Molal activity

Table 21.9 Stoichiometric mean molal activity coefficients (7,) for aqueous inorganic...

Utilizing the above five experimentally derived rate constants and Eyring rate theory, the ten rate constants of Eq. 6 are all obtained. With the rate constants known, the probability of each occupancy state, /(ox) for example, can be calculated and finally the single channel current can be calculated as a function of molal activity of sodium ion. This is done for a 100 mV transmembrane potential in Fig. 9. It should be emphasized that Fig. 9 represents a calculation of single channel currents... 

The symbol used is dependent upon the method of expressing the concentration of the solution. The recommendations of the IUPAC Commision on Symbols, Terminology and Units (1969) are as follows concentration in moles per litre (molarity), activity coefficient represented by y, concentration in mols per kilogram (molality), activity coefficient represented by y, concentration expressed as mole fraction, activity coefficient represented by f... 

In practical electrochemistry, however, the molality m or molar concentration c is used more often than the mole fraction. Thus, the molal activity amy molal activity coefficient ym, molar activity ac and molar activity coefficient yc are introduced. The adjective molal is sometimes replaced by practical . 

If a2/ax = gim2lgxmx m2/mx (a = activity, g = molal activity coefficient, m = molality) if Henry s law is obeyed and a = gm, mh and m2 are the molal solubilities of the polymorphs, and if the standard molar enthalpies and standard molar entropies of solution are, respectively,... 

Of course, (4.9) cannot be used at higher ionic strengths. A more precise procedure is then required, such as the Robinson-Stokes equation for the mean molal activity coefficient [11] (see also [86a], chapter 1)... 

Table III. Molal Activity Coefficients at 25° C Comparison of Theory and Experiment...

Here is the chemical potential of i in its standard state and a, is its molal activity. This equation can be recast in the form known as the van t Hoff reaction isotherm ... 

Equation 6-24 and the equations that follow from it apply to molal activities. However, the concentration can be substituted for activity in very dilute solution where the behavior of the dissolved molecules approximates that of the hypothetical ideal solution for which the standard state is defined. For any real solution, the activity can be expressed as the product of an activity coefficient and the concentration (Eq. 6-26). 

In equation 3 the terms of fNa+ and 7H + are the rational activity coefficients of exchanging cations in the zeolite phase and the terms yNa+ and XM + are the molal single ion activity coefficients in the solution phase. Equation 4 can be rewritten as equation 5 when the two salts, NaX and MX2 have a common anion. The mean molal activity coefficients usually can be estimated from literature data. The corrected selectivity coefficient includes a term that corrects for the non-ideality of the solution phase. Thus any variation in the corrected selectivity coefficient is due to non-ideality in the zeolite phase (see equation 3). 

In the concentration range regarding the ED processes, the effective diffusion coefficient (Z>B) can be predicted via the Gordon relationship (Reid et al, 1987), which accounts for the partial derivative of the natural logarithm of the mean molal activity coefficient (y+) with respect to molality (m) and solvent relative viscosity (rjr) ... 

FIG. 2 Effect of solute molality (m) on the mean molal activity coefficient (y ) for sodium chloride (O), sodium acetate (O), and sodium propionate ( ) at 25°C, as extracted from Robinson and Stokes (2002). The continuous lines were calculated using Eq. 9 and the empirical coefficients At extracted from Fidaleo and Moresi (2005a,b, 2006). 

In some cases it is more convenient to define a molal activity coefficient for the solute in the polymer phase and a molar activity coefficient for the liquid phase. Combining Eq. (4-33) and (4-43) one gets ... 

The partition coefficient describing solute partitioning between air and polymer is often referred to as a solubility coefficient, S. The solubility coefficient can be expressed in terms of the molal activity coefficient for polymers using Eq. (4-40) ... 

Calculate the molal activity coefficients of the cane sugar in each of the solutions. 

Determine the mean molal activity coefficient at 25°C for A12(S04)3 present at 2 x 10-4 m concentration in a solution also containing a 10-4 m Na3P04. 

Two additional observations should be made. First, the methods used here treat each of the ionic types as a separate species that influences the thermodynamic properties of solutions very strongly by virtue of its associated charge. Second, it is instructive to examine the dependence of the mean molal activity coefficient for several different electrolytes as a function of the molality. Representative examples are shown in Fig. 4.3.1. One sees at first a very steep drop in as m is increased, and then either a gradual or a very sharp... 

FIGURE 4.3.1 Variation of mean molal activity coefficient as a function of molality for several salts in aqueous solutions. 

Determine the mean molal activity coefficient for LiCi at the concentrations c - 10-2, 3.3 x 10-2, 10 1 mol/liter. 

One notes that a knowledge of the mean molal activity of HCi in a solution of molality m and the tabulation of standard emfs enables one to calculate the value for the schematized cell. Normally, however, the procedure is used in reverse i.e., from a measurement of emfs the mean activity coefficients for ions in solution may then be determined. The procedure is now... 

Determine the equilibrium constant for the dissociation of Hg2Ci2 into ionic constituents. Determine both the mean molal activity coefficient and molality of the ions in equilibrium with the undissolved salt at 25°C. 

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