Enthalpies Pure components

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

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. 

The enthalpies of vaporization for the pure components are in excellent agreement with experiment, as is the composition of the azeotrope. The enthalpy of the saturated vapor is also in... 

The computation of pure-component and mixture enthalpies is implemented by FORTRAN IV subroutine ENTH, which evaluates the liquid- or vapor-phase molar enthalpy for a system of up to 20 components at specified temperature, pressure, and composition. The enthalpies calculated are in J/mol referred to the ideal gas at 300°K. Liquid enthalpies can be determined either with... 

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. 

Our immediate goal is an expression for AHj and we must remember that this is the difference in the enthalpies of the solution and the pure components. We need not worry about the absolute values of the enthalpies of the individual states. 

Fig. 3. Temperature—enthalpy representation of stream where A represents a pure component that is condensiag, eg, steam B and C represent streams having constant heat capacity, that are to be heated or cooled, respectively and D represents a multicomponent mixture that changes phase as it is...

Enthalpy of Vaporization The enthalpy (heat) of vaporization AHv is defined as the difference of the enthalpies of a unit mole or mass of a saturated vapor and saturated liqmd of a pure component i.e., at a temperature (below the critical temperature) anci corresponding vapor pressure. AHy is related to vapor pressure by the thermodynamically exact Clausius-Clapeyron equation ... 

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

The change in enthalpy with respect to temperature is not neghgible. It can be calculated for a pure component using the specific heat correlations like those in Table 7.1 ... 

As a thermodynamicist working at the Lower Slobbovian Research Institute, you have been asked to determine the standard Gibbs free energy of formation and the standard enthalpy of formation of the compounds ds-butene-2 and trans-butene-2. Your boss has informed you that the standard enthalpy of formation of butene-1 is 1.172 kJ/mole while the standard Gibbs free energy of formation is 72.10 kJ/mole where the standard state is taken as the pure component at 25 °C and 101.3 kPa. 

In Eq. (2), Ts is the sample temperature, T0 is the melting point of the pure major component, X, is the mole fraction of the impurity, F is the fraction of solid melted, and AHf is the enthalpy of fusion of the pure component. A plot of Ts against 1 IF should yield a straight line whose slope is proportional to X,. This method can therefore be used to evaluate the absolute purity of a given compound without reference to a standard, with purities being obtained in terms of mole... 

Figure 9 provides a comparison of the predictions of empirical methods with Wormald s data for a 50/50 mole percent mixture of steam and methane. As can be seen, the frequently used artifices of calculating mixture enthalpies by blending the pure component enthalpies at either total or partial pressures are very inaccurate. Likewise, the assumption of ideal gas enthalpy for the real gas mixture, equivalent to a zero enthalpy departure on the diagram, is an equally poor method. 

The equation-of-state method, on the other hand, uses typically three parameters p, T andft/for each pure component and one binary interactioncparameter k,, which can often be taken as constant over a relatively wide temperature range. It represents the pure-component vapour pressure curve over a wider temperature range, includes the critical data p and T, and besides predicting the phase equilibrium also describes volume, enthalpy and entropy, thus enabling the heat of mixing, Joule-Thompson effect, adiabatic compressibility in the two-phase region etc. to be calculated. 

Of course, with mixtures of components the total enthalpy is needed. If heat-of-mixing effects are negligible, the pure-component enthalpies ean be averaged ... 

Table 5.12 reports a compilation of thermochemical data for the various olivine components (compound Zn2Si04 is fictitious, because it is never observed in nature in the condition of pure component in the olivine form). Besides standard state enthalpy of formation from the elements (2) = 298.15 K = 1 bar pure component), the table also lists the values of bulk lattice energy and its constituents (coulombic, repulsive, dispersive). Note that enthalpy of formation from elements at standard state may be derived directly from bulk lattice energy, through the Bom-Haber-Fayans thermochemical cycle (see section 1.13). 

Table 5.36 Thermodynamic properties of pure pyroxene components in their various structural forms according to Saxena (1989) (1), Berman (1988) (2), and Holland and Powell (1990) (3) database. = standard state entropy of pure component at 7) = 298.15 K and Py = bar (J/mole) Hjp p = enthalpy of formation from elements at same standard state conditions. Isobaric heat capacity function Cp is... 

If the heat capacity functions of the various terms in the reaction are known and their molar enthalpy, molar entropy, and molar volume at the 2) and i). of reference (and their isobaric thermal expansion and isothermal compressibility) are also all known, it is possible to calculate AG%x at the various T and P conditions of interest, applying to each term in the reaction the procedures outlined in section 2.10, and thus defining the equilibrium constant (and hence the activity product of terms in reactions cf eq. 5.272 and 5.273) or the locus of the P-T points of univariant equilibrium (eq. 5.274). If the thermodynamic data are fragmentary or incomplete—as, for instance, when thermal expansion and compressibility data are missing (which is often the case)—we may assume, as a first approximation, that the molar volume of the reaction is independent of the P and T intensive variables. Adopting as standard state for all terms the state of pure component at the P and T of interest and applying... 

Although in crystalline phases determination of the enthalpy of formation from the constituent elements (or from constituent oxides) may be carried out directly through calorimetric measurements, this is not possible for molten components. If we adopt as standard state the condition of pure component at T = 298.15 K and P = bar , it is obvious that this condition is purely hypothetical and not directly measurable. If we adopt the standard state of pure component at P and T of interest , the measurement is equally difficult, because of the high melting temperature of silicates. 

Here Xa and Xb are the mole fractions of component A and B, respectively, and are related by Xa + Xg) = 1. We have used a superscript circle on the enthalpies and entropies of pure components A and B to indicate that these are standard state enthalpies and entropies of the pnre components. The standard state of a component in a condensed system is its stable state at the particular temperature and pressure of interest. So, depending on the temperatnre and pressure of the system, the standard state conld be either a liqnid or a solid for either of components A and B. 

The integral heat (enthalpy) of solution A/7soln is defined as the total heat liberated (under constant-P conditions) when a solution is formed from its pure components A, B ... 

For the problem to be tractable, the enthalpies of the two phases must be known as functions of the respective phase compositions. When heats of mixing and heat capacity effects are small, the enthalpies of mixtures may be compounded of those of the pure components thus... 

For purposes of distillation calculations, a rough diagram of saturated vapor and liquid enthalpy concentration lines can be drawn on the basis of pure component enthalpies. Even with such a rough diagram, the accuracy of distillation calculation can be much superior to those neglecting enthalpy balances entirely. Example 13.8 deals with preparing such a Merkel diagram. 

Solutions in which intermodular forces are stronger in the solution than in the pure components have negative deviations from Raoult s law and negative enthalpies of mixing they often form maximum-boiling azeotropes. Solutions in which intermodular forces are weaker in the solution than in the pure components have positive deviations from Raoult s law and positive enthalpies of mixing they often form minimum-boiling azeotropes. 

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