Pressure correction, enthalpy

When a Mollier chart is available for the gas involved the first method, which is illustrated by Figure 12-12A is the most convenient. On the abscissa of Figure 12-12A four enthalpy differences are illustrated. (Hg — Hj) is the enthalpy difference for the isentropic path. (Hg — Hi°) is the ideal gas state enthalpy difference for the terminal temperatures of the isentropic path. The other AH values are the isothermal pressure corrections to the enthalpy at the terminal temperatures. A generalized chart for evaluating these pressure corrections was presented previously. 

The pressure correction to the enthalpy of a substance, at constant temperature, is given by... 

We are at a loss to explain the discrepancy in the BF3 enthalpies of interaction with the sulfur donors. Steric effects may be operative, but this is far from the whole story for the BCI3 interaction is much larger than BF3 with these donors. Furthermore, using the tentative ( 113)3 parameters to estimate those of ( 2115)3 , we calculate an enthalpy from E and of 11.1 k.cal mole- for the BF3-P( 2H6)3 adduct compared to a measured value of 9.5 k.cal mole i. The authors report much difficulty with the sulfur donor system, but their error estimates could not possibly account for the difference between our calculated and the observed result. The behavior of ( 2115)35 compared to ( 2115)3 is clearly inconsistent with the behavior of these two donors toward ( 2H5)sAl where both enthalpies are correctly predicted with our parameters. It may be that the BF3-( 2115)25 system has an even lower equilibrium constant than reported and is completely dissociated over the temperature range studied. (This would require a very different entropy if the — AH predicted by E and were correct.) A slight impurity (reported to be less than 0.1%) or decomposition product could interact appreciably with BF3 and changing pressure contributions from this adduct with temperature could be attributed incorrectly to the sulfur donor adduct. The actual BF3-sulfur donor adduct would then be a very common example of an adduct which cannot be studied by the vapor pressure technique because it is completely dissociated at the temperatures at which one of the components has appreciable vapor pressure. We have examined the reaction of BF3 ( 2Hs) 2O with large excess of ( H2) 4S in dichloroethane solution at 25 ° and have found the equilibrium constant to be too low to be measured calorimetrically. 

A multiple-property technique was employed in developing the Lee-Erbar-Edmister equations. In this method, both measured values of the isothermal pressure correction to the enthalpy and the P-V-T data are used. 

For enthalpy, a slight pressure correction improves the accuracy. This amounts to adding an ideal pump work term to account for the enthalpy added due to increased pressure ... 

Very few refinery operations operate about 800°F. The coal gasification processes, on the other hand, start at about 1300 F and some operate up to nearly 3000°F. Many of the new processes operate at pressures of about 1000 psla. Reliable zero pressure enthalpies up to these temperatures are available for most of the materials found in gasifiers, but the mixing rules and pressure corrections which the trade has been using for nonpolar mixtures are probably inadequate. 

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. 

The enthalpy of a vapor mixture is obtained first, from zero-pressure heat capacities of the pure components and second, from corrections for the effects of mixing and pressure. 

In Equation (15), the third term is much more important than the second term. The third term gives the enthalpy of the ideal liquid mixture (corrected to zero pressure) relative to that of the ideal vapor at the same temperature and composition. The second term gives the excess enthalpy, i.e. the liquid-phase enthalpy of mixing often little basis exists for evaluation of this term, but fortunately its contribution to total liquid enthalpy is usually not large. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

When the reduced temperature is iess than 0.85, d(T depends very little on pressure. Table 4.8 gives values for and for enthalpy correction factorsi calculated by the Lee and Kesler method. 

AH = moisture-content correction of air saturated at wet-bulb temperature when barometric pressure differs from standard barometer, gr/lb dry air NOTE To obtain AH reduce value of AH by 1 percent where t — t, = 24 F and correct proportionally when t — is not 24 F h = enthalpy of moist air, Btu/lb dry air... 

Use of Psychrometric Charts at Pressures Other Than Atmospheric The psychrometric charts shown as Figs. 12-1 through 12-4 and the data of Table 12-1 are based on a system pressure of 1 atm (29.92 inHg). For other system pressures, these data must be corrected for the effect of pressure. Additive corrections to be apphed to the atmospheric values of absolute humidity and enthalpy are given in Table 12-2. 

The theoretical values for enthalpy may be read from a Mollier chart, where hj is the enthalpy of the steam at the turbine inlet, and hg is the enthalpy of the steam at the exhaust pressure and at the inlet entropy. The expansion of steam through the turbine is theoretically at constant entropy. These theoretical rates must be corrected for performance inefficiencies of the particular turbine. The calculations presented here are good for the average design, but exact values for a particular make and model turbine must be quoted by... 

Billmers and Smith recorded the UV-Vis absorption spectra of sulfur vapor at various pressures (9-320 Torr or 1.2-42.7 kPa) and temperatures (670-900 K) but failed in obtaining the correct reaction enthalpy for the interconversion of S3 and S4 from the absorption intensities [19]. The molar extinction coefficient of S3 at 400 nm exceeds that of S4 at 520 nm by more than one order of magnitude. While the S3 absorption band at 360-440 nm exhibits a vibrational fine structme, the two broad S4 absorption bands at... 

If the effect of pressure is likely to be significant, the change in enthalpy of the products and reactants, from the standard conditions, can be evaluated to include both the effects of temperature and pressure (for example, by using tabulated values of enthalpy) and the correction made in a similar way to that for temperature only. 

The values for the enthalpies of the streams in the database were based on the Curl-Pitzer congelations (Green, 1997). The enthalpies are calculated from correlations at zero pressure (functions of temperature and composition only) and then corrected via the enthalpy deviation ... 

The standard enthalpy of formation of monomeric HF is a hypothetical state that must be related to that of the real associated liquid, gas, or aqueous solution met in calorimetiy. Considerable difficulty has been encountered in allowing for the heat of association, which varies with temperature and pressure. For example, the presence of traces of water can affect the polymerization by entering into the hydrogen bonding (30) the treatment of results will depend on the association model adopted. The magnitude of corrections for gas imperfections has... 

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