Phase Diagrams and Phase Rule

Phase Transitions and Phase Rule Dr. Ruchi S. Pandey

Thermodynamics and Phase transitions A Phase is a region of space (a thermodynamic system), throughout which all physical and chemical properties of a material are essentially uniform Phase changes are governed by laws of thermodynamics First Law of Thermodynamics Enthalpy – “ Heat transferred between the system and surroundings carried out under constant pressure.” H cannot be measured directly, only change in enthalpy  H can be measured (at constant pressure P); Second Law of Thermodynamics “ In a system, a process that occurs will tend to increase the total Entropy of the universe.” q rev is the heat that is transferred when the process is carried out reversibly at a constant temperature . Dr. Ruchi S. Pandey

Thermodynamics and Phase transitions (2) Spontaneous Process:  S > 0 Total entropy change of the universe is given by For natural isobaric processes, q rev =  H   S =  H / T Also, for energy conservation,  H sys = -  H surr Hence , we can write The quantity -T  S univ is also called the Gibbs Free Energy of the system Dr. Ruchi S. Pandey  G = 0  G > 0  G < 0 exergonic equilibrium endergonic

Phase Diagrams Phase a form of matter that is uniform throughout in chemical composition and physical state Boundaries Solid-Liquid ( Fusion ), Liquid-Gas ( Vaporization ), Solid-Gas ( Sublimation ) Also Solid-Solid and Liquid-Liquid Points Critical Point – beyond this a gas cannot be liquefied Boiling Point – vapor pressure of the gas = atmospheric pressure Melting Point – solid and liquid phase coexist (equilibrium) Triple Point - solid, liquid and gas phase coexist Dr. Ruchi S. Pandey

Phase Boundaries Chemical Potential ( µ ): For a 1-component system it is the molar Gibbs energy ( G m ) and defines the potential of a system to undergo a physical or a chemical change At the phase boundary where phases α and β coexist, µ α = µ β (at equilibrium) This gives us the Clapeyron Equation: Clapeyron Eqn. takes different forms for different phase boundaries Dr. Ruchi S. Pandey Slopes of the boundaries Solid-Liquid Boundary Liquid-Vapor Boundary Solid-Vapor Boundary Clausius-Clapeyron Equation  V = V g -V l/s ~ V g V g = RT/P (ideal gas)

Gibbs’ Phase Rule P is the number of phases C is number of components , i.e. the chemically “independent” constituents, of the system, which can describe the composition of each phase present in the system “ independent” means- If you have equilibrium balance between reactants and products, the number of components will be reduced by one If you have equal amounts (concentrations) of products formed, the number of components will also be reduced by one F is the degrees of freedom of the system Dr. Ruchi S. Pandey

Phase a form of matter that is uniform throughout in chemical composition and physical state Homogeneous phase is uniform throughout in its chemical composition and physical state. (no distinction or boundaries) Water, ice, water vapor, sugar dissolved in water, gases in general, etc. Heterogeneous phase is composed of more than one phase These phases are distinguished from each other by boundaries. A cube of ice in water. (same chemical compositions but different physical states) Oil-water mixture. The two phases are said to be coexistent . Dr. Ruchi S. Pandey

Number of Components NaCl(s) dissolved in water Available chemical constituents are four. Na + , Cl - , NaCl and H 2 O Because Na + and Cl – have the same amount “equal neutrality” as NaCl, then c = 2 and not 4 Decomposition of calcium carbonate Available chemical constituents are three. Is it correct to say c = 3 ? Because of the equilibrium condition the number of independent components is reduced by one. Thus, c = 2 instead of 3; C = 2, P = 3  F = 2 – 3 + 2 = 1 Decomposition of ammonium chloride Available chemical constituents are three. Is it correct to say c = 3 ? Because of the equilibrium condition the number of independent components is reduced by one. And also because the products formed form a single phase and are formed in equal amounts, the no. of independent components are further reduced by one. C = 1, P = 2  F = 1 – 2 + 2 = 1 Decomposition of PCl 5 Available chemical constituents are three. Is it correct to say c = 3 ? Because of the equilibrium condition the number of independent components is reduced by one. C = 2, P = 3  F = 2 – 3 + 2 = 1 Dr. Ruchi S. Pandey

Degrees of Freedom Number of intensive variables that can be changed independently without disturbing the number of phases in equilibrium Simplistically speaking, there are only three intensive variables which can describe any phase of a chemical system Temperature (T), Pressure (P) and Composition/Concentration (  ) But what happens to the no. of degrees of freedom or the variance of a system when there are more than one phases? To count these, lets assume that we have a heterogeneous system “in equilibrium” consisting of ‘C’ components distributed in ‘P’ phases. Lets now derive our phase rule to know the degrees of freedom of such a system. Dr. Ruchi S. Pandey

