Equilibrium problems calculating pressures

Solve different types of equilibrium problems calculate K given unknown quantities (concentrations or pressures), or unknown quantities given K, set up and use a reaction table, apply the quadratic equation, and make an assumption to simplify the calculations ( 17.5) (SPs 17.4-17.8) (EPs 17.30-17.45)... 

GASEQ A Chemical Equilibrium Program for Windows. GASEQ is a PC-based equilibrium program written by C. Morley that can solve several different types of problems including composition at a defined temperature and pressure, adiabatic temperature and composition at constant pressure, composition at a defined temperature and at constant volume, adiabatic temperature and composition at constant volume, adiabatic compression and expansion, equilibrium constant calculations, and shock calculations. More information can found at the website http //www.arcl02.dsl.pipex.com/gseqmain.htm. 

The completely reliable computational technique that we have developed is based on interval analysis. The interval Newton/generalized bisection technique can guarantee the identification of a global optimum of a nonlinear objective function, or can identify all solutions to a set of nonlinear equations. Since the phase equilibrium problem (i.e., particularly the phase stability problem) can be formulated in either fashion, we can guarantee the correct solution to the high-pressure flash calculation. A detailed description of the interval Newton/generalized bisection technique and its application to thermodynamic systems described by cubic equations of state can be found... 

One further vapor/liquid equilibrium problem is the flash calculation. origin of the name is in the change that occurs when a liquid under press passes through a valve to a pressure low enough that some of the liquid vapori or flashes, producing a two-phase stream of vapor and liquid in equilibri We consider here only the P.f -flash, which refers to any calculation of quantities and compositions of the vapor and liquid phases making up a two-ph system in equilibrium at known P, T, and overall composition. 

Using equilibrium constants calculate the bubble-point and dew-point pressures at 120° F for the hydrocarbon system described in Problem 9. Answer BPP = 48 psia. 

Take a mixture of two or more chemicals in a temperature regime where both have a significant vapor pressure. The composition of the mixture in the vapor is different from that in the liquid. By harnessing this difference, you can separate two chemicals, which is the basis of distillation. To calculate this phenomenon, though, you need to predict thermodynamic quantities such as fugacity, and then perform mass and energy balances over the system. This chapter explains how to predict the thermodynamic properties and then how to solve equations for a phase separation. While phase separation is only one part of the distillation process, it is the basis for the entire process. In this chapter you will learn to solve vapor-liquid equilibrium problems, and these principles are employed in calculations for distillation towers in Chapters 6 and 7. Vapor-liquid equilibria problems are expressed as algebraic equations, and the methods used are the same ones as introduced in Chapter 2. 

Conceptually, the simplest method for solving phase-equilibrium problems is the phi-phi method, but computationally it is usually more complicated than other methods. The conceptual simplifications arise in part because no decisions need to be made about reference states the reference state is the ideal gas and the choice of the ideal-gas reference is implicit in choosing to work with fugacity coefficients. Usually, the same pressure-explicit equation of state is used for all components in all phases, for this produces consistency in the results and helps in organizing the calculations. (The same calculations are to be done for all components in all phases, and therefore computer programs can be structured in obvious modular forms.) However, this need not be done different equations of states can be used for different phases. 

Comment The same method can be applied to gaseous equilibrium problems to calculate Kp, in which case partial pressures are used as table entries in place of molar concentrations. Your instructor may refer to this kind of table as an ICE chart, where ICE stands for Initial - ange - Equilibrium. 

The impact of these liquid phase reactions on the phase equilibrium properties is thus an increased solubility of NH3, CO2, H2S and HCN compared with the one calculated using the ideal Henry s constants. The reason for the change in solubility is that only the compounds present as molecules have a vapour pressure, whereas the ionic species have not. The change thus depends on the pH of the mixture. The mathematical solution of the physical model is conveniently formulated as an equilibrium problem using coupled chemical reactions. For all practical applications the system is diluted and the liquid electrolyte solution is weak, so activity coefficients can be neglected. 

A 1.00-g sample of I2 is heated at 1200°C in a 500-mL flask. At equilibrium the total pressure is 1.51 atm. Calculate Kp for the reaction. [Hint Use the result in problem 15.65(a). The degree of dissociation a can be obtained by first calculating the ratio of observed pressure over calculated pressure, assuming no dissociation.]... 

For petroleum fractions or similar systems the treatment of phase equilibria will now be discussed briefly. The basic principles are the same as those outlined for polymer systems without recourse to segment-molar quantities. For petroleum fractions the phase-equilibrium problem of importance is the so-called flash calculation that is analogous to the calculation of coexistence curves for a polydisperse polymer solution and in the simplest case a single distribution function is required. For example, the system may contain many alkanes characterized by their normal boiling-point temperatures Tb that in this work will be denoted by x. At moderate pressures the equilibrium condition is given by the continuous thermodynamics form of Raoult s law ... 

