Molality of the species

Of the various factors that cause redox disequilibria, the most effective are biologic activity (photosynthesis) and the metastable persistence of covalent complexes of light elements (C, H, O, N, S), whose bonds are particularly stable and difficult to break (Wolery, 1983). For the sake of completeness, we can also note that the apparent redox disequilibrium is sometimes actually attributable to analytical error or uncertainty (i.e., difficult determination of partial molalities of species, often extremely diluted) or even to error in speciation calculations (when using, for instance, the redox couple Fe /Fe, one must account for the fact that both Fe and Fe are partly bonded to anionic ligands so that their free ion partial molalities do not coincide with the bulk molality of the species). 

In this equation, AG°eact is the change in the GFE for the reaction as written for reactants and products in their standard states it is calculated from Eq 2.20. The a s are the activities of the species indicated by the subscripts each activity is raised to a power equal to the stoichiometric coefficient of the species as it appears in the reaction. The activity is frequently called the effective concentration of the species because it naturally arises as a function of the concentration, that is necessary to satisfy the changes in the thermodynamic functions (here, the GFE). In electrochemical systems, the activity is usually related to the molality of the species (moles per 1000 g of solvent) by the following equation ... 

In dilute solutions, the activity and molality are numerically equivalent. The molality of the species and the activity are related by... 

The integral terms representing AH and AH can be computed if molal heat capacity data Cp(T) are available for each of the reactants (i) and products (j). When phase transitions occur between T and Tj for any of the species, proper accounting must be made by including the appropriate latent heats of phase transformations for those species in the evaluation of AHj, and AH terms. In the absence of phase changes, let Cp(T) = a + bT + cT describe the variation of (cal/g-mole °K) with absolute temperature T (°K). Assuming that constants a, b, and c are known for each species involved in the reaction, we can write... 

Since an ionic solution contains two species of solute particles, the positive and negative ions, it is often useful to mention the molality of each species. If barium chloride, for example, dissolved in a solvent, is completely dissociated into Ba++ ions and Cl- ions, the molality of the Ba++ will be equal to the molality of the solute BaCb, while the molality of the Cl- will be twice as great. 

The following values may be used for the molal heat capacities (at constant pressure) of the species involved in the reaction. 

The mole fraction X in the previous equation is replaced with a new unitless variable at, the species activity. The standard potentials pt° are defined at a new standard state a hypothetical one-molal solution of the species in which activity and molality are equal, and in which the species properties have been extrapolated to infinite dilution. 

This choice of a standard state seems like impossible mental gymnastics, but it allows activity to follow a molal scale, so that in dilute solutions activity and molality - despite the fact that activity is unitless - are equivalent numerically. A species molality m , the number of moles of the species per kilogram of solvent, is related to its activity by... 

Here, we have represented the activities of aqueous species with the product y m of the species activity coefficients and molalities, according to Equation 3.6. The symbol IT in this equation is the product function, the analog in multiplication to the summation . Table 3.2 lists the meaning of each variable in this and following equations. 

Some of the species concentrations predicted by the mathematical model are too small to be physically meaningful. The predicted concentration of H2(aq), for example, is 4 x 10-45 molal. Multiplying this value by Avogadro s number... 

To show mass balance, we add the molalities of each species containing a component (but not species concentrations in mg kg-1, since the mole weight of each species differs) to arrive at the input constraint. Taking component SO4 as an example, we find the total mole number (A/,) from the molalities (m, and m.j) of the sulfur-bearing species... 

Here, the notations SSO - and SII2S(aq) refer, respectively, to the sum of the molalities of the sulfate and sulfide sulfur species in solution. 

Fig. 15.11. Concentrations (molal) of the predominant carbonate species over the course of a reaction path in which NaOH is added to a fluid that maintains equilibrium with C02 in the atmosphere.

The membrane-water distribution ratio Dmw is defined by the ratio between the sum of the molalities of all species of the considered compound in the... 

