Mole fraction, defined

In addition to the representation of concentration with the help of the equivalent ionic fraction (Equations 7.2a and b), there are other forms of expressing the concentration in ion- exchange experiments such as the cationic mole fraction defined as [33]... 

From the above relationship, we can sense that molecular distrihution has something to do with entropy generation during mixing. R, the Gas Constant, has the dimensions of entropy (energy per unit absolute temperature) and and Ng are dimensionless mole fractions defined by... 

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. 

Another way to measure concentration is with mole fraction, defined as the number of moles of a given component of a solution... 

Two related dimensionless concentrations are the mass fraction and molar (mole) fraction, defined, respectively, by... 

The brackets represent the thermodynamic activity. At low concentrations in water, the concentration value can be used for activity at higher concentrations or with other ions in solution, the concentration value must be multiplied by the activity coefficient. The activity of the ions on the ion-exchange medium is not readily available the mole fraction, defined as the moles of an individual component divided by the total moles of all components in the phase, has been used in its place (Rieman and Walton 1970). 

These expressions suggest another way to understand partial pressures. We might choose to express the concentration of each component gas in terms of its mole fraction, defined as... 

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) ... 

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