Nonpolar compressibility factor

From the ideal gas equation, it is found that for 1 mole of gas, PV/KT = 1, which is known as the compressibility factor. For most real gases, there is a large deviation from the ideal value, especially at high pressure where the gas molecules are forced closer together. From the discussions in previous sections, it is apparent that the molecules of the gas do not exist independently from each other because of forces of attraction even between nonpolar molecules. Dipole-dipole, dipole-induced dipole, and London forces are sometimes collectively known as van der Waals forces because all of these types of forces result in deviations from ideal gas behavior. Because forces of attraction between molecules reduce the pressure that the gas exerts on the walls of the container, van der Waals included a correction to the pressure to compensate for the "lost" pressure. That term is written as w2a/V2, where n is the number of moles, a is a constant that depends on the nature of the gas, and V is the volume of the container. The resulting equation of state for a real gas, known as van der Waals equation, is written as... 

This equation is useful for gases above the critical point. Only reduced pressure, /J, and reduced temperature, T, are needed. In the form represented by equation 53, iteration quickly gives accurate values for the compressibility factor, Z. However, this two-parameter equation only gives accurate values for simple and nonpolar fluids. Unless the Redlich-Kwong equation (eq. 53) is explicidy solved for pressure in nonreduced variables, it does not give accurate liquid volumes. 

The relative simplicity of the generalized virial-coefficient correlation does much to recommend it. Moreover, the temperatures and pressures of most chemical-processing operations lie within the region where it does not deviate by a significant amount from the compressibility-factor correlation. Like the parent correlation, it is most accurate for nonpolar species and least accurate for highly polar and associating molecules. 

Some corresponding-statescorrelations use the critical compressibility factor Z, ratlier tlian tile acentric factor m, as a third parameter. The two types of correlation (one based on Tc, Pc, and Zc, the other on Tc, Pc, and w) would be equivalent were tliere a one-to-one correspondence between and w. The data of App. B allow a test of tliis correspondence. Prepare a plot of Z vs. w to see how well Z correlates witli w. Develop a linear correlation (Zc = a for nonpolar substances. 

We illustrate the effects of a by comparing Equation 9.26 with the experimental data for the compressibility factor shown in Figure 9.17a. At lower pressures, for example 200 atm, the intermolecular forces reduce z for CH4 to a value significantly below the ideal gas value. For N2, the effect that decreases z is readily apparent but it is smaller than the effect that increases z. For H2, the effect that decreases z is completely dominated by the forces that increase z. These results are consistent with the u-parameter value for CH4 being about twice that for N2 and about 10 times that for H2 (see Table 9.3). The values of a originate in the structure of the molecules and vary significantly between highly polar molecules such as H2O and nonpolar molecules such as H2. 

A new pressure-explicit equation of state suitable for calculating gas and liquid properties of nonpolar compounds was proposed. In its development, the conditions at the critical point and the Maxwell relationship at saturation were met, and PVT data of carbon dioxide and Pitzers table were used as guides for evaluating the values of the parameters. Furthermore, the parameters were generalized. Therefore, for pure compounds, only Tc, Pc, and o> were required for the calculation. The proposed equation successfully predicted the compressibility factors, the liquid fugacity coefficients, and the enthalpy departures for several arbitrarily chosen pure compounds. 

Compressibility Factors. A total of 2772 Z values of Pitzer s table was used to test the capability of the proposed equation for calculating compressibility factors of pure nonpolar compounds. 

For prediction of vapor density of pure hydrocarbon and nonpolar gases, the corresponding states method of Pitzer et al, is the most accurate method, with errors of less than 1 percent except in the critical region where errors of up to 30 percent can occur. The method correlates the compressibility factor by Eq. (2-75), after which the density can be calculated by Eq, (2-75) ... 

These forms of a generalized equation of state only require the critical temperature and the critical pressure as substance-specific parameters. Therefore, these correlations are an example for the so-called tsvo-parameter corresponding-states principle, which means that the compressibility factor and thus the related thermodynamic properties for all substances should be equal at the same values of their reduced properties. As an example, the reduced vapor pressure as a function of the reduced temperature should have the same value for all substances, provided that the regarded equation of state can reproduce the PvT behavior of the substance on the basis of the critical data. In reality, the two-parameter corresponding-states principle is only well-suited to reflect the properties of simple, almost spherical, nonpolar molecules (noble gases as Ar, Kr, Xe). For all other molecules, the correlations based on the two-parameter corresponding-states principle reveal considerable deviations. To overcome these limitations, a third parameter was introduced, which is characteristic for a particular substance. The most popular third parameter is the so-called acentric factor, which was introduced by Pitzer ... 

Figure 1.9 is a graph of the experimentally measured compression factor of a number of polar and nonpolar fluids as a function of reduced pressure at a number of reduced... 

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