Ag ... 

Titration Curves. I. General Equations for Impenetrable Spheres. 

The study given here is uncommon since it is systematically based on the general equations governing the redox titration curves and, more precisely, by starting with them. This is not the case in the literature, in which the general equations are rarely mentioned. 

A general equation exists that applies itself to any stage of the titration. It can be easily deduced from Eqs. (17.3)-(17.7). It is the following ... 

Considering the titration reaction as again being an oxidation reaction [with the result that the signs of exponentials 2 and e are the same as in relations (17.13) and (17.14)], the general equation is... 

The investigated titration may be studied like other asymmetrical titrations after the standard (or formal) potentials are replaced with the apparent one at the working pH, provided the latter is a constant. The general equation of the titration curve is... 

The general equation coming from this system of relations is not explicit in q> or in E. The study of the standard potential values of both couples shows that the titration reaction equilibrium constant K° is about 6 10 in sulfuric acid medium. The titration reaction may certainly be considered complete. In this condition and after having followed the arguments already developed, we find the simplified relations... 

By adopting the same symbolism as that used in the preceding chapter (Sect. 16.8) but by replacing Cn, C12, and C2 with Xi, X2, and Y in order to take the dilution into account, we find for the general equation of the titration curve. 

The general equation of the titration curve is at the final point ... 

The general equation of the titration curve is found by expressing P from Eq. (36.2) and by replacing it in (36.1) with its expression. This gives... 

Silver sulfate exhibits the solubility product Xs(Ag2S04)= 10 The rigorous general equation of the titration curve is obtained from the following three relations ... 

Sensitivity For an acid-base titration we can write the following general analytical equation... 

The last definition has widespread use in the volumetric analysis of solutions. If a fixed amount of reagent is present in a solution, it can be diluted to any desired normality by application of the general dilution formula V,N, = V N. Here, subscripts 1 and 2 refer to the initial solution and the final (diluted) solution, respectively V denotes the solution volume (in milliliters) and N the solution normality. The product VjN, expresses the amount of the reagent in gram-milliequivalents present in a volume V, ml of a solution of normality N,. Numerically, it represents the volume of a one normal (IN) solution chemically equivalent to the original solution of volume V, and of normality N,. The same equation V N, = V N is also applicable in a different context, in problems involving acid-base neutralization, oxidation-reduction, precipitation, or other types of titration reactions. The justification for this formula relies on the fact that substances always react in titrations, in chemically equivalent amounts. 

The relation between free phosphoric acid content and total phosphate content in a processing bath, whether based on iron, manganese or zinc, is very important this relation is generally referred to as the acid ratio. An excess of free acid will retard the dissociation of the primary and secondary phosphates and hinder the deposition of the tertiary phosphate coating sometimes excessive loss of metal takes place and the coating is loose and powdery. When the free acid content is too low, dissociation of phosphates (equations 15.2, 15.3 and 15.4) takes place in the solution as well as at the metal/solution interface and leads to precipitation of insoluble phosphates as sludge. The free acid content is usually determined by titrating with sodium... 

Weak acid and weak base. There is no sharp rise in the neutralisation curve and, generally, no simple indicator can be used. The titration should therefore be avoided, if possible. The approximate pH at the equivalence point can be computed from the equation ... 

Thus, the pKa value equals pH if the concentrations of protonated and deprotonated states are identical. For this reason, pKa is also called p/fi/2- Equation (10-4) can be rearranged and written in a generalized form in the presence of multiple titration sites,... 

The accuracy of PHMD methods and their feasibility for studying pH-dependent conformational phenomena of proteins can be assessed by pKa calculations. In this case, PHMD simulations are performed with several pH values. The resulting occupancy values for deprotonated states (.S dc prot) are plotted against pH (Figure 10-3). A titration curve and pATa values (Figure 10-3) can be obtained by fitting the data to the generalized HH equation (Eq. 10-5). 

Figure 10-3. Theoretical titration curves for the model compounds of Asp and His obtained from REX-CPHMD simulations [41]. Solid curves are the obtained by fitted the computed deprotonated fraction to the generalized Henderson-Hasselbach equation. The dashed lines indicate the computed pKa values...

---