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Phase Rule

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Presentation on Phase Rule

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    Phase Ruie 16-01-2018 1
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    SYLLABUS ' Phase rule- Statement ' Explanation of the terms involved ' One Component System (Water, Suphur systems) ' Condensed Phase Rule ' Thermal Analysis ' Two Component Systems: Simple Eutectic, Pb-Ag, Zn-Mg. 16-01-2018
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    Terminology used Phase: It is a form of matter which is uniform throughout in chemical composition and physical state. ' A system containing only liquid water is one-phase system ' A system containing water and water vapour (gas) is a two phase system ' A system containing liquid water, water vapour and solid ice is a three phase system. ' Pure substances (solid, liquid, or gas) made of one chemical species only, is considered as one phase,
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    Component ' It is defined as minimum number of chemically independent species which are required to express the composition of all the phases present in the system. ' Water system has three phases and the composition of all these phases is expressed in one chemical formula. Hence one component only. ' Sulphur system has four phases: rhombic sulphur, monoclinic sulphur, liquid sulphur and sulphur vapour and the composition of all these phases is expressed by one chemical individual. 'Therefore Sulphur system is one component system.
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    Degrees of freedom or Variance ' It is defined as smallest number of intensive variables (such as temperature, pressure and conc.) that can be changed independently without disturbing the number of phases in equilibrium 'State of a pure gas may be described by any two of the three variables P, T and density. If any two known third can be calculated. Hence it has two degrees of freedom called bivariant system. 'Univariant in which water and water vapor are in one system 'If all phases of water exist in equilibrium, no condition needs to be specified as the phases can coexist only at particular temp and pressure. 'This system has no degrees of freedom hence called invariant system.
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    Phase rule , It was first presented by Gibbs in 1875. ' It is very useful to understand the effect of intensive variables, such as temperature, pressure, or concentration, on the equilibrium between phases as well as between chemical constituents. ' It is used to deduce the number of degrees of freedom (F) for a system. Sometimes called: "the variance of the system".
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    Phase rule It states that : For every heterogeneous system in equilibrium, the sum of number of phases and degrees of freedom is greater than the number of components by two i.e.: F+P=C+2 C-P+2
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    1. 2. 3. 4. 5. 6. Advantages of Phase rule Provides convenient method of classification of equilibrium states of system. Predict the behavior of system with changes in the intensive variables. Indicate that different systems having the same number of degrees of freedom behave in the same manner. Applicable to macroscopic system It takes no account of nature of reactant and products in phase Applicable to physical and chemical equilibria.
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    1. 2. 3. 4. 5. Limitation of Phase rule Applicable only for the system in equilibrium Applicable to a single equilibrium state Considers only intensive variables Considers only number of phases not quantity of phases It requires that all the phases to be present under the same conditions of temperature and pressure.
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    1. 2. 3. 4. 5. Phase Diagram It is a convenient graphical representation formed by plotting the values of intensive variables for equilibrium conditions between two phases. It shows the properties such as mp, bp, phase transition point and triple point. The complex city of phase diagram increase with increase in number of component in the system. For a simple substance (one component system) phase diagram is two dimensional plot where P & T are independent variables. The phase diagram of a two component system is a three dimensional plot, where third axis is for composition.
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    Phase Diagram 6. Three dimensional plot can also converted into two dimensional plot by keeping one variable constant. Isobaric Isothermal 7. When one of the variable kept constant then phase rule equation is reduced to : F=C-P+I 8. This is known as reduced phase rule.
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    Phase Diagram Phase boundary (solid -l- liquid coexiso LIQUID SOLID s s Criti cal paint Phase boundary Cvapaur -F liquid coexist) Tri pl e VAPOUR paint Phase boundary (salid + vapaur coexist) TEMPERATURE http://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-the-phase-1
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    218.5 atrnosphere atrnosphere rnrn Phase Diagram for one component system (Water) Curve 2730c Absolute Zero 0.00980c Temperature +3740C Critical Teanp http://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-the-phase-l
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    1. 2. Water System Water exist in three possible phases: ice, water, vapors It is a one component system so maximum degrees of freedom is two, when one phase is stable at equilibrium. C-P+2 = 1-1+2=2 3. Phase diagram of water is two dimensional plot where P & T are taken as axes.
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    Areas of Phase Diagram of Water System Phase diagram is divided into three areas: 1. Area BOC — where ice has stable existence 2. Area COA — where water has stable existence 3. Area BOA — where water vapors has stable existence Phase Rule for this system: F = C-P+2 = 2 Degrees of freedom is two hence bivariant system.
