Real gases particle volume

A gas that obeys these five postulates is an ideal gas. However, just as there are no ideal students, there are no ideal gases only gases that approach ideal behavior. We know that real gas particles do occupy a certain finite volume, and we know that there are interactions between real gas particles. These factors cause real gases to deviate a little from the ideal behavior of the Kinetic Molecular Theory. But a non-polar gas at a low pressure and high temperature would come pretty close to ideal behavior. Later in this chapter, we ll show how to modify our equations to account for non-ideal behavior. 

Of course, real gas particles do have a finite volume and do exert forces on each other. Thus they do not conform exactly to these assumptions. But we will see that these postulates do indeed explain ideal gas behavior. 

Real gases deviate from behavior predicted for ideal gases because the particles of a real gas occupy volume and are subject to intermolecular forces. 

The analogy with the virial expansion of PF for a real gas in powers of 1/F, where the excluded volume occupies an equivalent role, is obvious. If the gas molecules can be regarded as point particles which exert no forces on one another, u = 0, the second and higher virial coefficients (42, Azy etc.) vanish, and the gas behaves ideally. Similarly in the dilute polymer solutions when w = 0, i.e., at 1 = , Eqs. (70), (71), and (72) reduce to vanT Hoff s law... 

Compressing a gas brings the particles into close proximity, thereby increasing the probability of interparticle collisions, and magnifying the number of interactions. At this point, we need to consider two physicochemical effects that operate in opposing directions. Firstly, interparticle interactions are usually attractive, encouraging the particles to get closer, with the result that the gas has a smaller molar volume than expected. Secondly, since the particles have their own intrinsic volume, the molar volume of a gas is described not only by the separations between particles but also by the particles themselves. We need to account for these two factors when we describe the physical properties of a real gas. 

The actual volume of the gas is less than the ideal gas. This is because gas molecules do have a finite volume and the more moles of gas present, the smaller the real volume. The volume of the gas can be corrected by the V -nb term, where n is the number of moles of gas and b is a different constant for each gas. The larger the gas particle, the more volume it takes up and the larger the b value. 

Of course, the real universe can fight back by changing another variable. In the real universe, for example, tires spring leaks. In such a situation, gas particles escape the confines of the tire. This escape decreases the number of particles, n, within the tire. Cranky, tire-iron wielding motorists on the side of the road will attest that decreasing n decreases volume. This relationship is sometimes expressed as Avogadro s law ... 

Before ending this discussion of gases, it s worthwhile expanding on a point made earlier The behavior of a real gas is often a bit different from that of an ideal gas. For instance, kinetic-molecular theory assumes that the volume of the gas particles themselves is negligible compared with the total gas volume. The assumption is valid at STP, where the volume taken up by molecules of a typical gas is only about 0.05% of the total volume, but the assumption is not valid at 500 atm and 0°C, where the volume of the molecules is about 20% of the total volume (Figure 9.14). As a result, the volume of a real gas at high pressure is larger than predicted by the ideal gas law. 

FIGURE 9.14 The volume taken up by the gas particles themselves is less important at lower pressure (a) than at higher pressure (b). As a result, the volume of a real gas at high pressure is somewhat larger than the ideal value. 

In the above equation, which constant is related to the fact that the particles of a real gas occupy a finite volume Which constant in the equation is related to the fact that interactions occur among the particles of a real gas ... 

The constant b is related to the correction for the finite volume of the particles in a real gas, and the constant a is related to the correction for particle-particle interactions. 

Of course, no gas is really ideal. The ideal gas theory ignores certain facts about real gases. For example, an ideal gas particle does not take up any space. In fact, you know that all particles of matter must take up space. Gas particles are small and far apart, however. Thus the space occupied by the particles is insignificant compared to the total volume of the container. You will learn more about the behaviour of real gases in Chapter 12. 

The particles of a real gas have a significant volume of their own. 

For an ideal gas we shall take the point particle with no forces between molecules. A real gas will approach this behavior when its density is such that the average distance between molecules is large compared to their diameter a. This means that the volume of the vessel is very large compared to the total volume occupied by the molecules themselves, or V Ntct /Qj where N = number of molecules in the volume V. 

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. 

Remember that this equation describes the behavior of a hypothetical gas consisting of volumeless entities that do not interact with each other. In contrast, a real gas consists of atoms or molecules that have finite volumes. Thus the volume available to a given particle in a real gas is less than the volume of the container, because the gas particles themselves take up some of the space. To account for this discrepancy, van der Waals represented the actual volume as the volume of the container, V, minus a correction factor for the volume of the molecules, nb, where n is the number of moles of gas and b is an empirical constant (one determined by fitting the equation to the experimental results). Thus the volume actually available to a given gas molecule is given by the difference V - nb. 

No gas perfectly obeys all four of these laws under all conditions. Nevertheless, these assumptions work well for most gases and most conditions. As a result, one way to model a gas s behavior is to assume that the gas is an ideal gas that perfectly follows these laws. An ideal gas, unlike a real gas, does not condense to a liquid at low temperatures, does not have forces of attraction or repulsion between the particles, and is composed of particles that have no volume. 

In the real world, no gas is truly ideal. All gas particles have some volume, however small it may he, because of the sizes of their atoms and the lengths of their bonds. All gas particles also are subject to intermolecular interactions. Despite that, most gases will behave like ideal gases at many temperature and pressure levels. Under the right conditions of temperature and pressure, calculations made using the ideal gas law closely approximate actual experimental measurements. 

In a real situation, pressure, temperature, and number of gas particles may all be changing, and predicting the effect of such a blend of changing properties on gas volume is tricky. Therefore, before we tackle predictions for real world situations, such as the weather balloon, we will consider simpler systems in which two of the four gas properties are held constant, a third property is varied, and the effect of this variation on the fourth property is observed. For example, it is easier to understand the relationship between volume and pressure if the number of gas particles and temperature are held constant. The volume can be varied, and the effect this has on the pressure can be measured. An understanding of the relationships between gas properties in controlled situations will help us to explain and predict the effects of changing gas properties in more complicated, real situations. 

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

---