Real gases intermolecular attractions

The presence of intermolecular forces also accounts for the variation in the compression factor. Thus, for gases under conditions of pressure and temperature such that Z > 1, the repulsions are more important than the attractions. Their molar volumes are greater than expected for an ideal gas because repulsions tend to drive the molecules apart. For example, a hydrogen molecule has so few electrons that the its molecules are only very weakly attracted to one another. For gases under conditions of pressure and temperature such that Z < 1, the attractions are more important than the repulsions, and the molar volume is smaller than for an ideal gas because attractions tend to draw molecules together. To improve our model of a gas, we need to add to it that the molecules of a real gas exert attractive and repulsive forces on one another. 

FIGURE 4.28 A plot of the compression factor, Z, as a function of pressure for a variety of gases. An ideal gas has Z = 1 for all pressures. For a few real gases with very weak intermolecular attractions, such as H2, Z is always greater than 1. For most gases, at low pressures the attractive forces are dominant and Z 1 (see inset). At high pressures, repulsive forces become dominant and Z 1 for all gases. 

As described in Section 4.12, at low temperatures, molecules of a real gas move so slowly that intermolecular attractions may result in one molecule being captured by others and sticking to them instead of moving freely. When the tempera-... 

The van der Waals parameters for carbon dioxide area = 3.640L2-atnvmol-2and b = 0.042 67L-mol 1. For carbon dioxide confined in a 1.00-L vessel at a constant temperature of 27°C, calculate the pressure of the gas by using the ideal gas law and the van der Waals equation for 0.100 to 0.500 mol C02 at 0.100-mol increments. Calculate the percentage deviation of the ideal value from the real value at each point. Under these conditions, which term has the larger effect on the real pressure of C02, the intermolecular attractions or the molar volume ... 

Real gases differ in their behavior from that predicted by the ideal gas law, particularly at high pressure, where gas particles are forced close together and intermolecular attractions become significant. 

There are many equations that correct for the nonideal behavior of real gases. The Van der Waals equation is one that is most easily understood in the way that it corrects for intermolecular attractions between gaseous molecules and for the finite volume of the gas molecules. The Van der Waals equation is based on the ideal gas law. 

Intramolecular interactions were introduced for the first time by van der Waals in 1873 he thus attempted to explain the deviation of the real gas from the ideal gas. In order to apply the ideal gas law equation to the behavior of real gases, allowance should be made for the attractive and repulsive forces occurring between molecules. From that time on, the dipole moment theory of Debye (1912) and the dispersion energy or induced dipole theory by London (1930) were the main driving forces of the research about intermolecular interactions. 

In 1873, J.D. van der Waals proposed his famous equation of state for a non-ideal, i.e., real gas. He modified the ideal gas equation by suggesting that the gas molecules were not mass points but behave like rigid spheres having a certain diameter and that there exist intermolecular forces of attraction between them. The two correction terms introduced by van der Waals are described below. 

One of his corrections assumed that the molecules in a real gas attracted one another. In his honor, the attractive forces between molecules are now called van der Waals forces. And these are the intermolecular forces that hold liquids together. Keep in mind that van der Waals forces exist in gases and solids, too. But their effect is most obvious in liquids, and that is where our discussion will be focused. 

Real versus ideal gases What does the term ideal gas mean An ideal gas is one whose particles take up no space and have no intermolecular attractive forces. An ideal gas follows the gas laws under all conditions of temperature and pressure. 

Second, molecules in a real gas do exhibit forces on each other, and those forces are attractive when the molecules are far apart. In a gas, repulsive forces are only significant during molecular collisions or near collisions. Since the predominant intermolecular forces in a gas are attractive, gas molecules are pulled inward toward the center of the gas, and slow before colliding with container walls. Having been slightly slowed, they strike the container wall with less force than predicted by the kinetic molecular theory. Thus a real gas exerts less pressure than predicted by the ideal gas law. 

At ordinary pressures, the voiume is large and gas molecules are too far apart to experience significant attractions. At moderately high external pressures, the volume decreases enough for the molecules to influence each other. As the close-up shows, a gas molecule approaching the container wall experiences intermolecular attractions from neighboring molecules that reduce the force of its impact. As a result, real gases exert less pressure than the ideal gas law predicts. 

The Van der Waal s Force give rise to intermolecular attractive forces between the molecules of gases, and are responsible for the deviation of the behaviour of real gases from the ideal gas laws. 

This order is reflected by the relative a values for these gases in Table 5.3. In Section 16.1, 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 of intermolecular attractions among gas molecules. 

SECTION 10.9 Departures from ideal behavior increase in magnitude as pressure increases and as temperature decreases. The extent of nonideality of a real gas can be seen by examining the quantity PV = RT for one mole of the gas as a function of pressure for an ideal gas, this quantity is exactly 1 at all pressures. Real gases depart from ideal behavior because the molecules possess finite volume and because the molecules experience attractive forces for one another. The van der Waais equation is an equation of state for gases that modifies the ideal-gas equation to account for intrinsic molecular volume and intermolecular forces. 

An ideal gas is defined as one that obeys the ideal-gas equation (Section 10.4), and an ideal solution is defined as one that obeys Raoulfs law. Whereas ideality for a gas arises from a complete lack of intermolecular interaction, ideality for a solution imphes total uniformity of interaction. The molecules in an ideal solution all influence one another in the same way—in other words, solute-solute, solvent-solvent, and solute—solvent interactions are indistinguishable from one another. Real solutions best approximate ideal behavior when the solute concentration is low and solute and solvent have similar molecular sizes and take part in similar types of intermolecular attractions. 

A Figure 10.22 In any real gas, attractive intermolecular forces reduce pressure to values lower than In an Ideal gas. 

As we have seen, a real gas has a lower pressure due to intermolecular forces, and a larger volume due to the finite volume of the molecules, relative to an ideal gas. Van der Waals recognized that it would be possible to retain the form of the ideal-gas equation, PV = nRT, if corrections were made to the pressure and the volume. He introduced two constants for these corrections a, a measure of how strongly the gas molecules attract one another, and b, a measure of the finite volume occupied by the molecules. His description of gas behavior is known as the van der Waals equation ... 

An ideal gas obeys the ideal-gas equation (Section 10.4), and an ideal solution obeys Raoult s law. Real solutions best approximate ideal behavior when the solute concentration is low and when the solute and solvent have similar molecular sizes and similar types of intermolecular attractions. 

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