Ideal gas mixtures and

The principle of corresponding states enables the enthalpy of a liquid mixture to be expressed starting from that of an ideal gas mixture and a reduced correction for enthalpy ... 

If the hquid phase is an ideal solution, the vapor phase an ideal gas mixture, and the hquid-phase properties independent of pressure, then 7, = 1,... 

Special cases of such phases are ideal gas mixtures, and the limiting case of a pure substance in any state of aggregation. 

As previously noted, the equilibrium constant is independent of pressure as is AG. Equation (7.33) applies to ideal solutions of incompressible materials and has no pressure dependence. Equation (7.31) applies to ideal gas mixtures and has the explicit pressure dependence of the F/Fq term when there is a change in the number of moles upon reaction, v / 0. The temperature dependence of the thermodynamic equilibrium constant is given by... 

For ideal gas mixtures and for dilute liquid solutions the activity is equal to the mole fraction, and then the various mass fluxes may be written 10... 

The fugacity coefficients are a function of pressure, temperature and the equilibrium mole fractions, so at given pressure and temperature eq. (2.4-20) can be solved for s and the equilibrium mole fractions can be calculated. Table 2.4-1 gives the calculated equilibrium composition of the reaction mixture at different pressures for an ideal gas mixture and in case the gas is described with the Redlich-Kwong equation of state. 

The mole fraction xA1 is the vapor pressure of A divided by the total pressure provided that A and B form an ideal gas mixture and that the solubility of gas B in liquid A is negligible. A stream of gas mixture A-B of concentration xA2 flows slowly past the top of the tube, to maintain the mole fraction of A at xA2. The entire system is kept at constant temperature and pressure. There is a net flow of gas upward from the gas-liquid interface. The transport process is in the i-direction and at steady state with no convective mass transfer, and the reaction source is... 

A dimensionless quantity whose magnitude is equal to molar concentration in an ideal solution equal to partial pressure in an ideal gas mixture and defined as 1 for pure solids or liquids. 

If surface equilibrium prevails, then it is relatively straightforward to generalize the interface condition to chemical processes that are more complex than equations (1) and (8). This of interest, since propellant materials often experience processes of this type for example, NH4CIO4 undergoes dissociative sublimation into NH3 and HCIO4 [33]. For a general process in which the condensed material is transformed to 1 the surface equilibrium condition (for an ideal gas mixture and a solid whose thermodynamic properties are independent of pressure) is... 

Given the component partial pressures of an ideal gas mixture and the total gas pressure, determine the mixture composition expressed in either mole fractions (or mole percents), volume fractions (or % v/v), or mass fractions (or % w/w). 

The application of Eq. (11.6) in later chapters to specific phase-equilibrium problems requiresuse of models of solutionbeliavior, wliichprovideexpressionsfor G and (ii as functions of temperature, pressure, and composition. The simplest of these, the ideal-gas mixture and tire ideal solution, are treated in Secs. 11.4 and 11.8. 

Generally mixtures are not ideal in either the vapor or liquid phase, and the pressure may not necessarily be low. However, if the pressure is low, the liquid is an ideal mixture, the vapor is an ideal gas mixture, and we have that XjP = y, F, then, summing over all species yields... 

Problems involving unsteady diffusion in more then one coordinete direction, such as a cylinder or finite length or a long slab of comparable width and depth dimensions, cun usually be solvnd by separation of variables. For example, for a cylinder of radius R and length L the governing equation and boundary conditions for an ideal gas mixture and constant surface conditions would be... 

Feinberg, M. Constitutive equations for ideal gas mixtures and ideal solutions as consequences of simple postulates. Chem. Eng. Sci. 32, 75-78 (1977)... 

Problem 9.2 Air is compressed from 1 bar, 25 °C to 50 bar, and subsequently is cooled to 300 K using cooling water. Assuming air to be an ideal-gas mixture and the compressor to be 100% efficient, calculate the work in the compressor and the heat removed in the heat exchanger per mol of air. Assume air to be ideal-gas mixture (79% N2, 21% O2) and use the heat capacities given in Perry s Handbook. 

It is convenient, for purposes of graph theory, to imagine a system with the same temperature, volume, and number of particles as the system of interest, but in which the particles do not interact with each other. Such a system is an ideal gas or ideal gas mixture, and its thermodynamic properties have a rather simple form. (Note, however, that if the original system is at high density, the imaginary system is a dense ideal gas. ) The partition function for this ideal gas will be denoted Oig(r, V, Ni,..., its Helmholtz free energy is Ajg(r, V, Ni,..., N ), and the relationship between these two quantities is the same as between A and Q. We now define the quantity pi, p2, .., p ), where... 

The chemical potential of component i in an ideal gas mixture and in an ideal pure gas can be written as... 

To a good approximation, by assuming an ideal gas mixture and neglecting the effect of total pressure on fugacity, we can apply Eq. 12.8.20 to a liquid-gas system in which the total pressure is not constant, but instead is the sum of pa and pb- Under these conditions, we obtain the following expression for the rate at which the total pressure changes with the liquid composition at constant T ... 

Assuming an ideal gas mixture and thus neglecting the influence of K, it is therefore clear that the equilibrium composition of a gas-phase reaction is affected by the system pressure for all reactions with Vi 0, that is, where the reaction causes a change in the overall number of molecules and thus in volume. 

Problem 14.2 Langmuir and lAST models The Langmuir and lAST models are not entirely different from each other despite their different origins and derivations. Assume a binary ideal gas mixture and using Equations 14.9, 14.13 and 14.1.1, prove that the Langmuir and lAST models lead to mathematically identical equations for the adsorbed mole fractions x under a simplifying assumption. What is the assumption required ... 

Thus, Oi = yiX. Vapor phases are mostly considered as ideal gas mixtures and partial pressures are used instead of concentrations. They are defined in the same manner as in Eq. (2.140), the mole numbers, however, are replaced by the respective... 

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