Introduction to Phase Equilibrium

• Phase equilibria involves applying thermodynamics to study equilibrium relationships within or between phases, dealing with homogeneous and heterogeneous systems.

Introduction to Phase Equilibrium

• Stable phase structures have the lowest free energy (internal energy) in a system.

• Changes in temperature, composition, and pressure increase free energy, shifting the system away from equilibrium, leading to another state.

• Key phases are defined individually but usually coexist.

• A glass of iced water exemplifies three coexisting phases: solid ice, liquid water, and vapor.

• The amount of ice is affected by the amount of ice, the temperature of the water, and the surrounding temperature.

• Equilibrium cannot be reached because the temperature increase converts ice to water which subsequently converts to vapor, releasing it into the large volume of air.

• Calcium carbonate undergoes thermal decomposition into CaO(s) + CO2 (g), resulting in 3 phases.

• This system consists of 2 solid phases (CaCO3 and CaO) and one gaseous phase (CO2).

• Ammonium chloride undergoes thermal decomposition into NH3 (g) + HCl (g), resulting in 2 phases.

• There are two phases present: one solid (NH4Cl) and one gaseous (a mixture of NH3 and HCl).

• A solution of NaCl in water has 1 phase.

Phase Definition

• A phase is a "physically distinct, homogeneous, and mechanically separable part of a system."
• Pure and miscible liquids constitute one phase.
• Immiscible liquids form two phases.
• A mixture of gases is considered one phase.
• A system of water and vapor is a 2-phase system.
• Water, vapor, and ice at equilibrium form a 3-phase system.
• Solids usually constitute a single phase unless they form a solid solution.
• Solid solutions are considered single phases.
• Each polymorphic form is a separate phase.

Components of a System

• The number of components is the smallest number of independently varying chemical constituents by which the composition of each phase can be expressed.
• For chemically reactive systems, C = N - E, where C is the number of components, N is the number of chemical species, and E is the number of independent equations relating concentrations.
• Each independent chemical equilibrium counts as one equation.
• In the ice, water, and vapor system, there is one component (H2O).
• A mixture of salt and water has 2 components.
• The sulphur system has one component because all phases can be expressed in terms of sulphur.
• A mixture of ethanol and water is a two-component system requiring both ethanol and water to express its composition.
• In the thermal decomposition of solid CaCO3 to CaO(s) + CO2(g), there are three distinct phases.
• There are two components: CaCO3, CaO, and CO2.
• Due to the equilibrium, only two constituents may be chosen as components.
• If CaO and CO2 are selected, CaCO3 is expressed as one mole of CO2 plus one mole of CaO.
• If CaCO3 and CO2 are chosen, CaO is expressed as one mole of CaCO3 minus one mole of CO2.

Degree of Freedom (Variance)

• The degrees of freedom are the minimum number of variables like temperature, pressure, or concentration that must be fixed to define the system completely.
• It is necessary to know the number of variable conditions to state the condition of the system at equilibrium.
• Variables must be defined to specify the state of each phase.
• Each phase is defined by independent variables like temperature or pressure.
• Coexistence of phases occurs over a range of variables.
• A gaseous mixture of CO2 and N2, characterized by three variables (pressure, temperature, composition), is a trivariant system.
• A system having only liquid water has two degrees of freedom and is bivariant, requiring both temperature and pressure.
• Adding ice to liquid water and allowing equilibrium creates a univariant system with one variable, temperature or pressure.
• Maintaining system pressure at 1 atm fixes the temperature at 0°C (normal ice melting point).

Phase Rule

• The phase rule is an important tool for quantitatively treating equilibrium systems and predicting conditions for equilibrium.

• Gibbs phase rule states that in a heterogeneous system at equilibrium, unaffected by gravity or electrical/magnetic forces, the degrees of freedom (F) relate to the number of components (C) and phases (P).

• F represents the degree of freedom

• C represents the number of components

• P is the number of phases

• Intensive variables must be fixed in equilibrium to describe or define the system.

• Phase is denoted by P.

• A gas or gaseous mixture in indicated as Phase = 1

• A solid alloy with two immiscible metals is P = 2, but miscible metals is P = 1.

• A liquid system's phases depend on solubility; sodium chloride in water is a single phase; partially miscible liquids have two phases (e.g., oil in water).

