Equilibrium ratios ideal

EXAMPLE 12—4 Repeat Example 12—1. Do not assume ideal solution behavior. Assume that the equilibrium ratio charts given in Appendix A can be used for this mixture. 

Pressure does not appear implicitly in Equation 12-21. Pressure is represented in the equilibrium ratio. Thus bubble-point pressure cannot be calculated directly as in the case of ideal solutions. 

Recalculate Exercise 12-9. Do not assume that the mixture acts like an ideal solution. Use equilibrium ratios from Appendix A. 

VAPOR-LIQUID EQUILIBRIUM RATIOS FOR IDEAL-SOLUTION BEHAVIOR 3.1... 

In an ideal system therefore, the equilibrium ratio of mole fractions of a component in the two phases depends solely upon the temperature and pressure, and is independent of the composition of the system. This is Nernst s distribution law, examples of the application of which will be discussed later (chap. XX). 

For vapor-liquid equilibrium, the ideal separation factor is termed the relative volatility and is written as the ratio of the vapor pressure of each component ... 

The equilibrium ratio [Equation (12.1)] involves physical equilibrium between phases. The system involved may be binary or multicomponent and ideal or nonideal, according to the terminology used in solution thermodynamics. Methods for correlating or predicting equilibria are based on an application of thermodynamics to each phase and to the solutions of the components within each phase. The techniques are described in standard reference works such as Walas and Reid et al. For multicomponent systems, the usual approach is to model the equilibria for each of the binary pairs and then combine the binary models in special ways to obtain the multicomponent model. 

Depending on the system at hand, the equilibrium ratio AT, may be either constant (as in Henry s law), or a function of temperature, pressure, and/or composition. In this book, the following phase equilibrium models are primarily models dealt with (1) constant relative volatilities, (2) ideal solutions using Raoult s law, and (3) nonideal solutions using a modified Raoult s law and the NRTL activity coefficient model, although other activity coefficient models are also applicable. Each of these three models is briefly discussed here. 

Ideal Solutions. The constant relative volatility assumption is often very good for a large number of systems. However, in many systems the equilibrium ratio is not constant but a function of temperature and pressure. Such a system may be modeled with Raoult s law, assuming that the vapor phase is an ideal... 

In a conceptual, ideal process, water would be continuously converted into hydrogen sulfide and back into water in the arrangement illustrated in Figure 4.6. This is known as a mono-thermal process because deuterium exchange occurs at only one temperature. Between the two conversions, the two species are repeatedly contacted. With an equilibrium ratio around... 

VAPOR-LIQUID EQUILIBRIUM RATIOS FOR IDEAL-SOLUTION BEHAVIOR 3.1 FUGACITY OF PURE LIQUID 3.3 NONIDEAL GAS-PHASE MIXTURES 3.4... 

Calculate the bubble point of the feed. This is done via procedures outlined in Section 3. In the present case, where both the vapor and liquid phases can be considered ideal, the vapor-liquid equilibrium ratio Ki equals vapor pressure of ith component divided by system pressure. The bubble point is found to be 94°C. At 40°C, then, the feed is subcooled 54°C. 

H-H ) - molar enthalpy departure frm the ideal gas state AHmix molar liquid heat of solution k - liquid thermal conductivity K - vapor-liquid equilibrium ratio P - absolute pressure Pref reference pressure R - gas constant T - absolute temperature - liquid molar volume - liquid partial molar volume X - mole fraction in liquid phase y - mole fraction in vapor phase relative volatility Y - liquid activity coefficient liquid viscosity... 

At atmospheric pressure, the vapor phase essentially follows the ideal gas law, so that deviations from idealism are due to liquid phase behavior. When the liquid phase is not ideal, the equilibrium ratio is modified by the activity coefficient (y) ... 

Equilibrium ratio Equilibrium ratio for ideal liquid... 

The concentration of hydrogen in the gas phase can be obtained fi-om the ideal gas law, chj = Pii2 / y while the equilibrium ratio of hydrogen (Khj) can be calculated from the tabulated value of equilibrium solubifity Henry s law ... 

For ideal mixtures (obeying Roult s law), the equilibrium ratio is... 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

The ideal exhaust gas composition is given in Table II, based on a fuel with an H to C molar ratio of 2.103, and assuming that the equilibrium is established and frozen at 4000°R 25). To complete the combustion in a rich exhaust, secondary air must be supplied to cover the deficiency in oxidants. 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

As noted before, short focal ratios imply severe difficulties in generating the aspherical departure from an ideal sphere. It is, however, directly related to the telescope length, hence to the structure and building sizes, which are major cost positions and performance issues in a telescope project -cost of large structures and buildings, improbable thermal equilibrium hence local turbulence, misalignments and flexures, etc. 

Reverse Reaction Rates. Suppose that the kinetic equilibrium constant is known both in terms of its numerical value and the exponents in Equation (7.28). If the solution is ideal and the reaction is elementary, then the exponents in the reaction rate—i.e., the exponents in Equation (1.14)—should be the stoichiometric coefficients for the reaction, and Ei mettc should be the ratio of... 

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