Chapter 6. Multiphase System

Normal point: the boiling temperature at 1atmTriple point: Solid, liquid and vapor phase co-existCritical temperature (Tc) and pressure (Pc): the liquid and vapor phase is identical above or on the right of this point.Sublimation point: The temperature T that equilibriums the vapor pressure against solid phase

Estimate vapor pressure

Clapeyron equation

Evaporation is a method that is specially used to separate high and low vapor pressure materials

Example 6.1-1

Antoine Equation

Gibbs Phase Rule

The minimum number of degrees of freedom for any system is zero. When F = 0, the system invariant.

This value of is the maximum number of phases witch can coexist at equilibrium for a system containing C chemical species.

ExampleHow many degrees of freedom have each of the following systems?(a) Liquid water in equilibrium with its vapor.(b) Liquid water in equilibrium with a mixture of water vapor and nitrogen.(c) A liquid solution of alcohol in water in equilibrium with its vapor.

Solution (a) The system contains a single chemical species existing as two phases (oneliquid and one vapor). Thus,

(b) In this case two chemical species are present. Again there are two phases.Thus,

(c) Here C = 2, and = 2, and

For gas-liquid system (Note: it is a phase equilibrium system)

pi is the partial pressure of chemical i in the vapor phase, and pi*

is the vapor pressure of pure chemical i at the same temperature.

If a vapor is less than its saturation amount (Note: it is not a phase equilibrium), it is referred to as a superheated vapor.

If a gas containing a single superheated vapor is cooled at constant pressure, the temperature at which the vapor becomes saturated is referred to as dew point. The difference between the temperature and the dew point is called the degrees of superheated of the gas.

Example 6.3-1

Problem 6.29

Example 6.3-2

Example 6.3-3

Multicomponent gas-liquid system

Example 6.4-1

Raoult’s Law

pA: the partial pressure of A in the gas phase; yA: the mole fraction of A in the gas phase; xA: the mole fraction of A in the liquid phase; pA*: the vapor pressure of pure liquid A at temperature T.

Roault’s law is an approximation that is generally valid when xA is close to 1.Henry’s law

Where HA(T) is the Henry’s law constant for A in a specific solvent. Henry’s law is generally valid for solutions in which xA is close to 0 (dilute solutions)

Example 6.4-2

Vapor-Liquid Equilibrium Calculations for Ideal Solutions

If the liquid is a mixture of more than one components, evaporation of one liquid will change the ratio of chemicals in liquid, so both T and P will change during the evaporation.

Bubble-point temperature: the temperature at which the first vapor bubble forms

Dew-point temperature: the temperature that the first liquid drop forms

Calculating bubble-point temperature or Dew-point temperature is complex for an mixture, but it can be done for ideal solution (following either Roault’s or Henry’s law) and ideal vapor (following ideal gas law).

Problem 6.52

Problem 6.56

Graphs of Vapor-liquid equilibrium

The diagraphs show the different contents of A and B in vapor and liquid phases.

If one component is evaporated, the fraction of liquid phase changed, so the boiling temperature also moved along the curves.

The boiling point of mixture solution can be determined approximately from

Solutions of solid in liquids

Solubility: the maximum amount of a solid can be dissolved in a special amount of liquid at equilibrium.

Supersaturated: the concentration of solute is higher than its solubility in that condition, but no solid (crystallization) happens.

Example 6.5.1

Solid Solubilities and hydrate salts

Solubility of solids is not sensitive to the pressure

Problem 6.78

Colligative property: lowering vapor pressure, depressing freezing point, increasing boiling point, and increasing osmotic pressure by dissolving (or dispersing) substance in solvent

Adsorption Isotherms: Adsorption equilibrium data at specific temperature

Adsorption on solid surface

Example 6.7-1