• Salt plus water systems: Various hydrates exist with different crystallization numbers; the system is two-component (C=2), one-phase (P=1).

• For water vapour confined under phase rule requires 2 independent variables; F = 1-1+2 = 2

• Liquid water has two degrees of freedom and is bivariant.

• Ice added to liquid water in equilibrium creates a univariant system, defined by one variable.

• For a CO2 and N2 gas mix, the number of components is 2 and the number of phases is 1.

• Three variables (pressure, temperature, composition) are required, making it a trivariant system.

Application of Phase Rule to Single Component Systems

• A system of gas, liquid, or solid has a number of phases of 1 and degrees of freedom of 2 and is bivariant.
• For gas-liquid, liquid-solid, or gas-solid, number of phases equals 2, is univariant, and can like anywhere on the line between the two phases
• Gas-liquid-solid, phases equals 3, degrees of freedom equals 0, it is an invariant system.

Phase Diagrams

• Phase diagrams (Equilibrium Phase Diagrams) outline solids, liquids, or gases substance conditions.
• They act as 'maps' showing information for the control of phase structures in material systems.
• Phase Diagrams represent the relationships among temperature, compositions, and quantities of phases at equilibrium.

Phase Diagram of Water

• The vapor pressure curve, also known as the boiling point curve shows that water coexists as liquid and water vapour under various conditions

• The upper limit for liquid is the critical temperature, 374°C, above that the water can not be liquified. The lower end terminates at 0.0098°C, which is called the triple point

• Along the vapour pressure curve, temperature and pressure cannot be varied independently.

• Pressure and temperature cannot be varied independently.

• Keeping pressure constant, increasing temperature converts all water to vapour.

• Sublimation curve OC is where vapor and solid exist together in equilibrium, and also known as sublimation curve for ice.

• Mass of ice converts to gas when heated below the pressures triple point

• It is valuable when drying substances sensitive to higher temperatures.

• Removal of water by sublimation means is freeze drying.

• Melting Point Curve (OB) shows liquid and solid equilibrium at various temperatures and pressures.

• The melting point of ice drops as pressure rises.

• Adding pressure while holding temperature causes solids to liquified, maintaining equilibrium

• The result of pressure changes or temperature changes can be found on the phase diagram

• Temperature and Pressure must remain constant to maintain equilibrium

• The only point that all phases exist is at where the boundary lines meet (point o).

• Due to the phase rule it shows all phases in equilibrium at 0.0098°C, F = 0 (F= 1-3+2 = 0)

• The system is invariant, any change would alter the phases.

• Gaseous state temperature held constant above the critical temperature the system remains a gas.

• Water vapour is converted to liquid water by increasing pressure due to compression at a temperature below the critical temperature.

• An increase of pressure on water in the vapor state converts the vapor first to ice and then at higher pressure converts into liquid water below the triple point on water.

• This is due to the fact that ice occupies a larger volume than liquid water below the triple point.

• Phase rule gives F = 1 – 1 + 2 = 2 where a substance is a solid, liquid or as vapour where Phase = 1

• Therefore, temp and pressure should be mentioned in equilibrium to describe/define the system, and it would not be sufficient to mention only one

• Along any three of the curves where two phases exist in equilibrium, it is F = 1.

• Therefore, we only need to define one condition: liquid water and water vapour equilibrium at 100°C, water pressure is 760 mm Hg water is sufficient and the line OB or OC

• Finally, and the triple point, ice- liquid water and water vapour- all phases we saw equilibrium is F = 0

• The triple point of air water is 0.0098°C, were as the freezing point the liquid is equilibrium to ice 1 atm is 0°C

Condensed Systems

• Condensed systems ignore the vapor phase and focus on solid and/or liquid phases.
• For two-component systems F can be 3 (T, p, concentration), but fixing p = 1 atm reduces it to 2.
• For three-component systems, the pressure and temperature are fixed.

Polymorphs

• Certain substances have more than one crystal structure.
• A reversible change from one crystal structure to another occurs at a definite temperature.
• Both structures co-exist in equilibrium at this temperature.
• A crystalline rhombic structure of sulphur is converted to the monoclinic structure at 368.5K.
• The transition reverses on cooling from a higher temperature.
• Since each version is a separate phase, the F value is limited to one.
• Systems with solids able to has 2 Polymorphs: is required to draw the boundary between the solid
• Including the boundary increases the number of triple points.

