Activity coefficient mole fraction

As examples of the use of these equations to fit activity-coefficient data, refer to Figs. 3.5 and 3.6, where the activity coefficient-mole fraction curves drawn are given by Eqs. (3.52) and (3.53), with the indicated values of the constants Aab and Aba-... 

A solution which obeys Raoult s law over the full range of compositions is called an ideal solution (see Example 7.1). Equation (8.22) describes the relationship between activity and mole fraction for ideal solutions. In the case of nonideal solutions, the nonideality may be taken into account by introducing an activity coefficient as a factor of proportionality into Eq. (8.22). 

In thermodynamics the formal way of dealing with nonideality is to introduce an activity coefficient 7 into the relationship between activity and mole fraction ... 

The two cases relating the activity of a component to its mole fraction, given above, are specific examples of a more general way of relating activity to mole fraction. The activity and the mole fraction of a component in a solution are related through a parameter known as the activity coefficient. 

The activity and mole fraction are so close that the activity coefficient is virtually unity. (It is of interest to note that the mole fraction N2 of the solute in a 1 molal aqueous solution is only 1.0000 — 0.9823 = 0.0177, and so it is not surprising to find that the solvent obeys Raoult s law.)... 

The ratio of activity and mole fraction defines the activity coefficient, a = Xs7s [76]. For an ideal solution the activity is equal to the mole fraction since the activity coefficient equals unity. 

A substance in solution has a chemical potential, which is the partial molar free energy of the substance, which determines its reactivity. At constant pressure and temperature, reactivity is given by the thermodynamic activity of the substance for a so-called ideal system, this equals the mole fraction. Most food systems are nonideal, and then activity equals mole fraction times an activity coefficient, which may markedly deviate from unity. In many dilute solutions, the solute behaves as if the system were ideal. For such ideally dilute systems, simple relations exist for the solubility of substances, partitioning over phases, and the so-called colligative properties (lowering of vapor pressure, boiling point elevation, freezing point depression, osmotic pressure). 

Activities and mole fractions in Table 14.4 are combined to give activity coefficients and plotted versus esioj02> respectively, just as in... 

Here the N b denote the mole fraction of glycine in water and benzene, respectively, and the fs denote proportionality constants, (activity coefficients) relating activity to mole fraction. One of these constants may be arbitrarily chosen it is convenient to make the choice so that = 1 in a very dilute aqueous solutionf. At equilibrium (o ), = ag)g, and hence from (2) ... 

The ratio of activity and mole fraction defines the activity coefficient, af = Xs js [108]. For an ideal mixture, the activity is equal to the mole fraction since the activity coefficient equals unity. That is, we may expand the first term on the RHS in a convenient manner, excluding xn (i.e., for a solvent containing several solutes it might be convenient to label the solvent as species N) ... 

At 300 K, an alcohol s partial pressure over a 0.5 mol water solution is found to be 0.05 bar, whereas over the pure liquid it is 0.08 bar. The partial pressure of water over the solution is found to be 0.02 bar compared to 0.03 bar over pure water. Compare the activities of the liquids in solution with their mole fractions. What are the values of the activity coefficients (ratio of activity to mole fraction) ... 

In the above, a — thermodynamic activity, X = mole fraction, and / and / are activity coefficients. / is the limiting activity coefficient at infinite dilution, which is assumed to be independent of concentration at the concentrations encountered in this investigation. It is ecjuivalent to the Henry s law constant [11]. 

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

LIQUTD-PHASE MOLE FRACTION ACTIVITY COEFFICIENTS... 

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. 

The stabiHty criteria for ternary and more complex systems may be obtained from a detailed analysis involving chemical potentials (23). The activity of each component is the same in the two Hquid phases at equiHbrium, but in general the equiHbrium mole fractions are greatiy different because of the different activity coefficients. The distribution coefficient m based on mole fractions, of a consolute component C between solvents B and A can thus be expressed... 

Liquid mole fraction Vapor mole fraction Temper- ature, R Relative volatifity Pressure activity coefficient Endialpy, Btu/ (Ib-mol) Heat capacity, Btu/(lb-mol- R)... 

T] Use with log mean mole fraction differences based on ends of column, t = rise time. No continuous phase resistance. Stagnant drops are likely if drop is very viscous, quite small, or is coated with surface active agent. A.y uiean dispersed liquid M.T. coefficient. 

Consequently, the partition ratio in mole-fraction units is a result of the ratio of activity coefficients in the two layers [Eq. (15-7)]. 

Activity coefficients are equal to 1.0 for an ideal solution when the mole fraction is equal to the activity. The activity (a) of a component, i, at a specific temperature, pressure and composition is defined as the ratio of the fugacity of i at these conditions to the fugacity of i at the standard state [54]. 

In Chapter 7 we found it convenient to distinguish between proton transfers involving a solvent molecule and those involving only solute particles but this difference will lose its significance when the distinction between solvent and solute begins to break down. We recall that in Sec. 54 the mole fraction of the solvent did not differ appreciably from unity and could be omitted from (72). In investigating concentrated solutions, however, there is no question of extrapolating to infinite dilution the mole fraction of the solvent will differ from unity and will have to be retained in all formulas. At the same time each of the mole fractions will need to be multiplied by its activity coefficient. 

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... 

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