For applications where the ionic strength is as high as 6 M, the ion activity coefficients can be calculated using expressions developed by Bromley (4 ). These expressions retain the first term of equation 9 and additional terms are added, to improve the fit. The expressions are much more complex than equation 9 and require the molalities of the dissolved species to calculate the ion activity coefficients. If all of the molalities of dissolved species are used to calculate the ion activity coefficients, then the expressions are quite unwieldy. However, for the applications discussed in this paper many of the dissolved species are of low concentration and only the major dissolved species need be considered in the calculation of ion activity coefficients. For lime or limestone applications with a high chloride coal and a tight water balance, calcium chloride is the dominant dissolved specie. For this situation Kerr (5) has presented these expressions for the calculation of ion activity coefficients. 

If proton (or deuteron) concentrations and OH (or, OD ) concentrations are measured in molalities, OTh+ (or, mo+) and moH (or, OTod ) respectively, then is defined as the product of the molalities of the positively charged and negatively charged species. Since is a thermodynamic constant, it is not surprising that it should vary with temperature. Defining pf = log... 

Evidence for the formation of such hydrogen-bonded cation pairs in solution has been obtained by three-phase vapor tensiometry studies on solutions of cis-Cr(bipy)2(H20)(0H)2+ in a saturated solution of barium nitrate (the total molality of chromium species was 0.1-0.2 m) (326, 330). It was shown that the equilibrium of Eq. (29) in concentrated solutions lies considerably to the right, and it was estimated that Kip-IM-1. 

A 1.00% NaCl(aq) by mass solution has a freezing point of —0.593°C. (a) Estimate the van t Hoff i factor from the data, (b) Determine the total molality of all solute species, (c) Calculate the percentage dissociation of NaCl in this solution. (Hint The molality calculated from the freezing-point depression is the sum of the molalities of the undissociated ion pairs, the Na+ ions, and the Cl ions.)... 

The Pseudo-Phase Model Consider a process in which surfactant is added to water that is acting as a solvent. Initially the surfactant dissolves as monomer species, either as molecules for a non-ionic surfactant or as monomeric ions for an ionic surfactant. When the concentration of surfactant reaches the CMC, a micelle separates from solution. In the pseudo-phase model,20 the assumption is made that this micelle is a separate pure phase that is in equilibrium with the dissolved monomeric surfactant. To maintain equilibrium, continued addition of surfactant causes the micellar phase to grow, with the concentration of the monomer staying constant at the CMC value. This relationship is shown in Figure 18.14 in which we plot m, the stoichiometric molality,y against mj, the molality of the monomer in the solution. Below the CMC, m = m2, while above the CMC, m2 = CMC and the fraction a of the surfactant present as monomer... 

Two methods are possible. In the first method we assume the nonionized species to be carbonic acid, H2C03, and define its molality as the sum of the molalities of the actual nonionized species. If we designate the molalities of the actual species by primes, then the chemical potential of the assumed species is written as... 

Equation (11.66) and, consequently, Equation (11.67) can be obtained on the assumption of an equilibrium between hydrogen ion and hydronium ion with water by the same methods used for carbonic acid. We assume the acid species to be either hydrogen ion or hydronium ion at a molality equal to the sum of the actual molalities of the two species, so... 

The value of K can be calculated provided that we know the molalities and activity coefficients of the species which are indicated. The molality of HA is (mt - mH,) and that of A is (m2 + mH+). When K is sufficiently small,... 

This equation gives the relation between F and P" when the equilibrium molalities of the ionic species and the activity coefficient of the water at the two pressures are known. If we choose to make use of the activity coefficient of water at the same pressure F, the equation becomes... 

In synthetic work AsF5-HF solutions are usually at or near ambient temperatures where, as was shown in subsequent Melbourne work [14], speciation is more complex than near the freezing point of HF. Raman spectra of a solution 0.1 molal in AsF5 demonstrated the presence at ambient temperature of peaks for each of the species in the following equation ... 

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