Gases behaviour

The topics included demonstrate how the behaviour of powders is often quite different from the behaviour of liquids and gases. Behaviour of particulate solids may be surprising and often counter-intuitive when intuition is based on our experience with fluids. The following are examples of this kind of behaviour When a steel ball is placed at the bottom of a container of sand and the container is vibrated in a vertical plane, the steel ball will rise to the surface. 

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 ... 

Equation (3.73) is the basis of the method proposed by Kiselev for the evaluation of surface area from the Type IV isotherm. If perfect gas behaviour is assumed it becomes... 

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.

Purely phenomenological as well as physically based equations of state are used to represent real gases. The deviation from perfect gas behaviour is often small, and the perfect gas law is a natural choice for the first term in a serial expression of the properties of real gases. The most common representation is the virial equation of state ... 

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. 

Thus real gases are those whose behaviour no longer fits the Ideal Gas Equation (31.1) and in this sense they are defined as non-ideal (imperfect) gases. The Ideal Gas Law is thus a limiting law in the sense that it serves to provide the demarcation between ideal gas and non-ideal (real) gas behaviour. 

Wid you realize that air turbulence is caused by the behaviour of gases Turbulence can be caused by changes in air pressure in the atmosphere. Airplanes are designed, however, to adjust to the behaviour of atmospheric gases. The combustion in the engines, the shape of the airplane, and the air mixture that passengers breathe are all designed to take gas behaviour into account. 

Gas behaviour and gas reactions are part of everyday life. For example, photosynthesis is a reaction that uses carbon dioxide gas, along with other reactants, to produce oxygen gas. High in the atmosphere, ozone gas interacts with dangerous ultra-violet light to protect us from the Sun s harsh rays. 

The molecular-level interpretation of gas behaviour given by the kinetic molecular theory helps to explain the macroscopic, or larger picture, properties of gases in the real world. One of the most important properties of gases is their compressibility—how they react to the application of an external force. In the next section, you will observe how gases behave under pressure. Later in this chapter, you will learn about some interesting applications of pressurized gases. 

There are no degree signs used in the Kelvin scale. More importantly, there are no negative values. What would happen if you tried to calculate a temperature twice as warm as -5°C Mathematically, the answer would be —10°C, but this is a colder temperature. When mathematical manipulations are involved in studying gas behaviour, you need to convert degree Celsius temperatures into kelvins. This is done using the relationship Tk= °C+ 273.15 or °C + 273... 

In the following ThoughtLab, you will examine one more factor affecting gas behaviour ... 

In this chapter, you will study more of the gas laws. Although these laws were discovered almost 200 years ago, they are still accepted today. You will learn how the gas laws allow you to solve many problems involving gas behaviour. You will also learn about some of the modern applications and technological advances associated with the gas laws. 

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). 

---