Derivation of the phase rule • In any system the number of intensive variables are: pressure, temperature plus the mole fractions of each component of each phase. • Only C-1 mole fractions are needed since » Thus for P phase, the number of intensive variables = P(C-1) + 2 • At equilibrium the chemical potential of each phase must be equal, i.e. μ P1 = μ P2 = μ P3 = μ P4 = μ P5 ….{there are P-1 such equations} Since there are C components, equilibrium requires that there are C(P-1) equations linking the chemical potentials in all the phases of all the components Now, F = total required variables - total restraining conditions F = P(C-1) + 2 - C(P-1) = PC - P + 2 -CP + C = C- P + 2 Dr. Ruchi S. Pandey

Phase Diagram of Water Dr. Ruchi S. Pandey A single phase is defined by an area on the phase diagram for these regions C=1, P=1  F = 2 one can vary either the temperature, or the pressure, or both (within limits) without crossing a phase line. Equilibrium of two phases is defined by the black lines in the diagram, also called the phase boundaries for these lines C=1, P=2  F = 1 If we want to stay on a phase line, we can't change the temperature and pressure independently Equilibrium of three phases is the single point O in the diagram at this point C=1, P=3  F = 0 Metastable state: supercooled water, curve OT If the vessel is clean and there is no scope of nucleation, water can be cooled several degrees below its freezing point.

Phase Diagram of Water (Experimental) Multiple known structures for solid phase. Five more known triple-points, other than the S-L-V point. An anomalous liquid! Robust Hydrogen bonding Negative slope of melting line Dr. Ruchi S. Pandey The Advance of Glaciers a natural consequence of negatively sloping melting line High pressure causes ice to melt and re-freeze on either side of a bump

Phase Diagram of Sulphur Dr. Ruchi S. Pandey Sulfur solid exists in two crystalline forms Orthorhombic, S 8 or S(rh) Monoclinic, S 4 or S(mo) Total no. of phases 4, C=1, F= C-P+2=-1 Negative variance is not possible so all 4 phases can never coexist Three triple points Boiling point at 444.6 o C S(rh) changes into S(mo) at 95.6C, only when heated slowly. If heated rapidly, rhombic sulphur passes directly in to the liquid phase The metastable triple point occurs at 114C

Two components systems Dr. Ruchi S. Pandey Need to know T, P and concentration to describe such systems – the 3D plot looks very complex, so one of the variables is fixed P-T graphs (isoplethal), P-C graphs (isothermal), T-C graphs (isobaric) Since we are fixing one of the variables the phase rule changes Reduced Phase Rule: F = C – P +1 Solid-Liquid Phase equilibria: condensed systems at constant pressure (atm. press.) Phase diagrams constructed using thermal analysis Mixtures of different compositions are first melted much above their melting points and then gradually cooled Thermal Analysis

Two component solid-liquid equilibria Depending upon the miscibility of the 2 components in the liquid state and nature of the solid that separates on cooling, 2 classes exist; I: when the two components are completely miscible in liquid state II: when the two components are partially miscible in liquid state Components that are miscible in liquid state (i) but not miscible in the solid state (Pb-Ag, Bi-Cd syatem) (ii) and form a stable compound which melts at a constant temp. to give a liquid with the same composition as that of the solid (FeCl 3 -H2O) (iii) and form an unstable compound which melts at a temperature lower than its melting point to give a new solid and a melt which is different from the compound (Na 2 SO 4 -H 2 O) Dr. Ruchi S. Pandey

Simple Eutectic System Some important elements of this phase diagram include Solidus : boundary below which no liquid phase exists. Liquidus : boundary above which there are no solid phases. Two solid+liquid fields between the solidus and the liquidus in which one of the two solids plus a liquid is present. Eutectic point : a point at which both of the solids and a liquid (three phases) coexist general shape: The freezing point of each end-member is depressed by a foreign substance Dr. Ruchi S. Pandey For Ag-Pb system Tm(Ag)=961, Tm(Pb)=327 Te(Pb(s)-Ag(s)-melt)=303 Eutectic composition:2.6% Ag, 97.4% Pb Pattison’s process Process of raising the proportion of silver in the alloy for its profitable recovery

2 component system where a stable compound with congruent melting point is formed In such a system, compounds are composed of various ratios of the two end members (A & B), or the basic components of the system. These end members are assumed to melt congruently. The intermediate compound AB2 melts congruently, because at some temperature (the top of the AB2 phase boundary line) it coexists with a liquid of the same composition. Dr. Ruchi S. Pandey

Peritectic point - The point on a phase diagram where a reaction takes place between a previously precipitated phase and the liquid to produce a new solid phase. The intermediate compound in this diagram (XY2) however is incongruently melting. Incongruent melting is the temperature at which one solid phase transforms to another solid phase and a liquid phase both of different chemical compositions than the original composition. This can be seen in this diagram as XY2 melts to Y and liquid. Dr. Ruchi S. Pandey 2 component system where a stable compound with incongruent melting point is formed

Multi-Component Systems 2-component systems Liquid-Liquid, e.g. nitrobenzene, hexane etc. Liquid-Solid, e.g. water + common-salt Solid-Solid, e.g. Tin-Lead solder 3-component systems L-L-L, e.g. water + acetic acid + butanol S-S-S, e.g. Steel (see figure) Dr. Ruchi S. Pandey

Phase Diagrams and Phase Rule

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Phase Diagrams and Phase Rule