Gases attractive forces

In 1873, van der Waals [2] first used these ideas to account for the deviation of real gases from the ideal gas law P V= RT in which P, Tand T are the pressure, molar volume and temperature of the gas and R is the gas constant. Fie argried that the incompressible molecules occupied a volume b leaving only the volume V- b free for the molecules to move in. Fie further argried that the attractive forces between the molecules reduced the pressure they exerted on the container by a/V thus the pressure appropriate for the gas law isP + a/V rather than P. These ideas led him to the van der Waals equation of state ... 

A substance exists as a liquid rather than a gas because attractive forces between molecules (mtermolecular attractive forces) are greater m the liquid than m the gas phase Attractive forces between neutral species (atoms or molecules but not ions) are referred to as van der Waals forces and may be of three types... 

When a gas comes in contact with a solid surface, under suitable conditions of temperature and pressure, the concentration of the gas (the adsorbate) is always found to be greater near the surface (the adsorbent) than in the bulk of the gas phase. This process is known as adsorption. In all solids, the surface atoms are influenced by unbalanced attractive forces normal to the surface plane adsorption of gas molecules at the interface partially restores the balance of forces. Adsorption is spontaneous and is accompanied by a decrease in the free energy of the system. In the gas phase the adsorbate has three degrees of freedom in the adsorbed phase it has only two. This decrease in entropy means that the adsorption process is always exothermic. Adsorption may be either physical or chemical in nature. In the former, the process is dominated by molecular interaction forces, e.g., van der Waals and dispersion forces. The formation of the physically adsorbed layer is analogous to the condensation of a vapor into a liquid in fret, the heat of adsorption for this process is similar to that of liquefoction. 

Gases have weaker attractive forces between individual molecules and therefore diffuse rapidly and assume the shape of their container. Molecules can be separated by vast distances unless the gas is subjected to high pressure. Their volumes are easily affected by temperature and pressure. The behaviour of any gas is dependent on only a few general laws based upon the properties of volume, pressure and temperature as discussed in Chapter 4. 

Notice that in Table 5.2 all the deviations are negative the observed molar volume is less than that predicted by the ideal gas law. This effect can be attributed to attractive forces between gas particles. These forces tend to pull the particles toward one another reducing the space between them. As a result, the particles are crowded into a smaller volume, just as if an additional external pressure were applied. The observed molar volume, Vm, becomes less than V , and the deviation from ideality is negative ... 

The magnitude of this effect depends on the strength of the attractive forces and hence on the nature of the gas. Intermolecular attractive forces are stronger in C02 than they are in 02, which explains why the deviation from ideality of Vmis greater with carbon dioxide and why carbon dioxide is more readily condensed to a liquid than is oxygen. 

Deviation of methane gas from ideal gas behavior. Below about 350 atm, attractive forces between methane (CH4) molecules cause the observed molar volume at 25°C to be less than that calculated from the ideal gas law. At 350 atm, the effect of the attractive forces is just balanced by that of the finite volume of CH4 molecules, and the gas appears to behave ideally. Above 350 atm, the effect of finite molecular volume predominates and V, > 1C... 

There is a reasonable explanation for this type of deviation. The kinetic theory, which explains the pressure-volume behavior, is based upon the assumption that the particles exert no force on each other. But real molecules do exert force on each other The condensation of every gas on cooling shows that there are always attractive forces. These forces are not very important when the molecules are far apart (that is, at low pressures) but they become noticeable at higher pressures. With this explanation, we see that the kinetic theory is based on an idealized gas—one for which the molecules exert no force on each other whatsoever. Every gas approaches such ideal behavior if the pressure is low enough. Then ihe molecules are, on the average, so far apart that then-attractive forces are negligible. A gas that behaves as though the molecules exert no force on each other is called an ideal gas or a perfect gas. 

Helium is a monatomic gas and, as yet, no stable compounds of helium have been found. The attractive forces between the atoms of helium are unusually weak, as shown by the normal boiling point. To liquefy helium, it must be cooled to — 268.9°C or 4.2°K. No other element or compound has a boiling point as low. Helium has another distinction which reflects these weak forces it is the only substance known which cannot be solidified at any temperature unless it is subjected to pressure. Helium becomes solid at 1.1 °K at a pressure of 26 atmospheres. 