The example discussed suggests another more realistic formulation of the equilibrium problem. Under the conditions of the previous problem, instead of P, and Pg, we specify the pressure in one phase, say, Pg. The system of Eqs. (8) and (9) is completed by the Laplace equation in the form of Eqs. (23). In the second equation, (23), the dependence /(/ ) is supposed to be known from the geometry of the porous space. The surface tension and the wetting angle are defined as known functions of the thermodynamic conditions (e.g., the surface is assumed to be wet by the condensate and the surface tension is calculated by the parachor method). The volumetric hquid... 

In all that follows on phase equilibrium, remember that for two or more phases to be in equilibrium, for each chemical species present in those phases the value of a quantity very much like the partial pressure or partial vapor pressure must be the same in all of the phases at equilibrium for the net rate of molecular movement from one phase to the other to be zero. The mathematical details may become complex, because nature seldom does things as simply as we would like, but ultimately all phase equilibrium calculations are based on finding the chemical compositions of the phases in equilibrium for which the values of this quantity, for each species, is the same in all the phases at equilibrium. For most common phase equilibrium problems that quantity will be a defined... 

For a two-component system, there are four variables that can be varied— temperature, pressure, and liquid and vapor compositions. In order to calculate the properties of the system, we must know two of these properties, from which we can calculate the other two. Since these are not completely independent, we end up with five different types of equilibrium problems that can be solved. These are ... 

Examining Equation (9.14), we see that, in a sense, we have divided our chemical reaction equilibrium problem into two parts—one represented by the left-hand side of the equation and the second by the right-hand side. To solve the left-hand side, we need to employ the extent of reaction formulation developed above. It is here where process variables such as feed composition and reaction pressure affect the value of The details of this part of the chemical reaction equilibrium calculation will be explored in Section 9.5. The solution of the right-hand side, on the other hand, simply depends on determining the value of Ag. As we just saw, Ag depends only on the temperature of the system. Thus, once the reaction stoichiometry has been defined, the reaction temperature is the only variable that needs to be specified to solve the right-hand side of Equation (9.14). 

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

The N equations represented by Eq. (4-282) in conjunction with Eq. (4-284) may be used to solve for N unspecified phase-equilibrium variables. For a multicomponent system the calculation is formidable, but well suited to computer solution. The types of problems encountered for nonelectrolyte systems at low to moderate pressures (well below the critical pressure) are discussed by Smith, Van Ness, and Abbott (Introduction to Chemical Engineering Thermodynamics, 5th ed., McGraw-Hill, New York, 1996). 

With a suitable equation of state, all the fugacities in each phase can be found from Eq. (6), and the equation of state itself is substituted into the equilibrium relations Eq. (67) and (68). For an A-component system, it is then necessary to solve simultaneously N + 2 equations of equilibrium. While this is a formidable calculation even for small values of N, modern computers have made such calculations a realistic possibility. The major difficulty of this procedure lies not in computational problems, but in our inability to write for mixtures a single equation of state which remains accurate over a density range that includes the liquid phase. As a result, phase-equilibrium calculations based exclusively on equations of state do not appear promising for high-pressure phase equilibria, except perhaps for certain restricted mixtures consisting of chemically similar components. 

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. 

The problem asks us to calculate equilibrium pressures of all reagents. 

For a first chemical model, we calculate the distribution of species in surface seawater, a problem first undertaken by Garrels and Thompson (1962 see also Thompson, 1992). We base our calculation on the major element composition of seawater (Table 6.2), as determined by chemical analysis. To set pH, we assume equilibrium with CO2 in the atmosphere (Table 6.3). Since the program will determine the HCOJ and water activities, setting the CO2 fugacity (about equal to partial pressure) fixes pH according to the reaction,... 

In general, the formulation of the problem of vapor-liquid equilibria in these systems is not difficult. One has the mass balances, dissociation equilibria in the solution, the equation of electroneutrality and the expressions for the vapor-liquid equilibrium of each molecular species (equality of activities). The result is a system of non-linear equations which must be solved. The main thermodynamic problem is the relation of the activities of the species to be measurable properties, such as pressure and composition. In order to do this a model is needed and the parameters in the model are usually obtained from experimental data on the mixtures involved. Calculations of this type are well-known in geological systems O) where the vapor-liquid equilibria are usually neglected. 

We will leave for a homework problem the calculation of the equilibrium conversion of methanol versus temperature and pressure. Figure 3-18 is a plot of the equilibrium conversion versus temperature. 

---