Thermodynamics gaseous systems

In the applications of the thermodynamic equations of equilibrium to gaseous systems we shall take in ... 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

Chapter 10, the last chapter in this volume, presents the principles and applications of statistical thermodynamics. This chapter, which relates the macroscopic thermodynamic variables to molecular properties, serves as a capstone to the discussion of thermodynamics presented in this volume. It is a most satisfying exercise to calculate the thermodynamic properties of relatively simple gaseous systems where the calculation is often more accurate than the experimental measurement. Useful results can also be obtained for simple atomic solids from the Debye theory. While computer calculations are rapidly approaching the level of sophistication necessary to perform computations of... 

We have considered volume changes resulting from density changes in liquid and gaseous systems. These volume changes were thermodynamically determined using an equation of state for the fluid that specifies volume or density as a function of composition, pressure, temperature, and any other state variable that may be important. This is the usual case in chemical engineering problems. In Example 2.10, the density depended only on the composition. In Example 2.11, the density depended on composition and pressure, but the pressure was specified. 

Thermodynamic expressions for the functional interdependence of a number of physical chemical parameters (usually, pressure, volume, temperature, and amount) of a particular substance. While equations of state have been developed for gases, liquids, and solids, the theories are most advanced for gaseous systems. 

Any system above zero absolute temperature has particles - atoms and molecules - in constant motion. Atoms and molecules in a gaseous system possess the maximum variety of motion - transport, spin, vibratory, etc. These particles constantly interact with each other and at each interaction, quantum of motion of all these types change - and in a very random manner as number of particles involved are huge (about 6 10 in a g.mole). If such interactions are all mechanical interaction i.e., free from chemical or similar changes, such as particles getting associated, or breaking up during interactions), the system remains amenable to statistical interpretation of thermodynamic properties. 

The effect of, pressure on the heat of reaction for gaseous systems depends on the deviation of the components from ideal-gas behavior. If the reactants and products behave as ideal gases, there is no effect. Even for rather nonideal systems the effect of pressure is generally small. Details of the methods of calculating the effects of temperature and pressure are discussed in standard thermodynamics textbooks. 

Since enthalpy is a state property, — Hp can be evaluated by any conveniently chosen path. Rigorously, for the path described, AH applies at the product temperature and the specific heat is for a mixture of the composition of the feed. Except for simple gaseous systems, the thermodynamic data available are insufiicient to take into account variations in AH with temperature and c with composition. Often these variations are small. 

Chemical equilibrium in homogeneous systems, from the thermodynamic standpoint—Gaseous systems—Deduction of the law of mass action—The van t Hoff isotherm—Principle of mobile equilibrium (Le Chateher and Braun)— Variation of the equilibrium constant with temperature—A special form of the equilibrium constant and its variation with pressure... 

Thermodynamic Deduction of the Mass Action Expression for Equilibrium in a Homogeneous Gaseous System We can do this by means of an isothermal reversible cycle The proposition we make use of is that the sum of all the work terms for 103... 

For the present we have of course to restrict the applications of equations (3) and (4) to the case of solid or liquid systems, for at the absolute zero, or in its neighbourhood, gases have no possible existence This restriction is, however, not of such importance as it seems, for it is possible by the aid of the first two laws of thermodynamics to calculate the affinity of a reaction occurring in a gaseous system (or in a dilute solution) if we know the affinity and heat relations for the same reaction when it occurs m the solid state... 

In Chapter X we applied our Heat Theorem to equilibria in which gases take part, but this application was only indirect, in that we started from condensed systems and operated thereafter solely with classical thermodynamics. We obtained the result that any equilibria, even in gaseous systems, are calculable from thermal data if there is available, for each molecular species which does not also take part as a condensed phase, a measurement of any other equilibrium, in the simplest case a measurement of vapour pressure. 

IN this chapter we shall develop a rather more general conception of the application of the older laws of thermodynamics and of the new Heat Theorem. We shall limit ourselves essentially to condensed systems we have dealt with gases sufficiently fully in Chapters X and XIII. Moreover, for anyone who accepts the theory of degeneration described in the previous chapter there is no longer any difference, as far as the application of our Heat Theorem is concerned, between condensed and gaseous systems. The substance of the following discussion may be found in a paper (93) laid before the Prussian Academy of Sciences in 1913. 

Equations of state are needed to describe the relationship among the intensive variables describing the thermodynamic state of a system. The ideal gas law and the van der Waals equation are two typical equations of state for gaseous systems. 

For these gaseous systems, as for condensed systems, the thermodynamic formulae provide complete information about the variation of equilibrium constant with temperature. They predict also the manner in which equilibrium is governed by concentration. They do not, however, provide information about the absolute values of the equilibrium constant. Knowledge of this depends upon the introduction of fresh conceptions. 

The gas in the tank is an open thermodynamic system with matter entering at 42 and entering or leaving at i4g (Fig. 1). When liquid oxygen enters As, that part of it which vaporizes becomes part of the gaseous system in chamber 2. Lox which accumulates in the bottom of the tank and which forms droplets in the tank does not constitute part of the system. 

Determining the numerical potential of Fig. 2.10 is a formidable task, even with modern computers. However, once the potential is known, it is relatively simple to use it to calculate thermodynamic and transport properties. It is therefore natural to hope that the argon potential could be expressed in a parametric form and used to compute properties of other gaseous systems. This would be particularly important for determining gas properties in regions of high temperature not easily reached in the laboratory. While the available data are insufficient to provide a completely reliable test, it appears that in a two-parameter form the potential of Fig. 2.10 can be used to correlate the properties of dilute rare gases. ... 

Having established the proper temperature scale for thermodynamics, we can return to the constant R. This value, the ideal gas law constant, is probably the most important physical constant for macroscopic systems. Its specific numerical value depends on the units used to express the pressure and volume. Table 1.2 lists various values of R. The ideal gas law is the best-known equation of state for a gaseous system. Gas systems whose state variables p, V, n, and T vary according to the ideal gas law satisfy one criterion of an ideal gas (the other criterion is presented in Chapter 2). Nonideal (or real) gases, which do not follow the ideal gas law exactly, can approximate ideal gases if they are kept at high temperature and low pressure. 

Gaseous systems are useful examples for thermodynamics because we can use various gas laws to help us calculate the amount of pressure-volume work when a system changes volume. This is especially so for reversible changes, because most reversible changes occur by letting the external pressure equal the internal pressure ... 

We will begin with a necessary (but nonchemical) review of some statistics that we later apply to gaseous systems. (We use gases almost exclusively in our discussion of statistical thermodynamics.) We will see how we can separate, or partition, a system into smaller units and define an important quantity called a partition function. In time, we will see that the partition function is related to the thermodynamic state functions that define our system. 

Equation 17.61 is one form of what is called the Sackur-Tetrode equation. It provides what is probably the best example of how well statistical thermodynamics applies to gaseous systems, because we can measure absolute entropies. The following example illustrates. 

In favorable cases, notably for dilute (nearly ideal) gaseous systems, a slightly different equilibrium constant of activation, can be estimated by the methods of statistical thermodynamics. 

Calculations Potential energy that can be released by a chemical system can often be predicted oy thermodynamic calculations. If there is little energy, the reaction stiU may be hazardous if gaseous produces are produced. Kinetic data is usually not available in this way. Thermodynamic calculations should be backed up by actual tests. 

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