Sulfur Phase Diagram

• Pink is only rhombic structures.
• Brown is only monoclinic structures.
• Green is only liquid structures.
• Blue indicates where it is a gaseous form.
• Lower left to 1 is the sublimation of rhombic
• 1 to 2 represents the Sublimation curve of monoclinic
• 2 to upper right is the vapour pressure with solid liquid
• 1 to 3 : transition of
• 2 to 3 = The melting point
• 3 to top: the melting point curves
• Triple point1 at 95.4 C & 1x10-4 latm rhombic state and have vapour in common
• 2 at 119 C & 5 x10 -4 latm Sl +Sm in equal form
• 3 to top @ 151: all are equal

System Two Components

• System components, the degree is F 3-0 (1, P 3) (2, P 2) (3, P 1) (4, P 0)

Solid-Vapour Systems of Two Components

Conversion of anhydrous to a hydrated structure where water exerts equal vapor pressure at a constant temperature

• Transition- A form will transition to a more hydrated form in a system
• Deliquescence/Hygroscopy- Is were moisture builds up, the final product most maintain lower vapor - Sodium hydroxide
• Hygroscopic Material- Exsiccated sodium sulphate Efflorescence- An equillibria system containing vapour, higher vapor will lose vapour to maintain the proper equillibrium, hydrate/anhydrates The higher rate of vapor causes the salt vapours to rate of Efflorescense increased Temp also does this.
• 1 is sulphate Peta hydrates
• 2 Is tri hydrates
• 3 sulphate mano hydrates

Liquid-Liquid Systems

• Solutions of two components aid in classifications
• Complete Miscible, F + 2 = 2 The system may need additional defining from vapor or temp. Otherwise, it should be able to follow a constant. Partially Miscible Immiscible

Miscible Liquids

• Ideal solutions follow the Raoult law, the pressure of a solution is proportional to the component ratio.
• Vapor pressures tend for similar intermolecular to create a similar stucture.
• Ex: Hexane and Pentane are like that- it follows similar boiling points along composition but slopes the line of opposing directions

Deviations from Raoult's Law

Positive Deviation

• Vapor preasures are greater resulting to Lower Boiling points
• Liquid is evaporating faster than desired
• Intermolecular Bond: Some intermolecular needs to be broken to mix
• Ex Ethanol and Water, Water=2 h Bond ethanol is less, when Bonds inferer that reduces volatility, as such Benze does to H

Negative Deviations

• The Vapor pressure is lower than in what we expect, and intermolecular force is increased with that of the boiling point
• Molecules are mixing with no hydrogen, to present one creating a Liquid
• Ex Trichloromethane (Cloriform) Ether ,Polar does not have lone pairs therefore does not create hydrogrens

Phase Separation

-Components differ in Polarity to each other -It's not a Raoults law

• A decrease in temp in misblicity is likely in a phase to phase change

Partically Mix Systems

3 Groups

• rise with temps

• Decrease with temps

• critical soluation temps

• The more water will sobluize with a soluvation More Phenols mean definite solubility with others

• With mixing layers can created

• More water will make more of a composition soluizity with solutions for equilbillty

There are 2 extremes 1 with OH Hg

Phase diagrams

Shows limitations and such

• Phenols water which is more equal

• the more the liquids are at a single equalibity

As a review a tier line is not all well

Calculation

• Example we added 28/6 to Water more will come with eauilibrium temp There'd be 24 perciant We had all phases and equal the total amount

Equations

• In a condensed we have several liquids
• Where 1 has F three Two is three with liquid 2, p with fixed equalibrty

Practice

Tie and Phase

• Phenols diagrams as the other diagram is with liquid

Phase Eutectic

Two with solid states miscible with liquids

• 2 Crystal
• Salt and tymol The two are crystals and miscible however
• An example and with solid which is good diagram

Phases in Diagrams

• eutectic*: relating to or denoting a mixture of substances that melts and freezes at a single temperature that is lower than the melting points of the separate constituents or of any other mixture of them. "a eutectic mixture is used as solder" Temperature =40
• Liquid Phase 2- Salol 3 Temps should rise for a bit because of the thymol

4- Thymol And Solual

Eutechtoid

• "Easily melted" system more equal
• Temps drop to liquid It the endo or points is a a invariet 2-3 h points

Eulectic example

• Proclomime (8C) More equal and point that's created with oil.