Consider first the state equations for pure substances. The representation of a state equation in a virial form lies at the basis of multi-coefficient equations. The gas pressure can be represented as a power series in 1/v, where v is the molar volume of the substance [Pg.86]

The equation of state data in the recommendations is given in terms of second virial coefficients for the pure substances, Bi(T), and their interaction coefficients with methane, Bjj(T). (Because of the low pressmes used in the industry, the simple equation PV/RT=1+ B(T)/V is sufficiently accurate). There are very few hydrocarbons for which there are measmed virial coefficient data in the temperature range of interest, and appreciable extrapolations are needed. Also some of the virial coefficients are based on indirect methods, and may be of marginal reliability. To overcome these problems, a correlation developed by K.R.Hall for virial coefficients for all of the hydrocarbon data has been used. It is valid for the range 0 to 25 °C and is based on a reduced equation of state. A computer program in GPA 2172-1985 [13], uses this correlation to calculate real gas properties. [Pg.16]

Of lesser importance are the properties of the pure compounds in the real gas state. These are used to calculate volrrmes needed to interpret flow measurements and to correct ideal- to real-gas enthalpies. Only simple equations of state are required. For pressures up to about one atmosphere, these PVT data can be represented by the second virial coefBcients of the prrre components and their interaction coefficients with methane. [Pg.14]

This ratio of / to p for a non-ideal gas of a pure substance may be calculated from the equation of state for real gases such as the virial equation and the van der Wools equation. [Pg.65]

Values of (p,- for species i in solution are readily found from equations of state. The simplest form of the virial equation provides a useful example. Written for a gas mixture it is exactly the same as for a pure species [Pg.377]

In later chapters of this book there will be occasion to apply thermodynamic derivations to virial equations of state of a pure gas or gas mixture. These formulas accurately describe the gas at low and moderate pressures using empirically determined, temperature-dependent parameters. The equations may be derived from statistical mechanics, so they have a theoretical as well as empirical foundation. There are two forms of virial equations for a pure gas one a series in powers of 1/ Fm [Pg.34]

Equation (5) is an equation-of-state for the adsorption of a pure gas as a function of temperature and pressure. The constants of this equation are the Henry constant, the saturation capacity, and the virial coefficients at a reference temperature. The temperature variable is incorporated in Equation (5) by the virial coefficients for the differential enthalpy. This equation-of-state for adsorption of single gases provides an accurate basis for predicting the thermodynamic properties and phase equilibria for adsorption from gaseous mixtures. [Pg.253]

In Eq. (77) p° is the standard pressure, p° = l atm quantity p

[Pg.28]

The equilibrium between a pure solid and a gaseous mixture is one of very few classes of solution for which an exact treatment can be made by the methods of statistical mechanics. The earliest work on the theory of such solutions was based on empirical equations, such as those of van der Waals,45 of Keyes,44 and of Beattie and Bridgemann.3 However, the only equation of state of a gas mixture that can be derived rigorously is the virial expansion,46 66 [Pg.104]

The evaluation of the pair correlation functions of both the solvent molecules and the solutes is feasible but troublesome. For electrolyte solutions, however, averaging over the solvent effects yields reliable approximations, as shown by McMillan and Mayer, who considered the solution in osmotic equilibrium with the pure solvent (Fig. 2). They stressed that solutes can be treated as an imperfect gas, provided that one uses the potential of mean force at infinite dilution. The calculation yields the osmotic pressure Tl = P — Pq (see Fig. 2) from the virial equation [Eq. (69)] in terms of the forces among the particles for the solution state (p, T). The independent variables of [Pg.88]

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