Equilibrium compositions, calculations

A zeolite catalyst operated at 1 atm and 325-500 K is so active that the reaction approaches equilibrium. Suppose that stack gas having the equilibrium composition calculated in Example 7.17 is cooled to 500 K. Ignore any reactions involving CO and CO2. Assume the power plant burns methane to produce electric power with an overall efficiency of 70%. How much ammonia is required per kilowatt-hour (kWh) in order to reduce NO , emissions by a factor of 10, and how much will the purchased ammonia add to the cost of electricity. Obtain the cost of tank car quantities of anhydrous ammonia from the Chemical Market Reporter or from the web. 

Table 1. Experimental Product Gas Composition Compared with Equilibrium Compositions Calculated for Given Feed Mixture and Experimental Temperature...

As in a thermodynamic system description used for a normal solubility equilibrium calculation, the system contains a gas phase, if considered relevant for the problem at hand, an aqueous solution phase (external to the fibres), and a number of solid phases, which appear either with fixed stoichiometry or as solid solutions. The fibres are described as a separate aqueous phase. The thermodynamic data and stoichiometry for the solute species inside the fibre phase are identical to those describing the species in the external solution volume, with the exception that the charge of the species in the two aqueous phases must be defined separately. This will ensure that, given valid input values, charge neutrality will apply to both aqueous phases individually in the equilibrium composition calculated by Gibbs energy... 

One reason for writing this book was the practical requirement of contemporary industry, where a rational utilization of equilibrium composition calculations may provide valuable information concerning processes under study in all stages of their implementation. A second reason was the need of a text-book for studying this part of chemical thermodynamics in the scope as taught at the Institute of Chemical Technology, Prague. 

All calculations and discussion in the following section are based on two stipulations (1) stream compositions are based on equilibrium composition calculations (2) all calculations performed are based on a 1000 kg concentrate of the following composition 30% Cu, 30% Fe, 32% S, 8% gangue [8-12]. 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Figure 7-1. Incipient equilibrium vapor-phase compositions calculated with subroutine BUDET.

Liquid-liquid equilibrium separation calculations are superficially similar to isothermal vapor-liquid flash calculations. They also use the objective function. Equation (7-13), in a step-limited Newton-Raphson iteration for a, which is here E/F. However, because of the very strong dependence of equilibrium ratios on phase compositions, a computation as described for isothermal flash processes can converge very slowly, especially near the plait point. (Sometimes 50 or more iterations are required. )... 

S. Gordon and B. J. McBride, Computer Program for Calculation of Complex Equilibrium Compositions. Rocket Peformance Incident and Reflected Shocks and Chapman-]ouquetDetonations, NASA-Lewis Research Center, NASA, Airport, Md., Mar. 1976. 

Table 3. Calculated Vapor—Liquid Equilibrium Composition for Propylene Hydration ...

The standard Gibbs energy change of reaction, is used ia the calculation of equilibrium compositions the standard heat of reaction, is used iu... 

For most LLE applications, the effect of pressure on the Yi < an be ignored, and thus Eq. (4-327) constitutes a set of N equations relating equilibrium compositions to each other and to temperature. For a given temperature, solution of these equations requires a single expression for the composition dependence of suitable for both liquid phases. Not all expressions for suffice, even in principle, because some cannot represent liquid/liquid phase splitting. The UNIQUAC equation is suitable, and therefore prediction is possible by the UNIFAC method. A special table of parameters for LLE calculations is given by Magnussen, et al. (Jnd E/ig Chem Process Des Dev, 20, pp. 331-339 [1981]). 

The standard Gibbs-energy change of reaction AG° is used in the calculation of equilibrium compositions. The standard heat of reaclion AH° is used in the calculation of the heat effects of chemical reaction, and the standard heat-capacity change of reaction is used for extrapolating AH° and AG° with T. Numerical values for AH° and AG° are computed from tabulated formation data, and AC° is determined from empirical expressions for the T dependence of the C° (see, e.g., Eq. [4-142]). 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Gordon, S. and McBride, B. J. 1976. Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations. Report SP-273. Interim Revision, Report N78-17724. National Aeronautics and Space Administration, Washington, DC. 

Step 4. To check the original assumed equilibrium composition in the evaporator, the total amount of propane and butane in the system must be determined. This total must be equal to the original charge. Therefore, the next step will be to calculate the volume of the total system. These calculations must necessarily be somewhat approximate because the exact installation conditions are not known. 

It is simple enough to calculate the equilibrium composition for any given starting composition, pressure, and temperature. It is no more difficult to do this for a range of starting compositions, pressures, and... 

EXAMPLE 9.7 Sample exercise Calculating the equilibrium composition by approximation... 

To calculate the equilibrium composition of a reaction mixture, set up an equilibrium table in terms of changes in the concentrations of reactants and products, express the equilibrium constant in terms of those changes, and solve the resulting equation. 

EXAMPLE 9.10 Calculating the equilibrium composition after addition of a reagent... 

The rest of this chapter is a variation on a theme introduced in Chapter 9 the use of equilibrium constants to calculate the equilibrium composition of solutions of acids, bases, and salts. We shall see how to predict the pH of solutions of weak acids and bases and how to calculate the extent of deprotonation of a weak acid and the extent of protonation of a weak base. We shall also see how to calculate the pH of a solution of a salt in which the cation or anion of the salt may itself be a weak acid or base. 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

Equilibrium Compositions for Single Reactions. We turn now to the problem of calculating the equilibrium composition for a single, homogeneous reaction. The most direct way of estimating equilibrium compositions is by simulating the reaction. Set the desired initial conditions and simulate an isothermal, constant-pressure, batch reaction. If the simulation is accurate, a real reaction could follow the same trajectory of composition versus time to approach equilibrium, but an accurate simulation is unnecessary. The solution can use the method of false transients. The rate equation must have a functional form consistent with the functional form of K,i,ermo> e.g., Equation (7.38). The time scale is unimportant and even the functional forms for the forward and reverse reactions have some latitude, as will be illustrated in the following example. 

Direct thermal decomposition of methane was carried out, using a thermal plasma system which is an environmentally favorable process. For comparison, thermodynamic equilibrium compositions were calculated by software program for the steam reforming and thermal decomposition. In case of thermal decomposition, high purity of the hydrogen and solidified carbon can be achieved without any contaminant. 

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