Calculations of pH Values in Aqueous Solutions

It is important to know how to calculate the pH value of an aqueous solution. The calculation is carried with the help of equations that result from general reasoning often encountered in analytical chemistry. 

Let s recall that the pH is expressed in terms of activities. In this chapter, activities and concentrations are mixed. This means that the solutions studied here are very diluted. Taking into account activities markedly complicates calculations, as we briefly show at the end of the chapter. The rate of acid-base reactions must be noted also. We can consider that acid-base equilibria are obtained immediately. Hence, there is no kinetic consideration in this chapter. This is quite justified since neutralization reactions in water arevery fast (kinetic constant = 1.3 x 10 L/mol/s at 25°C) after Eigen s work.  

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Aquatic chemists have defined their own electrochemical standard state to fecilitate calculation of redox speciation in aqueous solutions. In this standard state, all reactions are conducted at pH 7.0, 25°C, and 1 atm. The concentrations of all other solutes are 1 molal (unless otherwise specifically noted). Values so obtained are designated with the subscript w. The pe s for the most important redox couples in seawater are given in Table 7.4. 

To those beginning work in this field, the study reported by Zhou and Notari on the kinetics of ceftazidime degradation in aqueous solutions may be used as a study design template. First-order rate constants were determined for the hydrolysis of this compound at several pH values and at several temperatures. The kinetics were separated into buffer-independent and buffer-dependent contributions, and the temperature dependence in these was used to calculate the activation energy of the degradation via the Arrhenius equation. Ceftazidime hydrolysis rate constants were calculated as a function of pH, temperature, and buffer by combining the pH-rate expression with the buffer contributions calculated from the buffer catalytic constants and the temperature dependencies. These equations and their parameter values were able to calculate over 90% of the 104 experimentally determined rate constants with errors less than 10%. 

Generally, we can calculate the hydrogen ion concentration or pH of an acid solution at equilibrium, given the initial concentration of the acid and its value. Alternatively, if we know the pH of a weak acid solution and its initial concentration, we can determine its K. The basic approach for solving these problems, which deal with equilibrium concentrations, is the same one outlined in Chapter 14. However, because acid ionization represents a major category of chemical equilibrium in aqueous solution, we will develop a systematic procedure for solving this type of problem that will also help us to understand the chemistry involved. 

Enthalpies and entropies of activation for the decarboxylation of oxalic, malonic, and acetic acids are listed in Table 1 and are shown separately on the isokinetic plots in Fig. 8. Linear trends are observed for (1) aqueous acetic acid and sodium acetate in the presence of various catalysts (2) aqueous oxalic acid at several pH values (3) oxalic acid in different solvents and (4) malonic acid in different solvents and in aqueous solutions having a different pH. Note that the isokinetic trend for the decarboxylation of malonic acid in aqueous solutions at various pH is identical to that for the reaction in nonaqueous solvents, i.e., there is one isokinetic trend for malonic acid. Moreover, the effect of pH on the activation parameters for the decarboxylation of malonic acid in aqueous solution is minimal. On the other hand, the activation data for the decarboxylation of oxalic acid in aqueous solutions determined by Crossey (1991) do not follow the same isokinetic trend as do the corresponding data for this reaction in other solvents. By contrast, activation data calculated from the rate constants determined by Dinglinger and Schroer (1937) for oxalic acid in water (pH 0.5) fall on the isokinetic trend set by the decarboxylation of oxalic acid in nonaqueous solvents, as well as the rate data determined by Lapidus et al. (1964) in the vapor phase. The cause of the disparity between the isokinetic relationships determined by Crossey (1991) and the remainder of the oxalic acid results requires further investigation. The reaction could have been surface-catalyzed, but this is doubtful because some of the oxalic acid... 

For HCl, the value of is exceedingly large because the concentration of HCl in aqueous solution is vanishingly small. Because this is so, the pH of HCl solutions is readily calculated from the amount of HCl used to make the solution ... 

CD reactions sometimes proceed via a metal hydroxide intermediate the concentration of OH ions in the solution is particularly important in such cases. Since almost all CD reactions are carried out in aqueous solutions, the pH of the deposition solution will give this concentration. In translating pH into OH concentration, the very temperature-dependent ioiuzation constant of water should be kept in mind, as mentioned previously. The reason for this can be seen from Table 1.2, which gives the OH concentration in water at a pH of 10 (a typical pH value for many CD reactions), calculated from the ionization constant of water, from the relation... 

The hydroxy a-amino acids l-serine and l-threonine, used as models for the 2-amino-2-deoxy glyconic acids, have been complexed with Ni(II) at 37 °C in aqueous solutions of 0.15M potassium nitrate. Values for the stability constants were obtained from iso-pH titration data which were collected by alternate, small, incremental additions of metal ion and potassium hydroxide being made such that the pH of the solution remained nearly constant. The data were consistent with the predominance of MLn species, along with additional protonated and hydrolyzed complexes. There was no evidence for the involvement of the hydroxyl group in chelation. By the same iterative computations the complexes formed between borate and mannitol have been analyzed, and the stability constants have been calculated. Complexes with mannitohborate stoichiometries of I.T, 1 2, 1 3, and 2 1 were proposed. 

From these results (Figures 2 and 3) one can conclude that, in aqueous solutions contacting freshly prepared Np(IV) hydrous oxide, Np solution concentrations reach steady-state values within 70 days and show an expected pe dependence as described by Equation 2 for pH values less than approximately 8.5. Furthermore, with the aging of the Np solid phase, there is a corresponding change in the solubility such that the calculated log K° value decreases from approximately -7 to -10 (+1) within 200 days. It is not possible at this time to determine whether the solubility will continue to slowly decrease to lower values. 

Dependence of -potential on surfactant kind and concentration. Detailed study with the method of equilibrium foam film of h(Cej) and A(pH) dependences in the absence of a surfactant, as well as h(C) at very low surfactant concentrations, gave (po 30 mV at the interface aqueous electrolyte solution/air [169,170,197]. It is important to note that this value of (po could be reconsidered in view of some recent results on numerical calculation of dispersion interactions in foam films [106,166,198]. For example, as shown by Kolarov, the (po value of 30 mV is reduced to about 15 mV when using the data on dispersion interactions reported in [166],... 

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