Monatomic gas

The standard entropies of monatomic gases are largely determined by the translational partition function, and since dris involves the logarithm of the molecular weight of the gas, it is not surprising that the entropy, which is related to tire translational partition function by the Sackur-Tetrode equation,... 

As examples of the relative magnitudes of these contributions, only tire dispersion effect applies to monatomic gases, and in tire case of HCl (/ = 12.74eV, fjL — 1.03 debye), tire dispersion effect predominates, in NH3 (/ = 10.2eV, ijl — 1.49d) these effects are about equal, and in H2O (I — 12.6eV, IJL — 1.85 d), the orientation effect predominates. 

All the elements have stable electronic configurations (Is or ns np ) and, under normal circumstances are colourless, odourless and tasteless monatomic gases. The non-polar, spherical nature of the atoms which this implies, leads to physical properties which vary regularly with atomic number. The only interatomic interactions are weak van der Waals forces. These increase in magnitude as the polarizabilities of the atoms increase and the ionization energies decrease, the effect of both factors therefore being to increase the interactions as the sizes of the atoms increase. This is shown most directly by the enthalpy of vaporization, which is a measure of the energy required to overcome the... 

By the last two assumptions the theory, strictly speaking, is only applicable to the monatomic gases A, Kr, Xe, to a somewhat lesser extent to the almost spherical molecules CH4, CF4, SFe, and perhaps to nonpolar diatomic molecules. The rotation of even slightly nonspherical molecules like Q2 and N2 will not be free in the entire cavity when such a molecule comes close to the wall of its cage it will have to orient itself parallel to this wall. Furthermore, some of the cavities are somewhat oblate (cf. Section I.B), and thus the rotation of relatively large, oblong molecules may be seriously... 

For the monatomic gases the values of eK/k and gk determined by Whalley and Schneider were used,66 for the other gases, those reported by Hirschfelder, Curtiss, and Bird.15 To the unknown factor z eQlk) t the value 294 was assigned in order to fit the theoretical predictions to the aggregate of experimental data at present available. 

The highest value of c, 1 667, which is that predicted by the kinetic theory of gases, is observed only with monatomic gases (argon, mercury). Diatomic gases have the value 1 4, triatomic 1 3, and k decreases with increasing molecular complexity (cf. Chap. XVIII.). 

A similar explanation may account for the slight deviations exhibited by normal substances, but fails to explain the anomalous behavior of the monatomic gases. A mechanical interpretation of the theorem of corresponding states has, how ever, been advanced by Earnerlingh Onnes ( Principle of Uniformity ) which appears to embrace all known cases. 

These numerical values have been verified for monatomic gases. If the molecule consists of more than one atom, the value of C is greater than 2 98 and increases regularly with the temperature, and the value of k is less than 1 66 and also changes with the temperature. 

Table A4.1 summarizes the equations needed to calculate the contributions to the thermodynamic functions of an ideal gas arising from the various degrees of freedom, including translation, rotation, and vibration (see Section 10.7). For most monatomic gases, only the translational contribution is used. For molecules, the contributions from rotations and vibrations must be included. If unpaired electrons are present in either the atomic or molecular species, so that degenerate electronic energy levels occur, electronic contributions may also be significant see Example 10.2. In molecules where internal rotation is present, such as those containing a methyl group, the internal rotation contribution replaces a vibrational contribution. The internal rotation contributions to the thermodynamic properties are summarized in Table A4.6.

The molar heat capacities of gases composed of molecules (as distinct from atoms) are Higher than those of monatomic gases because the molecules can store energy as rotational kinetic energy as well as translational kinetic energy. We saw in Section 6.7 that the rotational motion of linear molecules contributes another RT to the molar internal energy ... 

C06-0138. According to Table 6H, molar heat capacities of monatomic gases (He, Ar) are significantly smaller than those of diatomic gases (N2, O2, H2). Explain in molecular terms why more heat must be supplied to raise the temperature of I mol of diatomic gas by I K than to raise the temperature of I mol of monatomic gas by 1 K. 

In contrast, the halogens and noble gases on the right of this block are distinctly nonmetallic. The noble gases, Group 18 of the periodic table, are monatomic gases that resist chemical attack because their electron configurations contain completely filled s and p orbitals. 

The boiling point of a substance depends on the magnitude of its intermolecular forces, which in turn depends on the polarizability of its electron cloud. Monatomic gases contain atoms rather than molecules, so we must assess interatomic forces for these substances. 

However when values of the calculated absorption coefficient are compared with those obtained experimentally, the agreement is often poor. For example if we take water at 20 °C for which = ICp, p = 1 g cm and c = 1500 m s and we pass a sound wave of 20 kHz, then a can be calculated to be approx. 3.5 x 10 cm". Experimentally a is found to be 8.6 x 10 cm i. e. approx, two and a half times larger. In fact only in the case of monatomic gases is the observed absorption, equal to the classical absorption. In all other cases the observed absorption is greater than the classical absorption by an amount called the excess absorption, (given by the expression 2n i1b/p complete accuracy, Eq. 2.16 should be further modified to take... 

For the reversible adiabatic expansion, a definite expression can be derived to relate the initial and final temperatures to the respective volumes or pressures if we assume that the heat capacity is independent of temperature. This assumption is exact at all temperatures for monatomic gases and above room temperature for diatomic gases. Again we start with Equation (5.39). Recognizing the restriction of reversibility, we obtain... 

The ionization process is quite complex, and to avoid even further complications, the following discussion will be limited entirely to the shock-ionization of monatomic gases. 

About 80% of the elements are solid metals in their standard states at 298 K. Of the metallic elements, only mercury is a liquid at 298 K and at 1 atmosphere pressure (caesium melts at 302 K, gallium at 302.9 K). The non-metallic elements exist as either discrete small molecules, in the solid (S8), liquid (Br2) or gaseous (H2) states, or as extended atomic arrays in the solid state (C as graphite or diamond). The elements of Group 18 are monatomic gases at 298 K. 

Another observable property of gases is the heat capacity. The molar heat capacity of monatomic gases was measured and found to be equal to (3/2)R, the value predicted for a perfect (point particle) gas. But, actual atoms had a well defined physical size. Since finite spheres would be expected to rotate, where was the heat capacity due to rotation Maxwell worried about this failure of the kinetic theory. Another type of eyes was required to see this result in its proper context. 

In Sec. II,A the equations of change are derived by assuming that the fluid is a continuum. A physically more satisfying derivation may be performed in which one starts directly from considerations of the fundamental molecular-collision processes occurring in the fluid. For dilute monatomic gases and gas mixtures one can start... 

The Chapman-Enskog theory was developed for dilute, monatomic gases for pure substances and for binary mixtures. The extension to multicomponent gas mixtures was performed by Curtiss and Hirschfelder (C12, Hll), who in addition have shown that the Chapman-Enskog results may also be obtained by means of an alternate variational method. Recently Kihara (K3) has shown how expressions for the higher approximations to the transport coefficients may be obtained, which are considerably simpler than those previously proposed by Chapman and Cowling these simpler formulas are particularly advantageous for calculating the coefficients of diffusion and thermal diffusion (M3, M4). 

How much simpler things would be if these were monatomic gases and there was no need for all the juggling between intermediate species to dispose of unused molecular fragments We saw in our discussion of LEED that molecules of this sort are chemisorbed at metal surfaces in the dissociated state. The combination of chemisorbed hydrogen and oxygen atoms to form water clearly follows a different mechanism than in the gas phase. The fact that the reaction occurs rapidly in the presence of platinum and not at all when the reactants are mixed without the metal shows that the activation energy has been lowered tremendously by this modification. 

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