A measurement of the density of helium gas shows that it is a monatomic gas. Molecules of He2 do not form. What difference between hydrogen atoms and helium atoms accounts for the absence of bonding for helium The answer to this question also must lie in the attractive and repulsive electrical interactions between two helium atoms when they approach each other. Figure 16-4A shows the attractive forces in one of our hypothetical instantaneous snapshots. There are, of course, four electrons and each is attracted to each nucleus. In Figure 16-4B we see the repulsive forces. Taking score, we find in Figure 16-4A eight attractive interactions, four... 

At very low pressures, deviations from the ideal gas law are caused mainly by the attractive forces between the molecules and the compressibility factor has a value less than unity. At higher pressures, deviations are caused mainly by the fact that the volume of the molecules themselves, which can be regarded as incompressible, becomes significant compared with the total volume of the gas. 

Thus the internal energy of the non-ideal gas is a function of pressure as well as temperature. As the gas is expanded, the molecules are separated from each other against the action of the attractive forces between them. Energy is therefore stored in the gas this is released when the gas is compressed and the molecules are allowed to approach one another again. 

The fourth assumption means that we are proposing, as part of the model, that there are no attractive forces between ideal gas molecules and no repulsive forces between them except during collisions. 

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. 

The virial equation is a general equation for describing real gases. The van der Waals equation is an approximate equation of state fora real gas the parameter a represents the role of attractive forces and the parameter b represents the role of repulsive forces. 

Intermolecular forces are responsible for the existence of several different phases of matter. A phase is a form of matter that is uniform throughout in both chemical composition and physical state. The phases of matter include the three common physical states, solid, liquid, and gas (or vapor), introduced in Section A. Many substances have more than one solid phase, with different arrangements of their atoms or molecules. For instance, carbon has several solid phases one is the hard, brilliantly transparent diamond we value and treasure and another is the soft, slippery, black graphite we use in common pencil lead. A condensed phase means simply a solid or liquid phase. The temperature at which a gas condenses to a liquid or a solid depends on the strength of the attractive forces between its molecules. 

The interaction of two alkali metal atoms is to be expected to be similar to that of two hydrogen atoms, for the completed shells of the ions will produce forces similar to the van der Waals forces of a rare gas. The two valence electrons, combined symmetrically, will then be shared between the two ions, the resonance phenomenon producing a molecule-forming attractive force. This is, in fact, observed in band spectra. The normal state of the Na2 molecule, for example, has an energy of dissociation of 1 v.e. (44). The first two excited states are similar, as is to be expected they have dissociation energies of 1.25 and 0.6 v.e. respectively. 

The bands of matrix-isolated molecules are frequently observed at the wavelengths which differ from those in gas-phase spectra. These matrix shifts are induced by the repulsive and attractive forces between the isolated molecules and the atoms which form the matrix site. Repulsions lead to small increases (1-15 cm ) of vibrational frequencies, and attractions decrease them. Matrix shifts depend on the type of matrix gas they rise in the sequence from neon to xenon. In general, the shifts are positive (the... 

According to this model, a substance will be a gas when its molecules are small and do not attract one another strongly. As we describe in Chapter H, small molecules usually have small attractive forces. Table 54 lists the substances that exist as gases under normal conditions. In accord with the model, they mostly are small molecules with molar masses less than 50 g/mol. 

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, ... 

Metals behave differently since the metal atoms are embedded in an electron gas. The attractive forces remain active even after mutual displacement of parts of a crystal has occurred. Metals therefore can be deformed without fracture. 

The particles in a disperse system with a liquid or gas being the dispersion medium are thermally mobile and occasionally collide as a result of the Brownian motion. As the particles approach one another, both attractive and repulsive forces are operative. If the attractive forces prevail, agglomerates result indicating an instability of the system. If repulsive forces dominate, a homogeneously dispersed or stable dispersion remains. 

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