Liquid-vapor transitions

This method is invalid because the temperature in the denominator of the equation must be the temperature at which the liquid-vapor transition is at equilibrium. Liquid water and water vapor at 1 atm pressure (standard state, indicated by ) are in equilibrium only at 100° C = 373 K. 

The liquid-vapor transition for H2O involves quite high evaporation enthalpy, which controls the thermal state of the system. 

A. Liquid-Vapor Transitions in One-Component Ionic Fluids... 

Apart from liquid-liquid transitions, liquid-vapor transitions in aqueous electrolyte solutions have played a crucial role in debates on ionic criticality [142-144], The liquid-vapor transition is usually associated with a mechanical instability with diverging density fluctuations, while liquid-liquid transitions are associated with a material instability with diverging concentration fluctuations. This requires, however, that both regimes are well-separated. Their interference can lead to complex phase behavior with continuous transitions from liquid-liquid demixing to liquid-gas condensation [9, 145, 146]. It is then not trivial to define the order parameter [147-149]. 

The continuous critical line for systems such as NaCl + H20 offers a temperature window for studying the behavior of electrolyte solutions near their liquid-vapor transition. Pitzer [4,13,142,144] compiled much evidence that the nonclassical fluctuations in pure water are apparently suppressed when adding electrolytes. Thus, from the application s point of view, a classical EOS may be quite useful. The pressing question is to what degree these observations withstand more quantitative analysis. 

While the early work on molten NH4CI gave only some qualitative hints that the effective critical behavior of ionic fluids may be different from that of nonionic fluids, the possibility of apparent mean-field behavior has been substantiated in precise studies of two- and multicomponent ionic fluids. Crossover to mean-field criticality far away from Tc seems now well-established for several systems. Examples are liquid-liquid demixings in binary systems such as Bu4NPic + alcohols and Na + NH3, liquid-liquid demixings in ternary systems of the type salt + water + organic solvent, and liquid-vapor transitions in aqueous solutions of NaCl. On the other hand, Pitzer s conjecture that the asymptotic behavior itself might be mean-field-like has not been confirmed. 

The transition to the continuum fluid may be mimicked by a discretization of the model choosing > 1. To this end, Panagiotopoulos and Kumar [292] performed simulations for several integer ratios 1 < < 5. For — 2 the tricritical point is shifted to very high density and was not exactly located. The absence of a liquid-vapor transition for = 1 and 2 appears to follow from solidification, before a liquid is formed. For > 3, ordinary liquid-vapor critical points were observed which were consistent with Ising-like behavior. Obviously, for finely discretisized lattice models the behavior approaches that of the continuum RPM. Already at = 4 the critical parameters of the lattice and continuum RPM agree closely. From the computational point of view, the exploitation of these discretization effects may open many possibilities for methodological improvements of simulations [292], From the fundamental point of view these discretization effects need to be explored in detail. 

Considering a liquid-vapor transition and I v ip Fliq. we get the approximate Clapeyron equation... 

Simulations of the RPM predict a phase transition for the RPM at low reduced temperature and low reduced density. It was difficult to localize because of the low figures of the critical data. By corresponding states arguments this critical point corresponds to the liquid/vapor transition of molten salts and to some liquid/liquid transitions in electrolyte solutions in solvents of low dielectric constant [23, 24],... 

In the first application will will exemplify the accurate localization of the condensation transition for a coarse-grained bead-spring polymer model. As discussed above, the order parameter of the liquid-vapor transition is the monomer number density, p. The equation of state of the polymer solution is... 

A lattice gas model for liquid-vapor transition has also been proposed, the interacting liquid-gas model (ILG)of Appert and Zaleski (1990. 199 l). The authors... 

The molar heats of fusion and vaporization of benzene are 10.9 kJ/mol and 31.0 kJ/mol, respectively. Calculate the entropy changes for the solid —> liquid and liquid —> vapor transitions for benzene. At 1 atm pressure, benzene melts at 5.5°C and boils at 80.1°C. 

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