Gases deviations from ideal

The raie gas atoms reveal through their deviation from ideal gas behavior that electrostatics alone cannot account for all non-bonded interactions, because all multipole moments are zero. Therefore, no dipole-dipole or dipole-induced dipole interactions are possible. Van der Waals first described the forces that give rise to such deviations from the expected behavior. This type of interaction between two atoms can be formulated by a Lennaid-Jones [12-6] function Eq. (27)). 

By combining Equations (8.4) and (8.6) we can see that the partition function for a re system has a contribution due to ideal gas behaviour (the momenta) and a contributii due to the interactions between the particles. Any deviations from ideal gas behaviour a due to interactions within the system as a consequence of these interactions. This enabl us to write the partition function as ... 

AH fluids, when compared at the same reduced temperature and reduced pressure have approximately the same compressibiHty factor and deviate from ideal gas behavior to the same extent, giving... 

Deviations from Ideal Gas Laws Compressibility See Figures 12-13A-D. 

Although real gases deviate from ideal gas behavior and therefore require different equations of state, the deviations are relatively small under certain conditions. An error of 1% or less should result if the ideal gas law were used for diatomic gases whenV> 5 f/ gm-mole (80 ftyib-mole) and for other gases and light hydrocarbon vapors when V > 20 f/gm-mole (320 ftyib-mole) [61, p. 67]. 

Both enthalpy and entropy can be calculated from an equation of state to predict the deviation from ideal gas behavior. Having calculated the ideal gas enthalpy or entropy from experimentally correlated data, the enthalpy or entropy departure function from the reference state can then be calculated from an equation of state. 

The reactor is to be designed to operate at 1 atm. Deviations from ideal gas behavior may be neglected. Note that while the volume changes associated with changes in mole numbers are negligible, you may wish to consider the effect of thermal expansion. 

From the ideal gas equation, it is found that for 1 mole of gas, PV/KT = 1, which is known as the compressibility factor. For most real gases, there is a large deviation from the ideal value, especially at high pressure where the gas molecules are forced closer together. From the discussions in previous sections, it is apparent that the molecules of the gas do not exist independently from each other because of forces of attraction even between nonpolar molecules. Dipole-dipole, dipole-induced dipole, and London forces are sometimes collectively known as van der Waals forces because all of these types of forces result in deviations from ideal gas behavior. Because forces of attraction between molecules reduce the pressure that the gas exerts on the walls of the container, van der Waals included a correction to the pressure to compensate for the "lost" pressure. That term is written as w2a/V2, where n is the number of moles, a is a constant that depends on the nature of the gas, and V is the volume of the container. The resulting equation of state for a real gas, known as van der Waals equation, is written as... 

Cl2 (g) shows a greater deviation from ideal gas behavior than does C02 (g). 

Figure 2.10 Schematic illustration of the pressure dependence of the chemical potential of a real gas showing deviations from ideal gas behaviour at high pressures.

Choose the gas that probably shows the greatest deviation from ideal gas behavior. 

Consider the conservation equations across a shock front (Eqns 19 20). There are four unknowns, u, U, v e, but only 3 equations relating them. Thus another equation is required to determine completely the shocked state. This missing equation is an EOS. Any EOS is basically a thermodynamic relationship, although microscopic considerations may be used to evaluate deviations from ideal gas behavior. The most generally applicable EOS is one that relates... 

D) Experimental results are frequently reported in terms of deviation functions. The usefulness of these functions arises from the fact many properties of various systems obey approximate laws. Thus, we speak of the deviations from ideal gas behavior or deviations from the ideal solution laws. The advantage of such deviation functions is that their values are usually much smaller than the whole value, and consequently greater accuracy can be obtained with simpler calculations, either graphically or algebraically. As an example, the molar volume of a mixture of liquids is approximately additive in the mole fractions, so that we may write c... 

Another approach to Henry s law based on Equation (10.35) is of interest. When the deviations from ideal gas behavior and the corrections for the pressure on the liquid phase are negligible, this equation may be written in the form... 

Under what conditions are real gases most likely to deviate from ideal gas behavior ... 

A more systematic way of approaching deviations from ideal gas behavior is by means of the compression factor, Z, defined as the ratio of the volume of the gas to that of an ideal gas at the same temperature and pressure ... 

Because deviations from ideal gas behavior result from intermolecular forces, which go to zero as the average distance between molecules gets very large, we expect Z to approach unity for real gases, as their molar density, n/ V = 1 / Vm, approaches zero. This suggests that it might be useful to expand Z in a series of powers of the molar density ... 

So, at high pressures or low temperatures, the behavior of gases will tend to deviate from ideal gas behavior. The amount of deviation also depends on the type of gas. Johannes van der Waals proposed an equation that was based on the ideal gas equation but that made corrections for the volume of a molecule (postulate 1) and the amount of molecular attraction (postulate 3). The van der Waals equation (which is provided for you on the AP test) is Equation 8.20 ... 

The correct answer is (E). When considering particles, remember that larger or more complex molecules will most likely deviate from ideal gas behavior. This is due both to their increased volume and to their increased likelihood of molecular attraction. 

Under conditions of high pressure and low temperature, real gases begin to deviate from ideal gas behavior. The van der Waals equation can be used to determine the behavior of a real gas. 

For use of the generalized Redlich/Kwong equation one needs only the critical temperature and critical pressure of the gas. This is the basis for the two-parameter theorem of corresponding states All gases, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor, and all deviate from ideal-gas behavior to about the same degree. 

Adsorption is brought about by the interactions between the solid and the molecules in the fluid phase. Two kinds of forces are involved, which give rise to either physical adsorption (physisorption) or chemisorption. Physisorption forces are the same as those responsible for the condensation of vapours and the deviations from ideal gas behaviour, whereas chemisorption interactions are essentially those responsible for the formation of chemical compounds. 

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