Effective mole fraction

It is sometimes convenient to retain the generality of the limiting ideal-gas equations by introducing the activity a, an effective pressure (or, as we shall see later in the case of solutions, an effective mole fraction. 

The ability of a solute to associate with itself can be expressed by the degree of association (/). The / is obtained by dividing the stoichiometric mole fraction of the solute by the effective mole fraction of the solute. Assuming that a single multimer species in equilibrium with a monomer is a dimer,/values range from 1.0 to 2.024). 

Yi = activity coefficient = (effective mole fraction)/(true mole fraction)... 

Figure 39.4 shows that if = 1 then a = X (i.e. the effective mole fraction corresponds to the actual mole fraction as made up) then we have ideal behaviour. As discussed before (Frame 33, Figure 33.2) both positive and negative deviations from ideality can occur in real liquid mixtures. 

The development of equations that successfully predict multicomponent phase equilibrium data from binary data with remarkable accuracy for engineering purposes not only improves the accuracy of tray-to-tray calculations but also lessens the amount of experimentation required to establish the phase equilibrium data. Such equations are the Wilson equation (13), the non-random two-liquid (NRTL) equation (14), and the local effective mole fractions (LEMF) equation (15, 16), a two-parameter version of the basically three-parameter NRTL equation. Larson and Tassios (17) showed that the Wilson and NRTL equations predict accurately ternary activity coefficients from binary data Hankin-son et al. (18) demonstrated that the Wilson equation predicts accurately... 

When the effective mole fraction of monomer molecules tends... 

The concentration of a pure liquid or a pure solid is usually given a value of one for the equilibrium expression. Concentrations are only approximations for activities. Activities for pure solids and pure liquids are like effective mole fractions. The mole fraction of a pure solid or liquid is one. Although solvents are not actually pure, they are usually considered ideally dilute on the MCAT, which means that their moLe fraction is one. The activity then of a pure solid or liquid is approximately one. Be aware that pure solids or liquids can still participate in the equilibrium. When they do, they must be present in order for equilibrium to exist. 

The term p puK n represents the chemical potential of the pure material, where x is unity. For non-ideal solutions, a term a, the activity of the solvent, which may be thought of as the effective mole fraction, is introduced, and we have, for component 1 ... 

Essentially, the activity of a species is its effective mole fraction. It is introduced in order to preserve the form of equations derived from ideal solution in nonideal situations. All of the deviations from ideality are contained within the activity. For nonideal solutions, we can further isolate this deviation from ideahty by invoking the activity coefficient ()/a)> which relates the activity and the mole fraction of the solute (5) ... 

This equation is the same as Henry s law except for the occurrence of the activity instead of the mole fraction. The activity is an effective mole fraction in expressing the chemical potential and the partial vapor pressure. Equation (6.3-31) is equivalent to... 

Activity may be thought of as an effective mole fraction. RT times the natural logarithm of the activity of a pure substance is the chemical potential relative to the chosen reference (standard state). This means the activity is exactly 1 for a substance in its standard state. For condensed phases, the standard state of a pure substance is its most stable phase. The pressure for standard states is 1 bar for liquids, solids, and the ideal gas. The standard state of a real gas corresponds to its fugacity being 1 bar. 

A negative value for alpha is not, however, compatible with the development of the NRTL equation for it must be positive, since it is proportional to 1/z, z being the coordination number of the liquid (i.e. the number of molecules per cell). The negative value of alpha was explained, therefore, through the concept of local effective mole fractions (LEMF). 

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