Mean molal ionic activity coefficient

Gerke [130] and HiUs and Ives [98] have reviewed papers concerning the electrode Hg Hg2Br2 Br. Standard potentials of this couple have been determined using mean molal ionic activity coefficients of HBr or by using the standard potential of the silver/silver bromide electrode. The obtained standard potential is 0.139 V, with deviations within the range of 1 mV. 

The LCM has proven to be useful in predicting data of molal ionic activity coefficients and vapor pressure depression of various single electrolyte, single solvent systems. The standard deviation of the natural logarithm of the mean activity coefficient was 0.01 for uni-univalent aqueous single electrolytes (17). Similar results... 

E6.12 The HC1 pressure in equilibrium with a 1.20 molal solution is 5.15 x 10 8 MPa and the mean ionic activity coefficient is known from emf measurements to be 0.842 at T = 298.15 K. Calculate the mean ionic activity coefficients of HC1 in the following solutions from the given HC1 pressures... 

The standard state for the mean ionic activity coefficient is Henry s constant H., f is the standard-state fugacity for the activity coefficient f- and x. is the mole fraction of electrolyte i calculated as though thi electrolytes did not dissociate in solution. The activity coefficient f is normalized such that it becomes unity at some mole fraction xt. For NaCl, xi is conveniently taken as the saturation point. Thus r is unity at 25°C for the saturation molality of 6.05. The activity coefficient of HC1 is normalized to be unity at an HC1 molality of 10.0 for all temperatures. These standard states have been chosen to be close to conditions of interest in phase equilibria. 

Remembering that a+ = y+m + and y2 = 7+7., where y is the mean ionic activity coefficient (appropriate to molality units), enables us to rewrite Equation (85) as... 

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

Figure 8.3 Schematic plot of mean ionic activity coefficient y versus molality (m) for typical strong electrolytes [1 1 (e.g., HC1), light dashed line 2 1 (e.g., H2S04), heavy dashed line], showing the extreme deviations from ideality (dotted line) even in dilute solutions.

At finite concentrations the effect of the solvent on the ion-ion interactions are superimposed on the solvent effect discussed above for infinite dilution. The former effect can be expressed as the mean ionic activity coefficient, y again, expressed conventionally on the molal scale, relative to infinite dilution in the solvent in question, which in dilute solutions, where the extended Debye-Huckel expression is deemed to hold, is ... 

Molal salt concentrations must be translated into mean ionic activity (Eq. (21.7)). The mean ionic activity coefficients of many salts are compiled in the literature as a function of salt concentration (see appendix 8.10... 

The mean ionic molality (m ) and the mean ionic activity coefficient (y ) are defined as... 

Massieu function 48 mathematical constants 83, 90 mathematical functions 83 mathematical operators 84 mathematical symbols 81-86 matrices 83, 85 matrix element of operator 16 maxwell 115 Maxwell equations 123 mean free path 56 mean international ohm 114 mean international volt 114 mean ionic activity 58 mean ionic activity coefficient 58 mean ionic molality 58 mean life 22, 93 mean relative speed 56 mechanics classical 12 quantum 16 mega 74 melting 51 metre 70,71,110 micro 74 micron 110 mile 110 Miller indices 38 milli 74... 

The standard potential of the silver-silver bromide electrode has been determined from emf measurements of cells with hydrogen electrodes and silver-silver bromide electrodes in solutions of hydrogen bromide in mixtures of water and N-methylacetamide (NMA). The mole fractions of NMA in the mixed solvents were 0.06, 0.15, 0.25, and 0.50, and the dielectric constants varied from 87 to 110 at 25°C. The molality of HBr covered the range 0.01-0.1 mol kg 1. Data for the mixed solvents were obtained at nine temperatures from 5° to 45°C. The results were used to derive the standard emf of the cell as well as the mean ionic activity coefficients and standard thermodynamic constants for HBr. The information obtained sheds some light on the nature of ion-ion and ion-solvent interactions in this system of high dielectric constant. 

Table VI. Mean Ionic Activity Coefficients (Molality Scale) of HBr in H20/NMA Solvent Mixtures at 25°C...

It is evident that smoothed values of the mean ionic activity coefficient of HBr (yHBr), scale of molality, can be derived by Equation 1 A and B are given in Table I, and a is 5.2 A. Values of ft (the slope of the E° vs. molality plot divided by — 2k) are listed in Table VI, along with yHBr at molalities from 0.005-0.1 for each solvent mixture at 25°C. For comparison, the corresponding values of the activity coefficient in pure water are listed (19). 

Some further nomenclature is now necessary to describe absorption equilibria in ion exchange systems. For a species i, m and C, represent the molal and molar concentrations respectively, whilst A and Xi denote the mole fraction and equivalent ionic fraction of i respectively. Single ion activity coefficients are denoted yj and mean ionic activity coefficients by yj . Whether the latter quantities refer to the molar or molal concentration scales is decided by the choice of units defining concentration. Thermodynamic activities and activity coefficients for the resin phase using the equivalent or mole fraction concentration scale (rational scale) are sometimes defined differently and are discussed in a later section. Finally, the exchanger and external solution phases are differentiated by subscripts r and s respectively. 

This expression provides a method for evaluating the mean ionic activity coefficient 7 in a hydrochloric acid solution of molality m from a measurement of the E.M.F., i.e., E, of the cell described above it is necessary, however, to know the value of , the standard e.m.f. For this purpose the data must be extrapolated to infinite dilution, and the reliability of the activity coefficients obtained from equation (39.58) depends upon the accuracy of this extrapolation. Two main procedures have been used for this purpose, but both are limited, to some extent, by the accuracy of b.h.f. measurements made with cells containing very dilute solutions. ... 

In the presence of 0.025 molal KCl, the solubility of the TlCl is 0.00869 molal calculate the mean ionic activity coefficient of TlCl in this solution. 

Problem Calculate the approximate mean ionic activity coefficient of a 0.1 molal uni-univalent electrolyte in water at 25° C. 

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