Pressure dependence of ionization constants

A model based on the density of the solvent together with the "iso-Coulombic" form of reactions has been used to estimate the pressure dependence of ionization constants of aqueous complexes. This model reproduces experimentally determined pressure dependencies of several ionization constants of aqueous complexes. Csdculated saturation states of calcite in seawater are -500 cal (100°C, 0.5 kbar) and 700 cal (100°C, 1.0 kbar) greater, and the temperatures of excite saturation are 80°C (0.5 kbar) and 40°C (1.0 kbar) higher, than the values obtained when the effect of pressure on ionization constants is neglected. 

The molar volume change in ionization reactions at higher temperatures and pressures cannot be calculated for most of the aqueous complexes because of a lack of data on isobaric expansion and isothermal compressibility coefficients. Entropy and heat capacity correlations have recently been used to generate equation of state parameters for estimating molal volumes of aqueous complexes at elevated temperatures and pressures (Sverjensky, 12). These coefficients are available for aqueous complexes only of univalent anions and, therefore, the pressure dependence of ionization constants at elevated temperatures cannot be estimated using Equation 4. 

Marshall and Mesmer have used a relationship based upon the density of the solvent for calculating the pressure dependence of ionization constants ... 

Equation 9 also cannot be used to estimate the pressure dependence of ionization constants when the term (AV /RTB ) shows a temperature dependence (Fig. 1). The following technique can be used to alleviate this problem. 

The technique presented in this paper to estimate the pressure dependence of ionization constants is simple to use and requires minimal data. Excellent agreement is observed between the calculated and measured values of ionization constants of several aqueous complexes at higher pressures, at least up to 200°C. The discussion presented above shows that the effect of pressure on ionization constants must be considered in geochemical calculations of mineral-solution equilibria at low and high temperatures. 

Entropy of activation (continued) sign of, 256 Entropy unit, 242 Enzyme catalysis, 102 Enzyme-substrate complex, 102 Equilibrium, 60, 97, 99, 105, 125, 136 condition for, 205 displacement from, 62, 78 in transition state theory, 201, 205 Equilibrium assumption, 96 Equilibrium constant, 61. 138 complexation, 152 dissociation, 402 ionization, 402 kinetic determination of, 279 partition functions in, 204 pressure dependence of, 144 temperature dependence of, 143, 257 transition state, 207 Equivalence, kinetic, 123 Error analysis, 40 Error propagation, 40 Ester hydrolysis, 4 Euler s method, 106 Excess acidity method, 451 Exchange... 

Equation 9 has been successfully used to reproduce experimental values of the ionization constants of water and several aqueous complexes at higher temperatures and pressures . Eugster and Baumgartner (1 have used a relationship similar to Equation 9 for estimating the pressure dependence of aqueous complexes in supercritical fluids. 

Estimates of pressure dependence of the ionization constant of PbCL based on Equation 9 are compared in Table 1 with those obtained by using Equation 4 (1 . Both approaches result in similar values for pressures up to 1000 bars. At higher pressures, estimated pressure dependence based on Equation 9 is lower, especially at higher temperatures. As mentioned earlier, disagreement at higher temperatures may be due to the temperature dependence of the reaction volume. In addition, the error of estimation in the data of Sverjensky (12) is unknown. 

Table 1. Pressure dependence of the ionization constants of PbCP calculated using Equation 9 (from the data in Sverjensky, 12)...

The pressure dependence of mineral dissolution reactions in SOLMINEQ.88 is calculated using data from (8JL18). The ionization constants at higher pressures for aqueous complexes are calculated using the "iso-Coulombic" form of Equation 9. The coefficient of isothermal compressibility and density of water are obtained from the data in (19). Molal volume change in the ionization reaction of aqueous complexes (Table 3) are obtained from experimental studies, when available, or are estimated based on nations 6 to 8. 

Rate constants for the ion-molecule reactions occurring in chemical ionization can be obtained from studies of the pressure dependence of ion intensities. The effect of benzyl acetate pressure on the chemical ionization mass spectrum of benzyl acetate obtained with has been investigated... 

Electron ionization sources produce constant ion beams of about 10 8 A with low initial energy spread. The ion current measured depends strongly on the ionization degree of the gas analyzed (type of atoms and molecules). Positive ions and electrons are formed by the interaction of electrons of sufficient energy with gas atoms or molecules. The ion current /+ is proportional to the pressure (p) of the gaseous sample, to the electron current /e, the length (/) of the collision chamber and the differential ionization (s) of elements as a function of the ionization energy ... 

We turn our attention in this chapter to systems in which chemical reactions occur. We are concerned not only with the equilibrium conditions for the reactions themselves, but also the effect of such reactions on phase equilibria and, conversely, the possible determination of chemical equilibria from known thermodynamic properties of solutions. Various expressions for the equilibrium constants are first developed from the basic condition of equilibrium. We then discuss successively the experimental determination of the values of the equilibrium constants, the dependence of the equilibrium constants on the temperature and on the pressure, and the standard changes of the Gibbs energy of formation. Equilibria involving the ionization of weak electrolytes and the determination of equilibrium constants for association and complex formation in solutions are also discussed. 

Fig. 5 illustrates the relative dependence of the fluorescence yield of the 337 nm line on different electron energies at a pressure of 400 hPa. The drawn curve corresponds to the Bethe-Bloch function [6] for ionization energy loss which was fitted to the data by a constant factor. The statistics in this plot is still very limited but the number of emitted fluorescence photons indeed seems to be proportional to the energy loss as it is suggested by Eq. (2). 

An ionization instrument for the analysis of gas has been developed in which the gas passes through a small chamber where it is irradiated by a small radioactive source. For a constant source of radiation, the ions produced in the gas d nd on the flow velocity of the gas and on its temperature, pressure and atomic composition. The dependence of the ionization on the atomic composition is a consequence of the different ionization potentials of the differrat types of atoms of the gas and the different probabilities for electron capture and collision. The ion current is collected on an electrode and measured. This current is a function of the gas pressure and velocity since the higher the pressure, the more ions form, while at higher velocity, the fewer ions are collected as more ions are removed by the gas prior to collection. Such ionization instruments are used in gas chromatographs and other instruments as well as in smoke detection systems (the normal radiation source is Am, usually 40 kBq), where secondary electrons condense on smoke particles, leading to lower mobility for the electrons and a decreased ion current. 

Application of high pressure changes the position of the electronic conduction level, Vq (see Section 6.9), and it increases the dielectric constant of the liquid. Both effects have an influence on the ionization energy of a solute. The dependence of Vo(p) is complicated and experimental data must be used. The effect of pressure on the dielectric constant is due to the increase in density and it is well described by the Clausius-Mossotti equation (see Section 1.6). In Figure 8a the photoconductivity spectrum of TMPD in neohexane is shown as a function of pressure. The variation of the photoconductivity threshold with pressure is depicted in Figure 8b. Evaluation of the data by means of Bom s formula (Chapter 7, Equation 94) led to the hypothesis that an additional increase of liquid density around the solute molecule due to fluctuations is responsible for the observed shifts (Katoh et al., 1995). 

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