Activity Coefficients of Neutral Molecules

Apart from the problem of lack of data, especially kinetic data, this situation probably constitutes the most serious problem in the application of thermodynamics to geochemical problems involving hydrothermal solutions. The development of an algorithm which is more accurate than the B-dot method as presently used, but which could still be used for any species at any T and P would be a significant advance in geochemical modeling practice. 

The determination of the activity coefficients of species that exist dominantly as neutral molecules, such as Si02(a ), H2S(a ), and C02(aq), is much simpler. In these cases it is usually possible to establish a two-phase equilibrium between the substance in its pure state (solid or gaseous) and the substance in its aqueous or dissolved state. This leads to a simple and rigorous determination of the activity coefficient in solutions of varying composition. 

For example, consider HjS gas in equilibrium with H2S(a ). The first ionization constant of HjS is about 10 , so that species other than molecular HjS can be neglected in this connection. The reaction of interest is 

If the solution of interest is a solution of neutral salt B in water, having concentration m-Q, eliminating the first term in Equation (15.28) gives 

An extensive review of neutral solutes in aqueous salt solutions is given by Randell and Failey (1927a, b, c). See also Long and McDevit (1952) and Oelkers and Helgeson (1991). Note that we have only spoken of neutral species of the type that can be obtained as the dominant species in a solution activity coefficients for the neutral species of weak electrolytes and other neutral species in a matrix of charged particles constitute a more difficult problem. Their activity coefficients are usually assumed to be 1.0, or are taken as equal to those 

7i(m solution of interest, i.e., a salt solution)/7j(m pure water). 

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The approximation of taking concentrations instead of activities was justified by the authors on the basis of the small degree of dissociation owing to the low e, and by the assumption that activity coefficients of neutral molecules and ion pairs are not significantly different from unity in the low range of concentrations studied. From eqns. 4.54 and 4.55 one obtains for the overall dissociation constant of HX... 

In equations (3), (4), (5) and (6), the subscripts M, c, and c present cations different cations X, a, and a express anions in mixture solution. Nc, Naand Nn express the numbers of cations, anions, and neutral molecules Tm, Zm, me and rx, Zx, nia, d present the ion activity coefficient, ion valence number, ion morality, and the pxsrmeability coefficient pn, nin, Xnc, and Ana express activity coefficient of neutral molecule, morality of neutral molecule the interaction coefficient between neutral molecules with cations c and anion a... 

In the region in which the Debye-Hiickel limiting law is applicable, the activity coefficient of the molecules of undissociated MA is probably very close to unity, as may be inferred from the known variation of the activity coefficient of a neutral molecule in the presence of added electrolytes (cf. 39m). It follows, therefore, upon taking logarithms of equation (41.17) that... 

It is assumed that the activity coefficient of HOCl is unity, since the ionic strength at which activity coefficients for neutral molecules deviate significantly from unity is of the order of O.I M. 

As an example, take the molecule aminoazobenzene, one of the solutes listed in Table 39. When colorimetric measurements were made at room temperature on very dilute aqueous solutions of HC1, containing a trace of this substance, it was found that neutral molecules and (BH)+ ions were present in equal numbers when the concentration of the HCl was 0.0016 molal.1 At this low concentration the activity coefficient of the HCl is very near unity, and we may use (216) to find how far the vacant proton level provided by the aminoazobenzene molecule in aque-... 

Activity coefficients in the aqueous phase, yiw, of neutral molecules are set equal to one because of the zero charge, and under the assumption that the activity coefficient of the infinitely diluted solution equals the actual activity coefficient. The activity coefficients of the charged species can be approximated with the Davies equation ... 

Equations (7), (8), (9a) thus permit the basicity constants to be determined if the concentrations and activity coefficients of the ions and neutral molecules present in the solution are known. 

Figure 8,11 Activity coefficients for neutral gaseous molecules dissolved in aqueous solutions of various ionic strengths. All values are for T = 25 °C and P = 1 bar, except for hydrogen (T = 15 P = I bar). Reprinted from Garrels and Christ (1965), with kind permission from Jones and Bartlett Publishers Inc., copyright 1990.

