Standard mole fraction

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. ... 

According to Equation (14), the fugacity of component i becomes equal to the mole fraction multiplied by the standard-... 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

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]. 

But that is not all. For dilute solutions, the solvent concentration is high (55 mol kg ) for pure water, and does not vary significantly unless the solute is fairly concentrated. It is therefore common practice and fully justified to use unit mole fraction as the standard state for the solvent. The standard state of a close up pure solid in an electrochemical reaction is similarly treated as unit mole fraction (sometimes referred to as the pure component) this includes metals, solid oxides etc. 

The Conventional Standard Free Energy of Solution. Returning now to the solution of a crystalline solid, let us consider the free energy of solution. Taking a uni-univalent substance let AF denote the change in free energy per mole when additional ions are added to a solution at temperature T where the solute has the mole fraction x and let us fix attention on the quantity... 

Figure 6.12 shows a graph of u and a2 as a function of mole fraction for mixtures of. yi H O +. Y2CCI4J12 at T = 308.15 K.. A Raoult s law standard state has been chosen for both components. The system shows negative deviation from Raoult s law over the entire range of composition, with it less than. Y and a2 less than. V2. so that all -r.i and 7R.2 are less than 1. 

Equations (7.93) and (7.94) are usually applied to mixtures of nonelectrolytes where Raoult s law standard states are chosen for both components. For these mixtures, Hi is often expressed as a function of mole fraction by the Redlich-Kister equation given by equation (5.40). That is... 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

Standard state unit mole fraction in solution and unit coverage in monolayer. r=-15 °C. 

We connected our earlier definition of activity to a standard state of 1.0 bar or 1.0 M or a mole fraction of unity. None of these make much sense for electrons, but we may define electron... 

Standard substances of defined purity must be available for major components and the main impurities (criteria mole fraction, toxicity, legal... 

Monton and Llopis (1994) presented VLE data at 6.66 and 26.66 kPa for binary systems of ethylbenzene with m-xylene and o-xylene. The accuracy of the temperature measurement was 0.1 K and that of the pressure was 0.01 kPa. The standard deviations of the measured mole fractions were less than 0.001. The data at 26.66 for the ethylbenzene (1) - o-Xylene (2) are given in Table 15.8 and the objective is to estimate the NRTL and UNIQUAC parameters based on these data. 

The standard term p is the chemical potential of the pure component i (i.e. when Xj = 1) at the temperature of the system and the corresponding saturated vapour pressure. According to the Raoult law, in an ideal mixture the partial pressure of each component above the liquid is proportional to its mole fraction in the liquid,... 

In Eq. (2), Ts is the sample temperature, T0 is the melting point of the pure major component, X, is the mole fraction of the impurity, F is the fraction of solid melted, and AHf is the enthalpy of fusion of the pure component. A plot of Ts against 1 IF should yield a straight line whose slope is proportional to X,. This method can therefore be used to evaluate the absolute purity of a given compound without reference to a standard, with purities being obtained in terms of mole... 

Equation 29 implies that is the chemical potential of a hypothetical solution in which XA = 1, but the vapor pressure over the solution still obeys Henry s law as extrapolated from infinite dilution. Thus the standard state is a hypothetical Henry s law solution of unit mole fraction. 

To evaluate the logarithm, we must measure the vapor pressure Pa of A in equilibrium with a solution where its mole fraction is XA in the limit where the solution becomes infinitely dilute. That is, in the limit of infinite dilution where y is 1, the free energy of solvation can be obtained from measurement of the solute vapor pressure (in the appropriate standard state units) over a solution of known concentration. 

Here, R is the gas constant, 7k is absolute temperature, and XB is the mole fraction of B in the solution phase. Using this equation, we can calculate the equilibrium point of reactions in ideal systems directly from tabulated values of standard potentials p°. 

The mole fraction X in the previous equation is replaced with a new unitless variable at, the species activity. The standard potentials pt° are defined at a new standard state a hypothetical one-molal solution of the species in which activity and molality are equal, and in which the species properties have been extrapolated to infinite dilution. 

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