Ideal gas behaviour

This can be illustrated by showing the net work involved in various adiabatic paths by which one mole of helium gas (4.00 g) is brought from an initial state in whichp = 1.000 atm, V= 24.62 1 [T= 300.0 K], to a final state in whichp = 1.200 atm, V= 30.7791 [T= 450.0 K]. Ideal-gas behaviour is assumed (actual experimental measurements on a slightly non-ideal real gas would be slightly different). Infomiation shown in brackets could be measured or calculated, but is not essential to the experimental verification of the first law. 

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 ... 

The filling gas pressure of a CVGT must be carefully chosen it must be high enough to get a good sensitivity and low enough to approximate the ideal gas behaviour. 

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.

Nitrogen contained in a large tank at a pressure P = 200000 Pa and a temperature of 300 K flows steadily under adiabatic conditions into a second tank through a converging nozzle with a throat diameter of 15 mm. The pressure in the second tank and at the throat of the nozzle is P, = 140000 Pa. Calculate the mass flow rate, M, of nitrogen assuming frictionless flow and ideal gas behaviour. Also calculate the gas speed at the nozzle and establish that the flow is subsonic. The relative molecular mass of nitrogen is 28.02 and the ratio of the specific heat capacities y is 1.39. 

Suppose the bubble now changes size to some new radius, R, as a result of a change in the hydrostatic pressure to a new value P(. Then, assuming ideal gas behaviour, the new gas pressure (P ) inside the bubble will become Pg (R /R) and the new pressure in the bubble (P i,) will be given by ... 

Assuming ideal gas behaviour, calculate the reactor volume needed for a 90% conversion of A if the process is conducted (i) isothermally at 1000 K and (ii) adiabatically with an inlet temperature of HOOK. 

As N2 is a relatively large molecule, it may not be able to enter small pores. Furthermore, owing to its non ideal gas behaviour, N2 cannot be used for surface areas < 1 m g . These problems can be overcome to some extent by replacing N2 with water (area 0.108 nm /molecule) which can enter very small pores, or with Ar (0.138 nm /molecule) which, with a lower saturation vapour pressure, can be used to measure samples with very low surface areas. 

The process of hydration of an ion refers to the conversion of one mole of the gaseous ions under standard conditions at a pressure of I bar to the hydrated ions at a molar concentration of 1 mol dm-3. The process may be divided into two parts. These are the compression of the one mole of gaseous ions into a volume of 1 dm3 followed by the interaction of the ions with water to produce the hydrated ions. Assuming ideal gas behaviour, the compression of one mole of a gas at standard pressure and at 298.15 K into a volume of I dm3 requires the expenditure of enthalpy given by RT ln(24.79/l. 0) = +7.96 kJ mol -. The quoted values of ionic hydration enthalpies include a contribution from the compression of the gaseous ions and the enthalpy changes associated with the hydration process are given by the equation ... 

Since for 1 mole of ethylbenzene entering, the total number of moles increases to 1 + or, the mole fractions of the various species in the reaction mixture at the reactor outlet are shown in column b above. At a total pressure P, the partial pressures are given in column c (assuming ideal gas behaviour). If the reaction mixture is at chemical equilibrium, these partial pressures must satisfy equation A above ... 

These units for diA and CA will eventually lead to the units m3 for the volume of the reactor when we come to use equation 1.35. When we substitute for 0iA in equation 1.35, however, to integrate, we must express CA in terms of aA, where the reactant A is CjHt. To do this we first note that CA-yAC where yA is the mole fraction and C is the molar density of the gas mixture (kmol/m3). Assuming ideal gas behaviour, C is the same for any gas mixture, being dependent only on pressure and temperature in accordance with the ideal gas laws. Thus 1 kmol of gas occupies 22.41m3 at 1 bar (= 1.013 x 105 N/m2) and 273 K. Therefore at 1.4 bar = 1.4 x 10s N/m3 and 1173 K it will occupy ... 

