Phase Equilibria and Gibb's Phase Rule

Phase Equilibria

• Phase is a portion of a system where intensive properties do not change abruptly as a function of position.
• A Homogeneous system is a single-phase system.
• A Heterogeneous system contains two or more phases, also known as a mixture.
• Solvent refers to the host or major component of a solution.
• Solute refers to the minor component of the solution.
• Solubility limit is the maximum amount of a component that can be dissolved in a solution.

State of Equilibrium

• Equilibrium is the stable state achieved when given sufficient time
• Metastable refers to the point where the system appears stable but is on a path toward equilibrium.

Gibb's Phase Rule

• The phase rule relates the degrees of freedom (F) to the number of components (C) and phases (P) in a system and temperature, pressure and concentration by the equation: F + P = C + 2
• Phase diagram is a graphical representation of equilibrium phases of a system as a function of temperature, pressure, and composition.
• Phase is any homogeneous and physically distinct part of a system with uniform physical and chemical properties.
• Component is the least number of independent chemical constituents needed to express the composition of every phase.
• Degrees of freedom refers to the number of variable factors of a system that must be specified to completely define the system.
• A monovariant or unvariant system, will have F=1
• A bivariant system, will have F=2
• A nonvariant system, will have F=0

Water System Phase Diagram

• The triple point of water is at 0.01 °C and 0.6 kPa, where solid, liquid, and gas coexist.
• AB on the phase diagram shows the solid-vapor equilibrium, also known as the sublimation curve of ice.
• BC shows the liquid-vapor equilibrium, or the vapor pressure curve of liquid water.
• BD represents the equilibrium curve between ice and liquid water.
• The slope of BD is negative, indicating the melting point of ice decreases with increasing pressure.
• The slopes of AB, BC, and BD are determined by the Clapeyron equation.

CO2 System Phase Diagram

• Triple point occurs at -56.7 °C and 5.1 atm.
• The solid-liquid equilibrium curve slopes to the right.
• Liquefaction of solid CO2 happens at pressures of 5 atm or higher.
• The 1 atm line passes only through the sublimation curve, where Solid CO2 changes directly to vapor.

Sulfur System Phase Diagram

• Lines AB and BC represent the sublimation curves of rhombic and monoclinic sulfur, respectively.
• CD illustrates the vapor pressure curve of liquid sulfur.
• At point B, rhombic sulfur transitions to monoclinic sulfur.
• Point C indicates where monoclinic sulfur melts, corresponding to a three-phase equilibrium.
• Point E represents the three-phase equilibrium.
• EF represents the melting point of rhombic sulfur.
• Monoclinic sulfur only exists in stable conditions within the area BEC.
• At point G, the metastable S(r)-S(vapor) line intersects the metastable S(liquid)-S(vapor) line, yielding the metastable invariant point S(r)-S(liquid)-S(vapor).
• When metastable equilibria appear, rhombic sulfur transforms directly to liquid along GE or to vapor along BG, without monoclinic sulfur.

Clausius-Clapeyron Equation

• Relates the change in temperature to the change in pressure in a system of a pure substance in equilibrium: ln(P2/P1) = - (ΔHvap/R) * (1/T2 - 1/T1)

Binary Isomorphous Systems

• Liquidus line separates the liquid phase from the liquid + solid phase
• Solidus line separates the solid phase from the liquid + solid phase
• Atomic size difference between the components should be less than 15%.
• Components should have similar crystal structures.
• Electronegativity difference should be small.
• Components should have almost similar valency.
• The complete solubility in the Copper-Nickel System occurs because both Cu and Ni have the same crystal structure FCC, similar radii and electronegativity.

Binary Phase Diagrams

• For a given Temp and Composition the phases are
• What is the phase
• What is their composition
• What are the relative fractions of the phases

Lever Rule

• Locate composition and temperature on diagram
• In the two phase reason, draw the tie line, and isotherm
• Determine a phases fraction by taking the length of the tie line to the phase boundary for the other phase, and dividing by the total length of the tie line.
• All material must be in one phase or the other: Wa + Wb= 1
• Mass of a component that is present in both phases equal to the mass of a component in phase one, plus a second phase where: WaCa + WbCb= C。
• The lever rule: WB = (Co – Ca)/(CB – Ca) and Wa = (CB – C)/(CB – Ca)

Binary Eutectic Systems

• The Solvus line separates a solid solution from a mixture of solid solutions, showing the solubility limit
• Occurs at the Eutectic Point where three phases exist simultaneously.

Gibb's Triangular Phase Diagrams

• Shows the phases and components of a system
• Apices of the triangle represent the three pure components (L: lightest component, H: heavy component, medium component)
• The distance from an apex measures concentration.
• The top apex represents 100%L
• Each side represents a composition while each side constitutes and is measured as H = 100% M.
• As you move from one side (0%), the composition of a component increases to 100% and at which point it is considered in pure condition gradually.
• Any point within this triangle represents the overall composition of this system at a fixed temperature and pressure
• Each point represents the binary combinations of all three components
• On those components, a fraction of the third component is zero meaning nothing is present in the system.

Miscible Liquids

• Any prepared system along the tie line will have to phases with constant composition.
• Tie Line: is a line in the connectivity between equilibrium points
• The AC depicts the binary mixtures of A and C and represent the solubility levels
• The Plait point = a converging tie line where both liquid phases have the same composition

Lever Rule for Ternary Diagram

• F/S = SM / MF
• mass balance: S + F = M and Geometry: MF + SM = SF
• F/M = SM/SF where S the solve and F is the solution.
• R /E= EM/MR
• mass balance: E + R = M and Geometry: MR + EM = RE
• R/M = EM/ER Where E is referred to Extract, R is referred to Raffinate

Distribution Law

• Concentration of A over B is equal to Const
• Also, the number of passing molecules solvent into/out is proportional to its concentration in and. The rate of migration is equal
• Constant temp
• Equilibrium condition is already established
• Dilute Solutions: concentration must be low/ no high concentrations allowed
• 2 solvents should avoid being miscible must but have slight solubility in each other
• All solvents should remain unaltered during the addition.
• Solubility law = C1( concentration) / C2 = [S1 solubility] / S2 = KD ( constant)
• S1 Solubility and S2
• Henery's Law constant Temp- solubility gas in liquid is proportional above. C=kp where C is the concen, P is gas pressure , k is henrys consant

Application of Distribution Law

• Desilverization of Lead (Parke’s Process), solvent extraction, determination of association and solubililty and confirmatory test