Fugacity pure components

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

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 ... 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

These were converted from vapor pressure P to fugacity using the vapor-phase corrections (for pure components), discussed in Chapter 3 then the Poynting correction was applied to adjust to zero pressure ... 

CALCULATE PURE COMPONENT LIQUID FUGACITY AT SPECIFIED TEMP AND ZERO PRESSURE IF IVAP.LE.2 C PURE CCMPDNENT VAPOR PRESSURE IF IVAP.EQ.3... 

GET PURE COMPONENT LIQUID FUGACITIES, FIP 120 CALL PURF[Pg.292]

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

FO(I) Vector (length 20) of pure-component liquid standard-state fugacities at zero pressure or hypothetical liquid standard-... 

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 ... 

Calculation of the total fugacity of the pure component in the liquid phase. ... 

The chemical literature is rich with empirical equations of state and every year new ones are added to the already large list. Every equation of state contains a certain number of constants which depend on the nature of the gas and which must be evaluated by reduction of experimental data. Since volumetric data for pure components are much more plentiful than for mixtures, it is necessary to estimate mixture properties by relating the constants of a mixture to those for the pure components in that mixture. In most cases, these relations, commonly known as mixing rules, are arbitrary because the empirical constants lack precise physical significance. Unfortunately, the fugacity coefficients are often very sensitive to the mixing rules used. 

In a system that involves gaseous components, one normally chooses as the standard state the pure component gases, each at unit fugacity (essentially 1 atm). The activity of a gaseous species B is then given by... 

Choosing the reference state of each component in the pseudobinary solution to be the pure component (1 and 2 ), the reference state fugacities are given by... 

In this approach the standard state fugacity of a liquid or solid component is usually the fugacity of die pure solid or liquid component, and is closely related to the sublimation pressure P- b or vapour pressure P.at, respectively. I.e., on the sublimation curve of a pure component we have... 

The enhancement factor contains three terms supercritical phase, ideal behaviour of the pure component 2 in the vapour phase at the sublimation pressure, and the Poynting factor that describes the influence of the pressure on the fugacity of pure solid 2. 

For the evaluation of the solubility it is necessary to know the pure component properties and to use an equation-of-state model for the evaluation of the fugacity coefficients. In general, two problems arise ... 

The thermodynamic reaction equilibrium constant K, is only a function of temperature. In Equation 4.18, m, the activity of the guest in the vapor phase, is equal to the fugacity of the pure component divided by that at the standard state, normally 1 atm. The fugacity of the pure vapor is a function of temperature and pressure, and may be determined through the use of a fugacity coefficient. The method also assumes that an, the activity of the hydrate, is essentially constant at a given temperature regardless of the other phases present. 

With the above data, Equation 4.21 indicates that the hydrate number n may be obtained from a measurement of the increase of the hydrate pressure with an inhibitor present at a given temperature. The fugacity may be calculated for a pure component from any of a number of thermodynamic methods given a temperature and pressure. Only in the case of a pure ideal gas (very low pressure or very high temperature) may the fugacities be replaced with the pressure itself. 

In order to solve for thermodynamic equilibrium, the fugacity of water in the hydrate must be known. This method follows the common approach of solving for fugacity, using the standard state of the ideal gas of the pure component at 1 bar. 

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