Multiphase, Multi Component System



Multiphase, Multi Component System

A plot that shows conditions under which a pure substance exists in a particular phase - e.g. a liquid, a solid, or a gas. Often, the y-axis indicates pressure and the x-axis the temperature

Vapor-liquid equilibrium (VLE) curve: the locus of points for which liquid and vapor can coexist. In the above figure, where is the solid-vapor equilibrium curve? And where is the solid-liquid equilibrium curve? Vapor pressure: the pressure of vapor when it is in equilibrium with the liquid or solid phase. For a point (T,P) on the vapor-liquid equilibrium curve, P is the vapor pressure of the liquid. For a point (T,P) on the solid-vapor equilibrium curve, P is the vapor pressure of the solid (Lapiga 2007).

Boiling point temperature: for a point (T,P) on the VLE curve, T is the boiling point of the substance at the pressure P. The normal boiling point is the boiling point temperature for P = 1 atm. Freezing/melting point temperature: for a point (T,P) on the solid-liquid equilibrium curve, T is the freezing (equivalently, melting) temperature of the substance at the pressure P. Sublimation point temperature: for a point (T,P) on the solid-vapor equilibrium curve, T is the sublimation point temperature of the substance at the pressure P.

Where p* is the vapor pressure of the pure substance, T is the absolute temperature, Hv ? ˆ is the latent heat of vaporization (i.e. energy required to vaporize one mole of the liquid at a point (T,P) on the VLE curve), and Vg ˆ and Vl ˆ are the specific molar volumes of the gas and liquid phases (Kolev 2007). For ideal gases, equation can be simplified using Vg ˆ = RT/p* using the ideal gas EOS. Note that we are assuming to have a pure vapor in equilibrium with a pure liquid. This substitution yields

Moreover, if one mole of the liquid occupies a much smaller volume that one mole of the gas, the Vl ˆ term in the denominator can be neglected compared to RT/p*,

If Hv ? ˆ does not strongly depend on T, equation can be integrated to give the Clausius-Clapeyron equation

Where B is the constant of integration. B depends on the pure substance considered. Cox charts: these charts plot log p* vs T. The axes are scaled so as to make the plots come out linear. Antoine equation: An empirical but accurate equation for correlating p*(T) ...