Vaporization, partial enthalpy calculations

Measurements of the saturated vapor pressures of plasticizers over plasticized cellulose nitrate were used for calculation of chemical potentials of plasticizers and partial enthalpies and entropies of mixing. ... 

Some components will be in the vapor phase when their properties as a pure material indicate they should be liquid. Other components will be in the liquid phase at temperatures above their critical temperatures. Clearly, partial enthalpies should be employed to produce accurate results. A significant amount of work has been done in developing correlations for calculating partial enthalpies... 

The desired enthalpy of formation of 6,6-dimethylfulvene was determined by Roth citing measurement of hydrogenation enthalpies, and chronicled by Pedley citing enthalpies of combustion and vaporization. The two results differ by 7 kJ mol-1. We have opted for Roth s value because it is in better agreement with a value calculated using Roth s force field method. It is also to be noted that measurement cited by Pedley for the neat condensed phase could be flawed by the presence of partially polymerized fulvene and neither elemental abundance of the compound nor analysis of the combustion products would have disclosed this. Likewise, the measured enthalpy of vaporization would not have necessarily uncovered this contaminant. 

The last term in the formula (1-196) describes electrostatic and Van der Waals interactions between atoms. In the Amber force field the Van der Waals interactions are approximated by the Lennard-Jones potential with appropriate Atj and force field parameters parametrized for monoatomic systems, i.e. i = j. Mixing rules are applied to obtain parameters for pairs of different atom types. Cornell et al.300 determined the parameters of various Lenard-Jones potentials by extensive Monte Carlo simulations for a number of simple liquids containing all necessary atom types in order to reproduce densities and enthalpies of vaporization of these liquids. Finally, the energy of electrostatic interactions between non-bonded atoms is calculated using a simple classical Coulomb potential with the partial atomic charges qt and q, obtained, e.g. by fitting them to reproduce the electrostatic potential around the molecule. 

After freezing, the time to sublimate the solvent is given by the drying expressions in Tables 8.3 and 8.4, where the enthalpy of vaporization for drying is replaced by the enthalpy of sublimation. The enthalpy of sublimation is often equal to the sum of the heats of fusion and vaporization [16]. The enthalpy of sublimatian is also substituted for the enthalpy of vaporization in the Clausius Clapeyron equation (8.9) required for the calculation of the solvent partial pressure. The same rate determining steps of boundaiy layer mass transfer and heat transfer as well as pore diffusion and porous heat conduction are applicable in sublimation. 

For true compatability of solute and solvent, matching of all these partial solubility parameters (i.e., 8, Bp, 8 ) is necessary. The total solubility parameter can be easily calculated [1, p. 307] finm the material s enthalpy of vaporization, vapor pressure as a function of temperature, surface tension, thermal expansion coefficient, critical pressure, and second virial coefficient of its vapor, as well as by calculating its value for the chemical structure of the material. For the calculation of the Hildebrand solubility parameter fi om chemical structure, we use Small s [58] equation ... 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partially for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihringline [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

AjH (LlBr, g, 298.15 K) -36.8 3 kcal mol" (-153.971 13 kJ mol"" ) Is calculated from the selected enthalpy of vaporization and the enthalpy of formation for lithium bromide (t). Lithium bromide vaporizes to a mixture of monomeric and dimeric gases. (Higher polymers have been neglected In the calculation.) The enthalpies of vaporization to monomer and to dimer were chosen to satisfy (1) the total vapor pressure data measured by von Wartenberg and Schulz (1 ) and by Ruff and Mugdan (2) the partial vapor pressures of monomer and dimer derived from Miller and Kusch (3 ) In an analysis of the velocity distribution of molecules In... 

The adopted value of the enthalpy of formation, AjH"(Cs2S0, g, 298.15 K) = -268.3 4.0 kcal mol , is based on JANAF analyses of the vaporization data given below. The calculated 3rd law A H (298.15 K) may have an uncertainty of 4 kcal mol since the JANAF Gibbs energy functions are partially based on the estimated molecular constants of Cs S0.(g). 

However, the measured pressure of the chemical equilibrium is the total pressure of three partial pressures, namely, P(SOg), P(S02>, and P(02>. In order to calculate the enthalpy change of Reaction (1), the partial pressures of SOg(g) were evaluated from the total vapor pressure data at each temperature. Based on the derived values for P(S02), the a H (298.15 K) value for Reaction (1) was calculated by both the 2nd and 3rd law methods. The results obtained are presented in the following table. The A H (Fe2(S0 )2, cr, 298.15 K) values were derived, using the 3rd law Aj.H (298.15 K). These determinations were not given any weight. 

