Partial fugacities

Derivatives of the reaction rates with respect to temperature and composition (e.g. expressed as mole fractions, fugacities, partial pressures, etc). 

It might at first seem strange that we can have a number of different mass transfer coefficients in contrast to essentially one heat transfer coefficient. However, consider the situation for chemical equilibrium constants where we also have a number of different constants (based on activities, fugacities, partial pressures, concentrations, etc). In dealing with the mass transfer coefficient it becomes very important to clearly know the characteristic driving force used for the system. While the units of the coefficients are helpful, they are not foolproof example both ky and k have same units). 

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 ... 

The amounts of each phase and their compositions are calculated by resolving the equations of phase equilibrium and material balance for each component. For this, the partial fugacities of each constituent are determined ... 

Utilizing the concept of partial fugacity which is defined by the relation J... 

The ratio fj/Pyj is written as (/>, and called the partial fugacity coefficient in the liquid phase, this coefficient is written as , and in the gas phase 0. ... 

In the calculation of vapor phase partial fugacities the use of an equation of state is always justified. In regard to the liquid phase fugacities, there is a choice between two paths ... 

The partial fugacity of component i in the liquid phase is expressed as a function of the total fugacity of this same component in the pure liquid state, according to the following relation ... 

For mixtures, the calculation is more complex because it is necessary to determine the bubble point pressure by calculating the partial fugacities of the components in the two phases at equilibrium. 

In the case of three-phase equilibria, it is also necessary to account for the solubility of hydrocarbon gases in water. This solubility is proportional to the partial pressure of the hydrocarbon or, more precisely, to its partial fugacity in the vapor phase. The relation which ties the solubility expressed in mole fraction to the fugacity is the following ... 

The properties of the solids most commonly encountered are tabulated. An important problem arises for petroleum fractions because data for the freezing point and enthalpy of fusion are very scarce. The MEK (methyl ethyl ketone) process utilizes the solvent s property that increases the partial fugacity of the paraffins in the liquid phase and thus favors their crystallization. The calculations for crystallization are sensitive and it is usually necessary to revert to experimental measurement. 

To avoid hydrate formation, it is necessary either to dry the stream, or to inject a substance that, dissolving the water, lowers its partial fugacity and, consequently, the temperature of hydrate formation. 

Thus the fugacity of species / in an ideal gas mixture is equal to its partial pressure. 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

In apphcatious to equilibrium calculations, the fugacity coefficients of species iu a mixture are required. Given au expression for G /RT as aetermiued from Eq. (4-158) for a coustaut-compositiou mixture, the corresponding recipe for In is found through the partial-property relation... 

Gaseous equilibria are expressed in terms oifugacities or fugacity coefficients. In terms of partial pressures,... 

Driving Force Gas moves across a membrane in response to a difference in chemical potential. Partial pressure is sufficiently proportional to be used as the variable for design calculations for most gases of interest, but fugacity must be used for CO9 and usually for Hg... 

Membrane System Design Features For the rate process of permeation to occur, there must be a driving force. For gas separations, that force is partial pressure (or fugacity). Since the ratio of the component fluxes determines the separation, the partial pressure of each component at each point is important. There are three ways of driving the process Either high partial pressure on the feed side (achieved by high total pressure), or low partial pressure on the permeate side, which may be achieved either by vacuum or by introduc-... 

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