It is not certain that the theoretical arguments, which led to the introduction of the term C t, are completely satisfactory, but it seems to be established that the experimental data require a term of this type. The aggregation of solvent molecules in the vicinity of an ion is the factor responsible for the so-called salting-out effect, namely, the decrease in solubility of neutral substances frequently observed in the presence of salts the constant C is consequently called the salting-out constant. The activity coefficient of a non-electrolyte, as measured by its solubility in the presence of electrolytes, is often given by an expression of the form log / = CV this is the result to which equation (62) would reduce for the activity of a non-electrolyte, i.e., when z+ and z arc zero, in a salt solution of ionic strength... 

Nonelectrolytes—dissolved gases, organic molecules, neutral ion pairs, and undissociated weak acids and bases—are also nonideal soiutes in water and are-common constituents of soil solutions. Their activities also vary nonlinearly with concentration, particularly at high concentrations. The activity coefficients of nonelectrolytes at low concentrations are approximated by... 

Medium activity coefficients, cf. Section 5.5, can be used to discuss these effects. Fig. 15 provides a summary of the changes in solvation energy of ions and neutral molecules of various types in solvents which are representative for the solvent classes of Table I. The energy scale, RTln j y, with methanol as the reference solvent is taken from Ref. The non-measurable medium activity coefficient of the activated complex can be estimated from similar stable mol niles or ions. 

The assumption is made that the extracted dye carboxylate exists as an ion-pair in the organic phase and that for the dilute solutions under study the activity coefficients of the neutral molecules (RCOOH) and of the ion-paired species in the organic phase are unity. Further, x could be expressed as the ratio of the optical density (O.D.) to the product of the extinction coefficient (tRDM of the dye carboxylate and the optical path length (l). Incorporating this in (U) we get... 

Water is a neutral molecule and its activity equals its concentration at all low to moderate ionic strengths. That is, its activity coefficient is unity. In solutions of low to moderate ionic strength, activity coefficients of ions decrease with increasing ionic strength because the ionic... 

The activity coefficients for neutral solutes are not described by the Debye-Hiickel theory. Here no long-range Coulomb forces but weak dipole-dipole or van der Waals interactions are effective. They lead only to a minor deviation of the activity coefficient of the value 1. However, the activity coefficients of these solutes are also affected when the amount of bound water molecules within their solvation shell gets close to the concentration of free water, i.e., at very high concentrations of solutes. 

The activated complex is much more dilute than the reactants and products. In many cases, it is therefore possible to have reactions involving only neutral molecules and establish that the activity coefficient of the activated complex within an infinitely dilute reference solution maintains a unit value. 

As mentioned earlier, ascorbate and ubihydroquinone regenerate a-tocopherol contained in a LDL particle and by this may enhance its antioxidant activity. Stocker and his coworkers [123] suggest that this role of ubihydroquinone is especially important. However, it is questionable because ubihydroquinone content in LDL is very small and only 50% to 60% of LDL particles contain a molecule of ubihydroquinone. Moreover, there is another apparently much more effective co-antioxidant of a-tocopherol in LDL particles, namely, nitric oxide [125], It has been already mentioned that nitric oxide exhibits both antioxidant and prooxidant effects depending on the 02 /NO ratio [42]. It is important that NO concentrates up to 25-fold in lipid membranes and LDL compartments due to the high lipid partition coefficient, charge neutrality, and small molecular radius [126,127]. Because of this, the value of 02 /N0 ratio should be very small, and the antioxidant effect of NO must exceed the prooxidant effect of peroxynitrite. As the rate constants for the recombination reaction of NO with peroxyl radicals are close to diffusion limit (about 109 1 mol 1 s 1 [125]), NO will inhibit both Reactions (7) and (8) and by that spare a-tocopherol in LDL oxidation. 

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