Vapor pressures for liquid KOH have been determined by static (1443-1600 K) (7) and transpiration (873-1323 K) (8 ) methods. In order to evaluate Ay pH (K0H, t, 298.15 K) we have used a trial and error variation of A pH (298.15 K) for the monomer and dimer, such that these values are in accordance with the adopted enthalpy of dimerization given above, and the sum of the calculated partial pressures for KOH(g) and [KOH] (g) is in good agreement with the experimental vapor pressure data. Since the... 

Lithium vapor contains an appreciable amount of dimer, whose enthalpy of dissociation has been selected by Evans (5), from spectroscopic and molecular beam measuresments to be 25.76 0.10 kcal mol at 0 K. This enthalpy of dissociation, together with the thermodynamic functions calculated in this work, has been used to find the partial pressures of Li(g) and Li2(g) from the measured total vapor pressures. Hartmann and Schneider (6), report values from 1204 to 1353 K while Mancherat (7) reports effusion measurements from 735 to 915 K. Mancherat s (7 ) pressures are calculated on the assumption of monatomic vapor and have been recalculated to fine the true total pressure. Effusion measurements by Lewis (8) and Bogros (9) have been disregarded. Mancherat (7) considers them to be inaccurate because of impurities In the lithium used, and Lewis (S used a doubtful calibration method. Enthalpy of sublimation to monatomic vapor calculated from the vapor pressures of Hartmann and Schneider (6) and of Mancherat (7) agree to within 2% and the average value has been adopted. The enthalpy of sublimation of the dimer was then calculated using this value. 

The use of the procedure of Rau et al. (2) leads to a set of thermal functions and associated enthalpies of formation which reproduce the observed sulfur vapor pressure data. That Is, the sum of the calculated partial pressures of all eight sulfur vapor species, S (g) to Sg(g), does closely reproduce the observed vapor pressure. [A difference between the calculated boiling point (at 1 atm) and the secondary reference temperature boiling point is due to the difference between the Ideal gas calculation and the real observed value.]... 

Snow and ice sublime spontaneously when the partial pressure of water vapor is below the equilibrium vapor pressure of ice. At 0°C the vapor pressure of ice is 0.0060 atm (the triple-point pressure of water). Taking the enthalpy of sublimation of ice to be 50.0 kj mol , calculate the partial pressure of water vapor below which ice will sublime spontaneously at -15°C. 

Initially, the vapor pressure measurements appear to be the most direct, but even here some assumptions are needed. The amount of alcohol in the micellar phase needs to be determined. To do this the difference in vapor pressure between a pure aqueous and a micellar solution is measured. If the ions of the surfactant salts out alcohol, the vapor pressure of pure water is not the correct comparison, and this could lead to lower partition coefficients. Thermodynamic data are well suited for model calculations, and both the models of DeLisi et al. ° ° and Hetu et al. fit the data well. Although in reasonable internal agreement, the partition coefficients calculated from partial molar volumes differ from those calculated from enthalpies the first is 927 or 944, the latter... 

The vapor and liquid enthalpies were calculated by use of the following values of the virtual values of the partial molar enthalpies... 

In addition to calculation of the saturation vapor pressure, a model for calculating the activity coefficient is required. The activity coefficient depends on concentration, and also on pressure and temperature. These dependences can be related to partial molar excess enthalpies and partial molar excess volumes ... 

The vaporization equations permit determination of absolute values of the equilibrium partial pressures of decomposition products, Pgq, which are directly related to the thermodynamic characteristics (enthalpy and entropy) of the reaction, or calculation of absolute values of the decomposition rates through the available thermodynamic characteristics of the reaction. 

The molar enthalpies of decomposition of both molten nitrates (Table 16.39) appear to be 20 kJ moP higher compared to the solid nitrates, which is in full agreement with the CDV mechanism involving partial transfer of the condensation energy to the reactant in the zone of the reaction between the solid reactant and solid product. If there is no such zone (in particular, in the case of reactant melting), the enthalpy of the decomposition (Ari7y/i/) should correspond to the enthalpy of the straight vaporization process calculated from the thermochemical data. The experi-... 

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