The forces of attraction between neutral, chemically saturated molecules, postulated by van der Waals to explain non-ideal gas behaviour, also originate from electrical interactions. Three types of such inter molecular attraction are recognised ... 

Apart from subtle exceptions, an isolated molecule differs from a molecule in a crystal in that the isolated molecule has no shape, whereas in a crystal it acquires shape, but loses its identity as an independent entity. This paradoxical situation is best understood through the famous Goldstone theorem, which for the present purpose is interpreted to state that any phase transition, or symmetry broken, is induced by a special interaction. When a molecule is introduced into an environment of other molecules of its own kind, a phase transition occurs as the molecule changes its ideal (gas) behaviour to suit the non-ideal conditions, created by the van der Waals interaction with its neighbours. An applied electric or magnetic field may induce another type of transformation due to polarization of the molecular charge density, which may cause alignment of the nuclei. When the field is switched off the inverse transformation happens and the structure disappears. The Faraday effect (6.2.3) is one example. 

For a gas phase. The standard state for a gaseous substance, whether pure or in a gaseous mixture, is the (hypothetical) state of the pure substance B in the gaseous phase at the standard pressure p = p and exhibiting ideal gas behaviour. The standard chemical potential is defined as... 

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. 

The successful application of the method is dependent on a number of requirements (Gravelle, 1978). The chromatographic column must be operating under almost ideal conditions to give sharp, symmetrical peaks and the carrier gas must not be adsorbed. Ideal gas behaviour is generally a good approximation, but if not then the non-ideality of the adsorptive vapour must be taken into account (Blu et al., 1971). 

Deviation from ideal gas behaviour can be best detected by plotting tcA vs. n, which should be consteuit for an ideal G-monolayer. Ideal gas behaviour is observed at n-values below typically 0.5 mN This implies that, at room temperature (where lcT= 4.11 X 10"2 N m), the area per molecule in the monolayer is above about 8.2... 

Extreme cases of non-selectivity are encountered at the maximum and minimum densities. At maximum densities, the supercritical fluid has maximum solvent power so usually everything that is soluble at the various discrete lower densities is soluble at the maximum density - i.e., there is no selectivity if just the highest density is used in the extraction scheme. At that point, a different selectivity can be superimposed on the highest-density supercritical fluid by adding additional components, called modifiers, to the bulk fluid to form solvent mixtures. Typical modifiers are methanol, ethanol, methoxy ethanol, and methylene chloride. With carbon dioxide, the onset of noticeable solvent power occurs at about 0.1 g/mL this is the point at which the carbon dioxide makes a transition from ideal-gas behaviour (PVT equations) to critical-region behaviour where the density is an even more sensitive function of pressure (compared to ideal-gas behaviour). The result is that liquid-like, but selective, solvation occurs for carbon dioxide over the density range of about 0.1... 

The fugacity of an ideal gas is equal to its pressure, and all gases approach ideal gas behaviour as the pressure is reduced. If the activity coefficient is greater than unity, the gas has a greater potential than if it were ideal at the same temperature and pressure. If the activity coefficient is less than unity, the gas has a lower activity and a lower chemical potential than if it were ideal. 

The dominant pressure and temperature corrections to Ysurf come from the vapour contribution [53]. po at some ambient pressure may be obtained from ideal gas behaviour [14] ... 

We are already used to the concept of standard state in respect of pure solids, liquids and gases. The standard state of a liquid or solid substance, whether pure or in a mixture, or for a solvent is taken as the state of the pure substance at 298 K and 1 bar pressure (1 bar = 1.00 x 10 Pa) the standard state of a gas is that of the pure gas at 298 K, 1 bar pressure and exhibiting ideal gas behaviour. 

The recommended units for expressing the levels of air pollutants are fig m [8] for gases and vapours pg m for the weight of particulate matter for particulate matter count, number per cubic metre for visibility, kilometres and for emission and sampling rates, m min . Air volumes should be converted to conditions of 10°C and 101.3 Pa, assuming ideal gas behaviour. 

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