Activity coefficient from

To determine values of the activity coefficient of hydrogen chloride over a range of concentrations in aqueous solution by measurement of e.m.f. and to fit these by a semi-empirical formula. 

values in (absolute) millivolts are given in table 1 where m denotes the molality of HCl. 

After we have obtained the value of E°, the activity coefficient y at each experimental concentration is given by 

Using these values we construct table 2. We plot E against m in fig. 1. 

We see that a straight line can be cirawn through all but the last two points. Most of the other points lie within 0.01 mV of the line. The intercept = 267.96 mV is in exact agreement with the value which Hills and Ives obtained by a somewhat less direct method of extrapolation. The line has a slope given by 

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There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Activity coefficients are dimensionless. With standard states selected as indicated above, activity coefficients will be unity in ideal systems. The degree of departure of a system from the ideal state is described by the departure of the activity coefficients from unity. 

Estimation of activity coefficients from azeotropic data... 

For systems that are only partially miscible in the liquid state, the activity coefficient in the homogeneous region can be calculated from experimental values of the mutual solubility limits. The methods used are described by Reid et al. (1987), Treybal (1963), Brian (1965) and Null (1970). Treybal (1963) has shown that the Van-Laar equation should be used for predicting activity coefficients from mutual solubility limits. 

Brian, P. L. T. (1965) Ind. Eng. Chem. Fundamentals 4, 100. Predicting activity coefficients from liquid phase solubility limits. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Given a prediction of the liquid-phase activity coefficients, from say the NRTL or UNIQUAC equations, then Equations 4.69 and 4.70 can be solved simultaneously for x and x . There are a number of solutions to these equations, including a trivial solution corresponding with x[ = x[. For a solution to be meaningful ... 

Here y,1 and y,2 are the corresponding activity coefficients of component i in phase 1 and 2, Xj1, and x,2 are the mole fraction of components i in the system and in phase 1 and 2 respectively. The interaction parameters between methylcyclohexane, methanol and ethyl benzene are used to estimate the activity coefficients from the UNIQUAC groups. Eqs. (1) and (2) are solved for the mole fraction (x) of component i in the two liquid phase.The UNIQUAC model (universal quasi -chemical model) is given by Abrams and prausnitz [8] as... 

Then, we find the pressure dependence of the activity coefficient from... 

Elaborate procedures have been developed for obtaining activity coefficients from freezing-point and thermochemical data. However, to avoid duplication, the details will not be outlined here, because a completely general discussion, which is applicable to solutions of electrolytes as well as to nonelectrolytes, is presented in Chapter 21 of the Third Edition of this book [6]. 

In Chapters 16 and 17, we developed procedures for defining standard states for nonelectrolyte solutes and for determining the numeric values of the corresponding activities and activity coefficients from experimental measurements. The activity of the solute is defined by Equation (16.1) and by either Equation (16.3) or Equation (16.4) for the hypothetical unit mole fraction standard state (X2° = 1) or the hypothetical 1-molal standard state (m = 1), respectively. The activity of the solute is obtained from the activity of the solvent by use of the Gibbs-Duhem equation, as in Section 17.5. When the solute activity is plotted against the appropriate composition variable, the portion of the resulting curve in the dilute region in which the solute follows Henry s law is extrapolated to X2 = 1 or (m2/m°) = 1 to find the standard state. 

Having obtained we can calculate mean activity coefficients from a rearrangement of Equation (19.34) to the form... 

Equations (126) and (127) can be used to calculate activity coefficients from evaporation data, for a, Zj, da fdt, and dz /dt are measurable quantities. The resonance spectrum of an evaporating droplet is highly sensitive to both size and refractive index, and the refractive index of a binary system is a unique... 

Because activity is related to molar concentration through the rational activity coefficient, from equation 3.157 we may derive... 

Because the values for the various salts in solution may be experimentally obtained with a satisfactory precision, equation 8.35 is used to derive the corresponding values of individual ionic activity coefficients from them. For instance, from a generic univalent chloride MCI, the y of which is known, we may derive the 7+ of M+ by applying... 

Therefore, similar to the attempts made to estimate vapor pressure (Section 4.4) there have been a series of quite promising approaches to derive topological, geometric, and electronic molecular descriptors for prediction of aqueous activity coefficients from chemical structure (e.g., Mitchell and Jurs, 1998 Huibers and Katritzky, 1998). The advantage of such quantitative structure property relationships (QSPRs) is, of course, that they can be applied to any compound for which the structure is known. The disadvantages are that these methods require sophisticated computer software, and that they are not very transparent for the user. Furthermore, at the present stage, it remains to be seen how good the actual predictive capabilities of these QSPRs are. 

As the magnitude of the charge of the ion increases, the departure of its activity coefficient from unity increases. Activity corrections are more important for ions with a charge of 3 than for ions with a charge of 1 (Figure 8-4). 

When the volume of titrant is Ve, pH = pK.d for the acid HA (neglecting activity coefficients). From an experimental titration curve, you can find the approximate value of pKa by reading the pH when Fb = Ve, where Vh is the volume of added base. (To find the true value of prequires activity coefficients.)... 

Figure 13-2 Activity coefficients from extended Debye-Huckel and Davies equations. Shaded areas give Debye-Huckel activity coefficients for the range of ion sizes in Table 8-1.

Mixture of KH2P04 and Na2HP04 including activity coefficients from Davies equation ... 

B. IB Repeat Exercise 13-A with activity coefficients from the Davies equation. 

D. 11 Include activity coefficients from the Davies equation to find the pH and concentrations of species in the mixture of sodium tartrate, pyridinium chloride, and KOH in Section 13-1. Consider only Reactions 13-1 through 13-4. 

HH A solution containing 0.008 695 m KH2P04 and 0.030 43 m Na2HP04 is a primary standard buffer with a stated pH of 7.413 at 25°C. Calculate the pH of this solution by using the systematic treatment of equilibrium with activity coefficients from... 

Given a measured cell voltage of +0.798 3 V and using activity coefficients from Table 8-1, find Ag+lAg- Be sure to express PUi in bar in the reaction quotient. 

TABLE 13.2. Activity Coefficients from Solubility Parameters and from the Wilson Equation... 

Fig. 5.5. Deviation of activity coefficients from COSMOSPACE and the BGY model from MC simulations for the system shown in Fig. 5.3.

Finally, there is the matter of ion activity coefficients. The Davies equation given in Chapter 1 will be used, because all of the solutions are in the dilute range. In addition, ion pairing corrections will be made for the CaHCC>3+ and CaC03° ion pairs. This step requires iteration in calculation of the ion activity coefficients. The sequence demanded by the problems is that the concentrations must be initially calculated using ion activity coefficients from the previous case. These new concentrations are then used to calculate new ion activity coefficients, and the process is repeated until the desired degree of precision is reached. Neutral species will be assumed to have an ion activity coefficient of 1, and the ion activity coefficients of H+, OH-, and CaHCC>3+ will be assumed equal. 

Mean Ionic Activity Coefficients from Experimental Data... 

Activity Coefficients from Partial Pressures of Vapors... 

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