Calculation from excess enthalpy

P4.5 Calculate the excess enthalpy of the system benzene (l)-cyclohexane (2) at =25 CandP = 1 bar for a mole fraction of benzene of xi =0.5 using the Soave-Redlich-Kwong equation of state. The required values can be taken from Appendix A. The binary interaction parameter is ki2 = 0.0246. 

Fig. 1.2 Effect of pressure p on excess molar enthalpies if. Comparison of (dlfldp r values of water + ethanol mixtures at 298.15 K , calculated from excess molar volume F measurements at different temperatures (80MAR2) using Eq.(1.24) o, calculated from if measurements at different pressures (860TT1) xi is the ethanol mole fraction...

For a detailed discussion of the calculation of activities (and excess Gibbs free energies) from freezing point measurements, see R. L. Snow. J. B. Ott. J. R. Goates. K. N. Marsh, S. O Shea, and R. N. Stokes. "(Solid + Liquid) and (Vapor + Liquid) Phase Equilibria and Excess Enthalpies for (Benzene + //-Tetradecane), (Benzene + //-Hexadecane). (Cyclohexane + //-Tetradecane), and (Cyclohexane +//-Hexadecane) at 293.15, 298.15, and... 

Harkins et al., 1940), where ne is the ESP, and Ae is the average area per molecule at the ESP as obtained from the 11/ 4 isotherm of the spread film. The temperature dependence of the ESP may then be used to calculate the excess surface entropies from (5) and enthalpies of spreading from (6). 

Calculation of enthalpies of formation from the enthalpies of combustion of reactants and products This method is generally applicable for any combustible material for which the gross molecular formula is known. The enthalpies of combustion may be determined in a calorimeter using excess oxygen. Analysis of the combustion products may be appropriate. 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

Enthalpy of dilution data can be used to calculate excess enthalpies by a procedure analogous to that we used to calculate relative molar enthalpy from enthalpy of dilution. We can describe the dilution of an aqueous solution of rii moles of water and 2 nioles of solute S with (riif — riu) moles of water by the equation... 

The (liquid 4- liquid) equilibria diagram for (cyclohexane + methanol) was taken from D. C. Jones and S. Amstell, The Critical Solution Temperature of the System Methyl Alcohol-Cyclohexane as a Means of Detecting and Estimating Water in Methyl Alcohol , J. Chem. Soc., 1930, 1316-1323 (1930). The G results were calculated from the (vapor 4- liquid) results of K. Strubl, V. Svoboda, R. Holub, and J. Pick, Liquid-Vapour Equilibrium. XIV. Isothermal Equilibrium and Calculation of Excess Functions in the Systems Methanol -Cyclohexane and Cyclohexane-Propanol , Collect. Czech. Chem. Commun., 35, 3004-3019 (1970). The results are from M. Dai and J.-P.Chao, Studies on Thermodynamic Properties of Binary Systems Containing Alcohols. II. Excess Enthalpies of C to C5 Normal Alcohols + 1,4-Dioxane , Fluid Phase Equilib., 23, 321-326 (1985). 

The heat capacities for the other compounds were derived using the estimation procedure described for the trichlorides, i.e., from the lattice and excess contributions. The former was derived from the enthalpy measurements, the latter from the crystal field energies. As the crystal energies of the tribromides and triiodides are poorly known, we have used the values for the trichlorides to approximate Cexs- The results thus obtained are listed in tables 10 and 11. The calculated data for TmG agree within 2% with the DSC results of Gardner and Preston (1991). 

Efficiency of starch dispersion can be further improved when an excess quantity of steam is used97 or when the starch is held under pressure in a retention device (tank or coil) before discharge to the atmosphere. Both processes require a flash chamber (cyclone) to remove excess steam and steam relieved by the pressure drop. Excess steam refers to a multiple of the quantity required to reach target temperature and pressure. The quantity of saturated steam to reach a target temperature can be calculated from its heat content, the slurry temperature, the specific heats of starch and water, and the enthalpy of starch gelatinization. The action of excess steam in the dispersion zone between the jet and back-pressure valve causes a shear effect that enhances disintegration of the starch granules. In many applications, a three-fold excess of steam is used. 

