Activity coefficients neutral species

The determination of the activity coefficients of species that exist dominantly as neutral molecules, such as Si02(ag), H2S(ag) and C02(ag), 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. 

With increasing water content, the dielectric constant of the medium and the degree of endgroup ionization will increase.30 This is likely to influence the end-group activity coefficients, depending on whether the polycondenzation reaction involves the condensation of predominantly neutral or ionized species. 

In the B-dot model, as currently applied (Wolery, 1992b), the activity coefficients of electrically neutral, nonpolar species [B(OH)3, C>2(aq), SiC>2(aq), CH aq), and H2(aq) are calculated from ionic strength using an empirical relationship,... 

Fig. 8.4. Activity coefficients y0 for neutral, nonpolar species as a function of ionic strength (molal) at 25 °C, 100 °C, and 300 °C, according to the activity model of Helge-son (1969).

STEP 8. Calculate activity coefficients ym, Yx, and yn for cations, anions, and neutral species,... 

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 ... 

The activity coefficients that are significant in determining the concentrations of the unknown species are the activity coefficients of Mg++, Ca++, SO3, SO4, and HSO3. The activity coefficient of Ca + is assumed to be equal to that of Mg++, and that of SOo equal to that of S0. The method for calculating the activity coefficients of Mg, SO4, and HSO3 was presented previously ( ). The activity coefficients of the neutral dissolved species and the fugacity coefficient of S02(g) are assumed equal to unity, as in (J ). 

Figure 8,12 Salting-out phenomenon for aqueous CO2. Activity coefficient of neutral species increases with increasing salinity, determining decreased solubility of aqueous CO2 in water, T and P conditions being equal. Reprinted from Garrels and Christ (1965), with kind permission from Jones and Bartlett Publishers Inc., copyright 1990.

This technique uses both direct and back titrations of weak acids and bases. Values of are obtained directly. In purely aqueous media, over the pH range 2-10, the titration of dilute (0.005 to 0.05 M) solutions of weak monovalent acids and bases with a glass electrode can lead to reliable thermodynamic pKs. Over this pH interval, the activity coefficients of the ionic species can be calculated by means of the Debye-Hiickel equation. Also, the activity coefficients of the neutral species remain essentially constant and... 

For ionic species, we compute activity coefficients with the Davies equation 13-18. For the neutral species H,P04, we assume that y 1.00. 

E. feU (a) Using the ion-pair equilibrium constant in Appendix J, with activity coefficients = 1, find the concentrations of species in 0.025 M MgS()4. Hydrolysis of the cation and anion near neutral pH is negligible. Only consider ion-pair formation. You can solve this problem exactly with a quadratic equation. Alternatively, if you use SOLVER, set Precision to le-6 (not le-16) in the SOLVER Options. If Precision is much smaller. SOLVER does not find a satisfactory solution. The success of SOLVER in this problem depends on how close your initial guess is to the correct answer. 

Considering just acid-base chemistry, not ion pairing and not activity coefficients, find the pH and concentrations of species in 1.00 L of solution containing 0.040 mol benzene-1,2,3-tricarboxyl ic acid (H3A), 0.030 mol imidazole (a neutral molecule, HB), and 0.035 mol NaOH. 

And, finally, the activity coefficient for a neutral species X is given by... 

This assumption limits application of the latter chemistries to low pressures. Activity coefficients for aqueous-phase gases (CO2, O2, and CH4) are calculated using the Pitzer equation for neutral species (Eq. 2.42). Activity coefficients for aqueous acids are calculated using the Pitzer equations for ions (Eqs. 2.40 and 2.41). For the case of HC1, the Henry s law constant is given by... 

Finally, there is the matter of ion activity coefficients. The Davies equation given in Chapter 1 will be used, because all of the solutions are in the dilute range. In addition, ion pairing corrections will be made for the CaHCC>3+ and CaC03° ion pairs. This step requires iteration in calculation of the ion activity coefficients. The sequence demanded by the problems is that the concentrations must be initially calculated using ion activity coefficients from the previous case. These new concentrations are then used to calculate new ion activity coefficients, and the process is repeated until the desired degree of precision is reached. Neutral species will be assumed to have an ion activity coefficient of 1, and the ion activity coefficients of H+, OH-, and CaHCC>3+ will be assumed equal. 

Case 1. A raindrop of pure water equilibrates with atmospheric CO2. Let a raindrop of pure water with a pH = 7 (At = 0) form and come to equilibrium with CO2 in the atmosphere at PCO2 = 330 patm. We assume that there is no Ca in the initial water. Also, At cannot change because a neutral species (CO2) is being added. The first thing that must be done is to establish clearly the conditions before the CO2 enters the raindrop. From the pH being equal to 7, it follows that aH+ = 10 7 and aoH = (Kw / aH+) = 10 7. Because H+ and OH- are not involved in ion pairing reactions, from the Davies equation their ion activity coefficients are equal. Therefore, their concentrations will also be equal. 

Finally, this section has focused primarily on ions in aqueous solution but it should be remembered that aqueous solutions also contain important dissolved neutral species, e.g. O2, CO2, H2CO3, Si(OH)4. For non-ideal solutions, the Setschenow Equation (1899) has traditionally been used to describe the ionic strength dependence of the activity coefficients for dissolved neutral species and can be written as... 

For an ideal solute, jj is 1, and the activity of species j equals its concentration. This condition can be approached for real solutes in certain dilute aqueous solutions, especially for neutral species. Activity coefficients for charged species can be appreciably less than 1 because of the importance of their electrical interactions (discussed in Chapter 3, Section 3.1C). 

Before the activity coefficients calculated on the basis of the Debye-Hiickel model can be compared with experiment, there arises a problem similar to one faced in the discussion of ion-solvent interactions (Chapter 2). Thae, it was realized the heat of hydration of an individual ionic species could not he measured because such a measurement would involve the transfer of ions of only one species into a solvent instead of ions of two species with equal and opposite charges. Even if such a transfer were physically possible, it would result in a charged solution and therefore an extra, undesired interaction between the ions and the electrified solution. The only way out was to transfer a neutral electrolyte (an equal number of positive and negative ions) into the solvent, but this meant that one could only measure the heat of interactions of a salt with the solvent and this experimental quantity could not be separated into the individual ionic heats of hydration. 

Thirdly, another corollary of the first limitation, is the inconsistency and inadequacy of activity coefficient equations. Some models use the extended Delbye-Huckel equation (EDH), others the extended Debye-Huckel with an additional linear term (B-dot, 78, 79) and others the Davies equation (some with the constant 0.2 and some with 0.3, M). The activity coefficients given in Table VIII for seawater show fair agreement because seawater ionic strength is not far from the range of applicability of the equations. However, the accumulation of errors from the consideration of several ions and complexes could lead to serious discrepancies. Another related problem is the calculation of activity coefficients for neutral complexes. Very little reliable information is available on the activity of neutral ion pairs and since these often comprise the dominant species in aqueous systems their activity coefficients can be an important source of uncertainty. 

It has been argued that the neutral species involved is an ion pair rather than HPFg, and that the mechanism involves acid-assisted dissociation . An activation energy of 25.2 kcal.mole" is claimed. Rate coefficients k -k are given in Table 15. 

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