Real gas behavior

The ideal gas is a useful model of the behavior of gases and serves as a standard to which real gas behavior can be compared. This is formalized by the introduction of residual properties. Another useful model is the ideal solution, which sei ves as a standard to which real solution behavior can be compared. This is formalized by introduction of excess propei ties. 

Compressibility of Natural Gas All gases deviate from the perfect gas law at some combinations of temperature and pressure, the extent depending on the gas. This behavior is described by a dimensionless compressibility factor Z that corrects the perfect gas law for real-gas behavior, FV = ZRT. Any consistent units may be used. Z is unity for an ideal gas, but for a real gas, Z has values ranging from less than 1 to greater than 1, depending on temperature and pressure. The compressibihty faclor is described further in Secs. 2 and 4 of this handbook. 

It would be useful to have an equation that describes the relationship between pressure and volume for a real gas, just as P V — n R T describes an ideai gas. One way to approach real gas behavior is to modify the ideal gas equation to account for attractive forces and molecular volumes. The result is the van der Waals equation, ... 

Solution The ideal gas equilibrium constants can be corrected for real gas behavior by multiplying the ideal gas equilibrium constant by K,f as defined by Equation 6.23, which for this problem is ... 

Table 6.9 Equilibrium conversion versus pressure for real gas behavior.

Real gas behavior deviates from the values obtained using the ideal gas equation because the ideal gas equation assumes that (1) the molecules do not occupy space and (2) there is no attractive force between the individual molecules. However, at low temperatures (just above the boiling point of the liquid), these factors become significant, and we must use an alternative equation, known as the van der Waals equation, that accounts for them. 

One of the over-arching goals of physical chemistry is to explain real systems by building upon what we know about ideal systems and examining the limitations of those idealized models. The study of real gas behavior using Virtual Substance is one of the most eye-opening assignments for the students. 

The first term on the right-hand side is the idea gas limit, and the remaining -logarithmic terms express the successive virial corrections for the real gas behavior. It is evidently most convenient for this problem to choose the standard state pressure as P° = 0, where all gases are ideal. With this choice, we can write the relationship between fugacity and pressure as... 

The dew point of the gas depends on the gas pressure and the carbon dioxide partial pressure. At fixed carbon dioxide composition, the dew point is lowered as total pressure decreases at fixed total pressure, the dew point is lowered as carbon dioxide composition decreases. Calculated dew points for a synthesis gas with 30 mol % carbon dioxide, for both ideal and real gas behavior, are shown in Figure 3 for syn gas pressures up to 1500 psia. 

A generalized method of presenting real gas behavior is due to Pitzer et al. [17]. They introduced an acentric factor, co, defined as... 

Real gas behavior can be partially accounted for by including the compressibility factor ... 

A convenient approach to account for real gas behavior is to use the dimensionless compressibility factor Z in the equation of state. 

We have seen that a very simple model, the kinetic molecular theory, by making some rather drastic assumptions (no interparticle interactions and zero volume for the gas particles), successfully explains ideal behavior. However, it is important that we examine real gas behavior to see how it differs from that predicted by the ideal gas law and to determine what modifications of the kinetic molecular theory are needed to explain the observed behavior. Since a model is an approximation and will inevitably fail, we must be ready to learn from such failures. In fact, we often learn more about nature from the failures of our models than from their successes. 

The adopted value of S (298.15 K) = 16.718 0.019 cal K mol is taken from the CODATA recommended value (JL). This was calculated by CODATA from the entropy of the ideal gas with appropriate corrections for real gas behavior and vaporization. 

Ideal Solution Model The ideal gas model is useful as a standard of comparison for real gas behavior. This is formalized through residual properties. The ideal solution is similarly useful as a standard to which real solution behavior may be compared. 

Equation [2] and subsequent equations are for ideal-gas models. The usual methods of correcting for real-gas behavior may be employed to evaluate the available energy as given by equation [1]. 

This equation is an approximation of real gas behavior at high temperatures or low pressures. The approximation remains good at lower temperatures at progressively lower pressures. Where the degree of approximation is acceptable, the equation is in common use for its simplicity. 

The uppermost curve at each temperature is the generalized z. The virial equation curves are based on virial coefficients from the same source. Close approximation of real gas behavior is obtained by the B-virial equation at pressures up to the vapor pressure at T = 0.8. At lower temperatures approximation is as good or better, as the existent pressure range of the gas phase is reduced. On the higher temperature side, at T, = 1, we see the B equation holds up till p reaches to about 0.5 and at T = 1.5, the B equation stays close to the generalized correlation up to about... 

To describe real gas behavior more accurately, we need to redesign the ideal gas equation to do two things ... 

The corrections to the kinetic molecular theory that van der Waals found necessary to explain real gas behavior make physical sense, which makes us confident that we understand the fundamentals of gas behavior at the particle level. This is significant because so much important chemistry takes place in the gas phase. In fact, the mixture of gases called the atmosphere is vital to our existence. In Section 5.10 we consider some of the important reactions that occur in the atmosphere. 

This order is reflected by the relative a values for these gases in Table 5.3. In Section 10.1, we will see how these variations in intermolecular interactions can be explained. The main point to be made here is that real gas behavior can tell us about the relative importance... 

Understanding how the ideal gas equation must be modified to account for real gas behavior helps us understand how gases behave on a molecular level... 

Van der Waals found that to describe real gas behavior we must consider particle interactions and particle volumes... 

The compressibility factor is the ratio of the ideal gas density to the real gas density when both are at the same temperature and pressure. The primary function of compressibility factor is to indicate the deviation of real gas behavior from that of the ideal gas. 

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