Gibbs functions for a real salt solution and the corresponding ideal salt solution containing m2 moles of salt in a kilogram of solvent. GE can be calculated for many aqueous salt solutions from published values of 0 and y . In the same way, the corresponding excess enthalpy HE can be defined and this equals the apparent partial molar enthalpy. Thus the properties of salt solutions can be examined in plots of GE, HE, and T SE against m2, where SE is the... 

Falcone and Wood179) have reported enthalpies of dilution in NMA for a large series of alkali metal halides as well as for a number of tetraalkylammonium halides (all measurements at 35 °C). These heats were expressed as excess enthalpies180,181) and values of the excess free energies calculated from the previously mentioned osmotic coefficients allowed calculation of the excess entropies. 

Combustion reactions are excessively used in propellant systems. The impulse of the gaseous combustion products is used to propel a payload. For obvious technical reasons, the burning temperature of a rocket engine is of interest. The adiabatic flame temperature of combustion (Tad) is the temperature at which reactants and products do not differ in enthalpy. The enthalpies of the components of the system have to be calculated from their standard enthalpy by adding of the enthalpy caused by heating to Tad. This is where the specific heat capacity Cv comes into play. Unfortunately, the component ratios of the system are functions of the temperature, necessitating the use of iterative calculations of Tad. 

The enthalpy, AH, and entropy, AS, of the transition were calculated from the heat capacity curve by integration of the excess heat capacity, ACp, and ACp/T, respectively. The normal heat capacities for the calculation were determined by interpolation of the heat capacities outside the transition region using the linear function... 

The absolute aulsorption isotherms for —30°C and TO C were calculated from the 20°C isotherm using the integrated form of Eq. (1) and the differential enthalpy plotted on Fig. 2. The reasonable approximation was made that the differentiaJ enthaJpy is independent of temperature. No other assumptions were needed to calculate the excess adsorption isotherms on Fig. 3. 

At constant temperature and pressure, the concentration-dependent activity coefficient can be determined from the free excess enthalpy by differentiation through the mole fraction. These equations are the basis for the methods of Wilson and Prausnitz to calculate the activity coefficient [19, 20], The Gibbs-Duhem equation is again a convenient method for checking the obtained equilibrium data ... 

The integral exchange enthalpy isotherm calculated from the flow microcalorimetric measurements is shown in Fig. 12. The course of the isotherm - in case of a U-shaped adsorption excess isotherm - is determined by the composition of the interfacial phase ( ) according to the following equation[45-47] ... 

An application of continuum solvation calculations that has not been extensively studied is the effect of temperature. A straightforward way to determine the solvation free energy at different temperatures is to use the known temperature dependence of the solvent properties (dielectric constant, ionization potential, refractive index, and density of the solvent) and do an ab initio solvation calculation at each temperature. Elcock and McCammon (1997) studied the solvation of amino acids in water from 5 to 100°C and found that the scale factor a should increase with temperature to describe correctly the temperature dependence of the solvation free energy. Tawa and Pratt (1995) examined the equilibrium ionization of liquid water and drew similar conclusions. An alternative way to study temperature effect is through the enthalpy of solvation. The temperature dependence of is related to the partial molar excess enthalpy at infinite dilution,... 

Figure 6.2.1. Excess Gibbs free energy and excess enthalpy of the acetone and water binary mixture at 293 K. The excess Gibbs free energy was calculated from VLE data as described in Section 5.1, The excess enthalpy data are as reported in the DECHEMA Chemistry Data Series Heat of Mixing Collection, Christiansen et al. 19S4, Vol, l,Pt. lb, pp. 148-9.

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