Mean molal

The following data (for 25°C) were obtained at the pzc for the Hg-aqueous NaF interface. Estimate and plot it as a function of the mole fraction of salt in solution. In the table,/ is mean activity coefficient such that a = f m , where m is mean molality. 

Sometimes tabulated values of the mean molal heat capacities Cp (T) are more easily accessible than C (T data, with respect to a reference temperature of T = 25°C (see Table 2-45). Since Cp is defined over the range T and T, by... 

Mean Molal Heat Capacities of Gases Between 25°C and T°C (Reference pressure = 0)... 

In the event the mean molal heat capacity data are available with a reference temperature other than = 25°C (see Table 2-46 for data with = 0°C), the following equation can be used to calculate AH (Tj) ... 

An alternative representation is useful when data on mean molal heat capacities Cj (T) are available with 25 C as the reference temperature (T ). Then the equation... 

Method 3. Use mean molal heat capacity data from Table 2-46 with reference conditions of 0°C and 1 atm. Then the equation for T, is... 

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

The mean molality values m (moles per kilogram), mole fractions x (dimensionless number) and concentrations c (moles per cubic decimetre) are related by equations similar to those for non-electrolytes (see Appendix A). 

The cost of refrigerant is 11.5 GJ 1, the mean molal heat capacity of the vapor is 40 kJ kmol-1K-1, and the latent heat of acetone is 29,100 kJ kmol-1. 

To achieve a uniform definition of y + for all electrolytes, it is convenient to define a mean molality m+ (for BaCl2, for example) as... 

In a solution of mixed electrolytes, the presence of common ions must be considered when calculating the mean molality. For example, in a solution in which mNaci = 0.1 and mivigcij = 0.2, the mean molality m +, for NaCl is... 

Thus, when calculating the mean molality of an electrolyte in a mixture, we must use the total molality of each ion, regardless of the source of the ion. 

In the most dilute solutions studied, the molality of chloride ion was considerably greater than the molality of the hydrogen ion, because of the solubility of AgCl. Therefore, the mean molality m+ is tabulated, rather than the molality of either ion. 

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)... 

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). 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

If 1 mol of the electrolyte AB Incomes split to a gram-ions A and a gram-ions B, with the remainder (1— a.) of the oompound AB undissociated, the so called total mean molal free energy Q of the dissolved electrolyte is expressed by the sum total of products of the potentials of all components of the electrolyte and the corresponding number of their moles or gram-ions, thus ... 

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. 

The Mean Molal Activity Coefficient Calculation for the Macro-Component Salts. The mean molal activity coefficients for the macro-component chloride and sulfate salts are given in Figures 2a and 2b, respectively. Because of the unavailability of measured activity coefficient data in brines, validation of the results presented in Figures 2a and 2b was not possible. 

Figure 2. Mean molal activity coefficients of macrocomponent salts as a function of ionic strength for sea water concentrates. Normalized molar composition ratios Na = 1.00 = 0.021 Mg = 0.136 Ca Cd Fh Zn = 0.001 CU...

Considering the assumptions incorporated into the carbonate subroutine and in using the mole-fraction statistical model for the partitioning of the mean molal activity coefficients into single Ion activity coefficients, the agreement between predicted and measured trace metal concentrations in GSL brine was better than expected. 

The mean molality of the electrolyte is defined, in an analogous manner, by... 

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