Ross and Olivier s Method From Virial Equation Experimental [Extrapolated) [Pg.59]

Since reduced pressure is below 0.4, use virial equation (2-67 ). Calculate B by tbe Tsonopoulos method, Eq. (2-68). [Pg.399]

Unlike the Debye-Hiickel equations, the virial methods provide little or no information about the distribution of species in solution. Geochemists like to identify the dominant species in solution in order to write the reactions that control a system s behavior. In the virial methods, this information is hidden within the complexities of the virial equations and coefficients. Many geochemists, therefore, find the virial methods to be less satisfying than methods that predict the species distribution. The information given by Debye-Hiickel methods about species distributions in concentrated solutions, however, is not necessarily reliable and should be used with caution. [Pg.130]

In this section we introduce several more complex but more accurate equations of state for single species the virial equation, the van der Waals equation, and the Soave-Redlich-Kwong equation. In Section 5.4 we introduce another approach to nonideal gas analysis that makes use of compressibility factors, and we describe Kay s rule, a method for performing PVT calculations on gas mixtures. [Pg.199]

Although the virial equation itself is easily rationalized on empirical grounds, the mixing rules of Eqs. (4-60) and (4-61) follow rigorously From the methods of statistical mechanics. The temperature derivatives of B and C are given exactly by [Pg.652]

Derive equations to calculate the enthalpy departure using each of the following methods (a) the ideal gas equation, (b) the virial equation of state truncated after the second virial coefficient, (c) the Soave-Redlich-Kwong equation of state. [Pg.70]

Many other equations of state have been proposed for gases, but the virial equations are the only ones having a firm basis in theory. The methods of statistical [Pg.39]

Virial Coefficient Method.—One of the most valuable methods of studying intermolecidar forces consists in direct measurements of the deviations of real gases from the equation of state of the perfect gas. In 1873, van der [Pg.143]

All of the methods used to determine molecular weight involve dilute solutions and all apart from SEC (or GPC) use virial equations. So, before we start discussing the details of each method you need to know what these are, in case you erased your memory banks after taking P. Chem. We will start our revision not with dilute solutions, but the ideal gas law (Equation 12-1) [Pg.358]

A related method is typified by Pitzer and Weltner s paper on methanol (2156). They used heat capacity expressions corresponding to the virial equation to calculate virial coefficients. They use the calculated fourth virial coefficient to argue that H bonded tetramers arc present. A corresponding interpretation of B is not given. [Pg.35]

The virial equation of state, first suggested by Kammerlingh-Ohnes, is probably one of the most convenient equations to use, and is used in this chapter to illustrate the development of the thermodynamic equations that are consistent with the given equation of state. The methods used here can be applied to any equation of state. [Pg.139]

These results are similar to those obtained using either the Lewis-Randall rule or the virial equation of state. However, greater differences between the methods occur for gases as the pressure is increased. At higher pressures the results from the Peng-Robinson equation of state are expected to be the most accurate. [Pg.425]

In later work, Ross and Morrison [7, 8] were able to make several advances. The van der Waals equation of state for real gases, which is the basis of the Hill-de Boer equation, is known to be rather inaccurate. Ross and Morrison based their kernel function on a two-dimensional form of the much better virial equation of state. But more importantly, advances in computing resources made it possible to solve Eqn (7.10) for the unknown distribution function using a nonnegative least squares method, rather than assuming a form a priori [9]. [Pg.153]

The same result can also be obtained directly from the virial equation of state given above and the low-density fonn of g(r). B2(T) is called the second virial coefficient and the expansion of P in powers of is known as the virial expansion, of which the leading non-ideal temi is deduced above. The higher-order temis in the virial expansion for P and in the density expansion of g(r) can be obtained using the methods of cluster expansion and cumulant expansion. [Pg.423]

Correlation Methods Vapor densities are not correlated as functions of temperature alone, as pressure and temperature are both important. At high temperatures and very low pressures, the ideal gas law can be applied whde at moderate temperature and low pressure, vapor density is usually correlated by the virial equation. Both methods will be discussed later. [Pg.399]

In their classic review on Continuous Distributions of the Solvent , Tomasi and Persico (1994) identify four groups of approaches to dealing with the solvent. First, there are methods based on the elaboration of physical functions this includes approaches based on the virial equation of state and methods based on perturbation theory with particularly simple reference systems. For many years [Pg.254]

Due to lack of space, the few results presented here are primarily intended to demonstrate the validity of the proposed method. The pore space of the adsorbent is assumed to consist of slit-shaped pores of width 15 A, with parameters chosen to model activated carbon. The porosity values are fixed at q = 0.45 and qp = 0.6. The feed stream is atemary gas mixture of H2/CH4/C2H6. The vtqx>r-phase fugacities were computed from the virial equation to second order, using coefficients taken from Reid et al [Pg.299]

One may sometimes have access to the parameters required for the Pitzer approaches, e.g., for some hydrolysis equilibria and for some solubility product data, cf. Baes and Mesmer [3] and Pitzer [4]. In this case, the reviewer should perform a calculation using both the B-G-S and the P-B equations and the full virial coefficient methods and compare the results. [Pg.259]

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