Mean molal ionic activity coefficient calculation

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. 

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 ... 

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. 

Problem Assuming to remain constant, calculate the relative change in the mean ionic activity coefficient of 1 molal sulfuric acid solution from 0 to 25 C. 

The solubility of silver chloride in pure water is 1.314 X 10 molal, and the mean ionic activity coefficient is then 0.9985 [Neuman, J. Am. Chem. Soc., 54, 2195 (1932)]. The heat of solution of the salt is 15,740 cal. mole". Taking the entropy of solid silver chloride as 22.97 e.u. mole ", and using the results of the preceding exercise, calculate the standard free energy and heat of formation and the entropy of the Cl" ion at 25 C. 

The E.M.F. of a lead storage battery containing 2.75 molal sulfuric acid was found to be 2.005 volt at 25 C. The aqueous vapor pressure of the acid solution at this temperature is about 20.4 mm., while that of pure water is 23.8 mm. The mean ionic activity coefficient of the sulfuric acid is 0.136. Calculate the standard free energy change of the cell reaction at 25 C and check the values from tabulated free energy data. 

A 0.1 m solution of MgCl2 in water has a density of 1.0047 gmL at 25°C. The mean ionic activity coefficient on the molal scale is 0.528. Calculate the mean activity and electrolyte activity on this scale. Repeat the calculations for the molarity scale. 

The exact calculation equations are given in [25], where it has also been proved that the Gibbs-Duhem equation is fulfilled. As well, NRTL parameters have been fitted up to molalities of 30mol/kg for a number of systems. Together with the ionic diameters, they are listed in [25]. Osmotic and mean ionic activity coefficients could be reproduced in an excellent way for a number of systems. Furthermore, the parameters fitted to binary systems have been successfully applied to ternary systems, that is, one salt in a binary solvent mixture, which always causes problems with the Electrolyte NRTL model [25]. 

From this expression comes the definition of the mean activity coefficient. Y+. in terms of the ionic activity coefficients Yc and Ya The mean activity coefficient is the property which is determined or calculated from experimental measurements. A similar expression results for the mean molality m, which is not generally used in reporting experimental measurements ... 

The mean molal activity coefficient of electrolyte CA in the multicomponent solution can be calculated by combining the ionic activity coefficients ... 

Figure 10.3 shows that with the proper choice of the parameter a, the mean ionic activity coefficient of HCl calculated from Eq. 10.4.7 (dashed curve) agrees closely with experiment (solid curve) at low molalities. 

Rard and Miller used published measurements of the freezing points of dilute aqueous solutions of Na2S04 to calculate the osmotic coefficients of these solutions at 298.15 K. Use their values listed in Table 10.2 to evaluate the mean ionic activity coefficient of Na2S04 at 298.15 K and a molality of wb = 0.15molkg For the parameter a in the Debye-Hiickel equation (Eq. 10.4.7), use the value a = 3.0 x 10 ° m. 

Fig. 6. Mean ionic activity coefficients of five bromide salts in aqueous solution at 25 °C as fimction of salt molality. Experimental data LiBr — squares, NaBr — stars, KBr — circles, RbBr — crosses, CsBr — triangles. The dotted lines represent ePC-SAFT calculations. Activity coefficients decrease with increasing size of the cation Ii+ > Na+ > K+ > Rb+ > Cs . (From Ref. 15, Elsevier, reprinted with permission.)...

If the validity of Eq. (1.3.31) is assumed for the mean activity coefficient of a given electrolyte even in a mixture of electrolytes, and quantity a is calculated for the same measured electrolyte in various mixtures, then different values are, in fact, obtained which differ for a single total solution molality depending on the relative representation and individual properties of the ionic components. 

The Macinnes convention leads to = Tci = 7 kci, We can now compute individual ion activity coefficients from their mean values measured in solutions of strong electrolytes using y Kci values as our starting point. (In the ideal strong electrolyte, cations and anions are unassociated with each other and thus do not form complexes [see Chap. 3].) It is important to remember that all such calculations must be done with y values for KCl and other salts measured at the same ionic strength, which is not the same molality except for monovalent-monovalent salts. 

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