Poynting pressure correction

Note the the Poynting pressure correction of this result to 3 bar total pressure is negligible.]... 

The exponential term in this equation, known as the Poynting pressure correction, accounts for the increase in fugacity due to the fact that the system pressure is higher than the vapor pressure of the liquid. Since the molar volmne of a liquid is generally much less than that of a gas (so that PV /RT -C 1), the Poynting term is only important at high pressures. (An exception to this is for cryogenic systems, where T is very low.)... 

Another approximation that can be made in Eq. 7.4-18 is to take into account the Poynting pressure correction, but to assume that the liquid is incompressible (Fig. 7.3-4 for the van der Waals equation of state, for example, does indicate that at constant temperature the liquid volume is only slightly pressure dependent). In this case... 

However, if the temperature of the mixture is well above the evaluation of fl iT, P) is more troublesome. A number of different procedures for estimating this hypothetical liquid fugacity have been proposed. Prausnitz and Shair have suggested that the simple approximate corresponding-states correlation of Fig. 11.1-1 be used to evaluate the liquid fugacity at 1.013 bar total pressure, that is, fl(T, P — 1.013 bar). To compute the hypothetical liquid-phase fugacity at any other pressure, a Poynting pressure correction is made to the value at 1.013 bar as follows ... 

The approximations that have been made are to neglect the Poynting pressure correction terms to the solid and liquid free energies (or fugacities), and to assume (.//p) 1-... 

Next, neglecting the activity coefficients of the solvent (which are usually close to 1 in value unless the solutions are concentrated in the solutes) and using the Poynting pressure correction, we obtain... 

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 ... 

If the data are correlated assuming an ideal vapor, the reference fugacity is just the vapor pressure, P , the Poynting correction is neglected, and fugacity coefficient is assumed to be unity. Equation (2) then becomes... 

Finally, at low pressures, the liquid fugacity can be calculated using Equation (5), i.e. we can assume that <() = 1 and that the Poynting correction = 1. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

The exponential term in equation 8.32 is known as the Poynting correction, and corrects for the effects of pressure on the liquid-phase fugacity. 

The fundamental fact on which the analysis of heterogeneous reactions is based is that when a component is present as a pure liquid or as a pure solid, its activity may be taken as unity, provided the pressure on the system does not differ very much from the chosen standard state pressure. At very high pressures, the effect of pressure on solid or liquid activity may be determined using the Poynting correction factor. 

Partial molar volumes at infinite dilution were adopted from the correlation of Brelvi and O Connell (20). (In the pressure range regarded here (p 100 atm) Poynting corrections are very small and can be neglected for all electrolytes as well as for water (eqs. E1, E2) ). ... 

Since the sublimation pressure is normally very low, the fugacity coefficient (/> is close to 1 and also the Poynting correction is not very different from 1 (usually less than 2). As a consequence, the most important term that contributes to a value of E is the fugacity coefficient in the supercritical phase. 

Additionally usually small corrections for pressure, called Poynting factors, also belong in Eq. (13.6) and following but are omitted here. The new terms are... 

The derivation of Equation (2.60) might be seen as a long-winded way of arriving at a trivial result. However, this derivation explicitly clarifies the assumptions behind this equation. First, a gradient in concentration occurs within the membrane, but there is no gradient in pressure. Second, the absorption of a component into the membrane is proportional to its activity (partial pressure) in the adjacent gas, but is independent of the total gas pressure. This is related to the approximation made in Equation (2.52), in which the Poynting correction was assumed to be 1. 

For the purpose of this discussion, Eq. (1.11) is simplified by omitting the Poynting correction, which is usually small at low pressures. Combining Eq, (1.11) with the definition of relative volatility, Eq. (1,2) gives... 

Here, the exponential term is the Poynting correction factor, which may be negligible at low to moderate pressures. Disregarding the Poynting factor, Eq. (1.218) becomes... 

The standard state used for the finite concentration data was usually the pure solvent at the temperature and pressure of the mixture. In most cases, the Poynting correction (pressure effect on the liquid) could be neglected. The end result of this approximation is that saturation pressure appears in the expression for the activity coefficient, but not the system pressure. 

The first two terms in the product on the right side of Equation (4C-14) give the fugacity at the saturation pressure. The exponential term, the Poynting correction, is a correction to the fugacity for compressing the condensed phase from the saturation pressure to pressure P. Assuming that the condensed phase molar volume does not vary with pressure this relation reduces to... 

The exponential term is the Poynting correction, which is the effect of pressure on the reference fugacity, and is only important at high pressure. 

Eq. (13-4). Otherwise is evaluated from vapor pressure data with a Poynting saturated-vapor fugacity correction. When the total pressure is less than about 202.6 kPa (2 atm) and all components in the mixture have a critical temperature that is greater than the system temperature, then Of =Pf /P and Of = 1.0. Equation (13-4) then reduces to... 

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