Fugacity of products

Detonation (and Explosion), Fugacity of Products of. Cook (1958), p 381 describes a method of calculating fugacities and the calcn of equilibrium concentrations using ratios of fugacities... 

Eq 18 is applicable to equilibrium constants in alternate form. For ideal gases the equilibrium constant Kp is expressed in terms of partial pressures (rather than fugacities) of products and reactants. Still another form of the equilibrium constant. JC. is exnressed in terms nf... 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

To predict vapor-liquid or liquid-liquid equilibria in multicomponent systems, we require a method for calculating the fugacity of a component i in a liquid mixture. At system temperature T and system pressure P, this fugacity is written as a product of three terms... 

Now consider the effect of pressure. For reversible reactions, pressure can have a significant effect on the equilibrium conversion. Even though the equilibrium constant is only a function of temperature and not a function of pressure, equilibrium conversion can still be influenced through changing the activities (fugacities) of the reactants and products. 

Figures 1 to 3 present calculated equilibrium molar ratios of products to reactants as a function of temperature and total pressure of 1 and 100 atm. for the gas-carbon reactions (4), (7), and (5), (6), (4), (7), respectively. Up to 100 atm. over the temperature range involved, the fugacity coefficients of the gases are close to 1 therefore, pressures can be calculated directly from the equilibrium constant. From Fig. 1, it is seen that at temperatures above 1200°K. and at atmospheric pressure, the conversion of carbon dioxide to carbon monoxide by the reaction C - - COj 2CO essentially is unrestricted by equilibrium considerations. At elevated pressures, the possible conversion markedly decreases hence, high pressure has little utility for this reaction, since increased reaction rate can easily be obtained by increasing reaction temperature. On the other hand, for the reaction C -t- 2H2 CH4, the production of methane is seriously limited at one atmosphere pressure and practical operating temperatures, as seen in Fig. 2. Obviously, this reaction must be conducted at elevated pressures to realize a satisfactory yield of methane. For the carbon-steam reaction.

Computation of the heat of any process. To compute the heat of any process involving the disappearance of a substance or substances in the states given in the table and the appearance of other or the same substances in states given in the table Add together the heat of formation (values for Qf) of the products of the process in the final states and subtract therefrom the sum of the heats of formation (values for Qf) of the reactants in their initial states. The value so obtained represents the heat evolved when the given process takes place at a constant pressure (or a fugacity) of one atmosphere and at a temperature of 18°. The following are examples ... 

Consequently, they are distributed on the surface randomly even if there is no surface migration. Therefore, in contrast to the discussion of adsorption and desorption processes in Section X, the mechanism (188) needs no assumed rapid surface migration (it is evident, of course, that if the migration occurs, it does not affect the results). The analysis of adsorption and desorption rates given in Section X needs only minor alterations to its application to stage 1 namely, products kbPb> would be substituted for rate constants of desorption on separate surface sites, k, and the fugacity of adsorbed particles I, px for p. Therefore, in analogy to (148) and (157), we obtain... 

These considerations can be extended to reversible processes. They also apply to single phase, liquid systems. For the case, rather common in heterogeneous catalysts, in which one reactant is in a gas phase and the others and the products are in a liquid phase, application of the principles given above is straightforward provided that there is mass transfer equilibrium between gas phase and liquid phase, i.e., the fugacity of the reactant in the gas phase is identical with its fugacity in the liquid phase. In such case, a power rate law for an irreversible reaction of the form... 

Hydrocarbon distributions in the Fischer-Tropsch (FT) synthesis on Ru, Co, and Fe catalysts often do not obey simple Flory kinetics. Flory plots are curved and the chain growth parameter a increases with increasing carbon number until it reaches an asymptotic value. a-Olefin/n-paraffin ratios on all three types of catalysts decrease asymptotically to zero as carbon number increases. These data are consistent with diffusion-enhanced readsorption of a-olefins within catalyst particles. Diffusion limitations within liquid-filled catalyst particles slow down the removal of a-olefins. This increases the residence time and the fugacity of a-olefins within catalyst pores, enhances their probability of readsorption and chain initiation, and leads to the formation of heavier and more paraffinic products. Structural catalyst properties, such as pellet size, porosity, and site density, and the kinetics of readsorption, chain termination and growth, determine the extent of a-olefin readsorption within catalyst particles and control FT selectivity. 

For the predominant component of a solution, i. e. the solvent, the 3tate of the pure liquid at the temperature of the systom and the pressure of 1 atm. is chosen as the standard state.. In so far as sufficiently diluted solutions are concerned (i. e. such solutions the composition of which differs but slightly from the pure solvent) the solvent can be considered to follow approximately Raoult s law valid for ideal solutions, according to which the fugacity / of the solvent in a solution can be expressed as the product of its molar fraction N-, ) and of the fugacity of the pure liquid substance f at the same temperature, thus ... 

Initially, a moles of species A and b moles of species B are contained in cylinders shown at the top of the box in Fig. 15.2. Each is stored in its cylinder t pure gas at temperature T and at a fugacity of 1 bar, i.e., in its standard state. following series of steps transforms these reactants into l moles of L and mm of Af, the pure product species in their standard states at temperature T and a fug of 1 bar. They are collected in the lower cylinders shown in Fig. 15.2. 

Finally, the products are isothennally expanded (or compressed) from their respective equilibrium fugacities to their standard-state fugacities of 1 bar. The Gibbs energy change is calculated as in step 1 ... 

In Eq. 2, F is the Faraday constant (96485 C mof ) and the negative sign denotes the thermodynamically non-spontaneous nature of the water splitting process. The actual voltage required for electrolysis will depend on the fugacities of the gaseous products in Reaction 1 as well as on the electrode reaction kinetics (overpotentials)... 

The analyses here differ from those of Gardiner (1996), Kotas (1995) and Moran and Shapiro (1993) because of the use of the fugacity calculations from the JANAF tables (Chase etal., 1998), and, more importantly, because the contents of the isothermal enclosure of the fuel cell are at concentrations determined by the equilibrium constant (high vacuum of reactants, high concentration of products). The introduction of a Faradaic reformer is new. 

Secondary reactions are affected by the residence time of primary products within the catalyst bed while primary reactions are controlled only by the fugacity of reactants (and products if they affect the rate and selectivity of primary reactions pathways). Therefore, studies of the effects of bed residence time and of the presence of reaction products in the H2/CO feed are... 

Intrapellet transport restrictions can limit the rate of removal of products, lead to concentration gradients within pellets, and prevent equilibrium between the intrapellet liquid and the interpellet gas phase. Transport restrictions increase the intrapellet fugacity of hydrocarbon products and provide a greater chemical potential driving force for secondary reactions. The rate of secondary reactions cannot be enhanced by a liquid phase that merely increases the solubility and the local concentration of a reacting molecule. Olefin fugacities are identical in any phases present in thermodynamic equilibrium thus, a liquid phase can only increase the rate of a secondary reaction if it imposes a transport restriction on the removal of reacting species involved in such a reaction (4,5,44). Intrapellet transport rates and residence times depend on molecular size, just as convective transport and bed residence time depend on space velocity. As a result, bed residence time and molecular size affect chain termination probability and paraffin content in a similar manner. 

The value of the parameter 2 13 in a gas mixture can he calculated from PVT data using any traditional EOS. Eor the mixtures that obey the Lewis-Randall rule [16] (the fugacity of a species in a gaseous mixture is the product of its mole fraction and the fugacity of the pure gaseous component at the same temperature and pressure), the fugacity coefficients of the components of the mixture are independent of composition. In such cases, the KB equation [13] for the binary mixtures 1-3 ... 

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