Activity coefficient of a component

Several formalisms have been developed to relate die activity coefficient of a component in the solution to the temperature and composition of the solution. We now discuss the following two models ... 

The liquid phase activity coefficient of a component in a L-V mixture is usually given by... 

Wilson s equation of state is found from Equations (14) and (15). It can be seen that for obtaining the activity coefficient of a component 1 in a pure solvent 2, we need four interaction parameters (A12, A21, An a A22, which are temperature dependent. It is evident that for calculating the value of the binary interaction parameters, additional experimental data, such as molar volume is needed. Other models which belong to the first category have the same limitations as Wilson s method. The Wilson model was used in the prediction of various hydrocarbons in water in pure form and mixed with other solvents by Matsuda et al. [11], In order to estimate the pure properties of the species, the Tassios method [12] with DECHEMA VLE handbook [13] were used. Matsuda et al. also took some assumptions in the estimation of binary interactions (because of the lack of data) that resulted in some deviations from the experimental data. 

The activity coefficient of a component in a mixture is a function of the temperature and the concentration of that component in the mixture. When the concentration of the component proaches zero, its activity coefficient approaches the limiting activity coefficient of th component in the mixture, or the activity coefficient at infinite dilution, y . The limiting activity coefficient is useful for several reasons. It is a strictly dilute solution property and can be used dir tly in nation 1 to determine the equilibrium compositions of dilute mixtures. Thus, there is no reason to extrapolate uilibrium data at mid-range concentrations to infinite dilution, a process which may introduce enormous errors. Limiting activity coefficients can also be used to obtain parameters for excess Gibbs energy expressions and thus be used to predict phase behavior over the entire composition range. This technique has been shown to be quite accurate in prediction of vapor-liquid equilibrium of both binary and multicomponent mixtures (5). 

Equations (8) to (11) indicate that, if for any reason the activity coefficient of a component i in a binary solution is raised to the extent that the product f.X. becomes larger than unity, phase separation will occur and the component i will flow from an area of lower concentration into an area of higher concentration. Thus the flux of the component i is against the concentration gradient but 1 follows the chemical potential gradient. 

The activity coefficient of a component can be changed for example by changing the temp>erature or the composition of the mixture, A typical example is the so-called "salting-out" effect, where the activity of the salt in an aqueous solution is raised by adding an organic solvent to such an extent that the salt precipitates from the solution. 

Thus, for a binary mixture, the excess functions are identically zero at the composition extremes Tor any anxture, the activity coefficient of a component approaches unity as that component approaches purity. 

In other words, the activity coefficient of water dissolved in chlorine is very nearly constant over the entire, but very small, soluble range. Now we go back to the fundamental equation that defines the liquid-phase activity coefficient of a component of a solution when there is ideal gas behavior ... 

The activity coefficient of a component of a solution is a numerical factor by use of which all the deviations of the solution from ideality can be correlated with each other. ... 

Therefore, knowing a state equation of gases and the mixing laws of the parameters of this state equation helps obtain the activity coefficient of a component in the solution this is so in the gas or hquid phase if this state eqnation can be applied to equally represent both the hquid phase and the gas phase. 

Sometimes the thermodynamic data are expressed in the form of an empirical equation. For example, the activity coefficient of a component in a solution is often expressed as a function of composition in terms of an empirical equation. In such cases, the Gibbs-Ouhem equation can be solved analytically instead of graphically. The following example illustrates the analytical integration of the Gibbs-Duhem equation. 

Coefficient in Wohl Eq.(13) y = Constant used in BWR-11 Eq. (Table II) y = Activity coefficient of a component in liquid 6 = Solubility parameter v(0) = Simple fluid liquid fugaclty coefficient v(l) = Liquid fugacity coefficient correction term TT = System pressure... 

Conventionally, the activity coefficient of a component tends toward 1 if the molar fiaction of the other component tends toward zero, so the limited expansion does not contain a constant term. 

Activity coefficients of a component with a pure-substance reference... 

For a binary solution, we use the excess partial molar Gibbs energy to deduce the activity coefficient of a component / ... 

The solubility which results from an equilibrium of a component between two phases - one the pure phase of one of the components, and the other the solution - can also be used to determine the activity or the activity coefficient of a component in a solution. In general, it pertains mainly to solutes, but it is also applicable to solutions for which the concept of a solvent is no longer clear. The two phases including the component in questions are usually the pure solid phase on the one hand, and the liquid solution on the other. 

Thus, relations [5.37] or [5.38] enable us to calculate the activity coefficient of a component if we know the composition of the solution, the temperature of solubility equilibrium chosen, the melting point of the pure component in its natural phase and its standard enthalpy of melting at the temperature in question. 

To a first approximation, the deviations from ideality may be expressed by regular solution theory (Guggenheim, 1952, p. 29), in which the activity coefficient of a component in a binary system is given by the simple expression ... 

Ganguly (1973). An expression for the activity coefficient of a component in a quaternary regular solution (without ternary or quaternary terms cf. Prigogine and Defay, 195 > p.257) is simplified on the basis of observed behaviour in the system diopside (plus hedenbergite) - jadeite - acmite - CATS molecule. The final form gives the activity coefficient of the jadeite component as a function of one adjustable Margules parameter,... 

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