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    1. 2. 3. 4. 5. Various Curves of Phase Diagram of Water S stem Melting point Curve (Curve OC) Vaporization curve or vapor pressure curve (Curve OA) Metastable equilibrium (Curve OA') Sublimation Curve (Curve 0B) Triple point O
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    1. 2. 3. Melting point Curve (Curve OC) Also known as melting point curve or freezing point curve or fusion curve. Represents equilibrium between ice & water It is enough to know either T or P because other variable gets automatically fixed. e.g. At atmospheric pressure, ice & water can be in equilibrium only at one temperature i.e. at freezing point of water. 4. Thus ice- water equilibrium line (Curve OC) has only one degree of freedom (Univariant system). Phase Rule: = 1-2+2 = 1
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    Vaporization Curve or vapor pressure curve (Curve OA) 1. Represents the equilibrium between two phases water & vapor.. 2. It enough to know either T or P because other variable gets automatically fixed. 3. Because at any temperature, Pressure of vapor in equilibrium is fixed in value. 4. Thus water & vapor equilibrium line OA has only one degree of freedom so univariant system. Phase Rule: = 1-2+2 = 1
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    Vaporization Curve or vapor pressure curve (Curve OA) 6. At higher end, curve OA terminates at point A which is critical temperature (374C) and Pressure (218atm.) of water. 7. At this point liquid & vapor phases become indistinguishable & merge into single fluid phase. 8. Under normal conditions terminus point is O where water freezes to form ice.
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    1. 2. 3. 4. 5. Vaporization Curve or vapor pressure curve (Curve OA') Curve OA' represents the meta-stable equilibrium. Under some special conditions pure water may be cooled down much below the freezing point without forming ice. Thus it is possible to extend vapor pressure curve even below freezing point of water. This equilibrium can be approached by cooling liquid water and not by heating ice. Metastable vapor pressure of super cooled liquid is higher than the vapor pressure of ice.
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    1. 2. 3. 4. Sublimation Curve (Curve 0B) Represents the condition for equilibrium between ice and vapors. Shows vapor pressure of ice at different temperature In order to describe the system along line 0B either value of T or P need to be specified. Because at any temperature, value of vapor pressure of ice is fixed.
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    1. 2. 3. IMP terms Critical Point: a point on a phase diagram at which both the liquid and gas phases of a substance have the same density, and are therefore indistinguishable. Triple point: The temperature and pressure at which a substance can exist in equilibrium in the liquid, solid, and gaseous states. The triple point of pure water is at 0.01 oc (273.16K, 32.01 OF) and 4.58 mm (611.2Pa) of mercury
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    Phase Diagram of Sulphur Sulphur Exist in four forms: 1. 2. 3. 4. Rhombic Sulphur (SR) (m.p. 1140 C) Monoclinic Sulphur (SM) (m.p. 1200C) Liquid sulphur (SD Vapour Sulphur (Sv) Monoclinic Sulphur Rhombic Sulphur
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    Phase Diagram of Sulphur 1 atm 1
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    1290 atm 1290 a try-t 3 I atrn Solid Rhornbic 0.04 mm of Hg 0.03m f rpm of Hg 95-6 Phase Diagram of Sulphur Liquid (L) o lid • o clinic Vapour (V) 114 120 165 444 _ 6 Ternoerature o c http ://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-the-phase-1
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    Curves In Phase Diagram , Curve AB: Sublimation Curve of Rhombic Sulphur , Curve BC: Sublimation Curve of Monoclinic Sulphur Vapor Pressure Curve of Liquid Sulphur Curve CD: Curve CE: Fusion Curve of Monoclinic Sulphur , Curve BE: Transition Curve Solid Sulphur Fusion Curve of Rhombic Sulphur Curve EG: At any curve, phase rule becomes: = - 1 (univarient)
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    Triple Point B ' Triple Point C ' Triple Point E At any Triple Point, phase rule becomes: F = 3-P= 3-3 = O (nonvarient) Triple Points 1290 atm Solid Rhombic (SR) 1 atm Solid Monoclinic F SM Vapour (V) G SR/L Liquid (L) D c 95.6 114 Temperature oc 120 165 444.6
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    Area ABEG (Rhombic Sulphur) 1290 atm Area BCEB (Monoclinic Sulphur) Area DCEG (Sulphur Liquid) Area ABCD (Sulphur Vapors) In an area, Phase Rule becomes: F = 3-P= 3-1 = 2 (bivariant) Areas Solid Rhombic (SR) 1 atm G SR/L Liquid (L) D Solid Monoclinic F SM/V Vapour(V) c 95.6 114 Temperature oc 120 165 444.6 http ://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-the-phase-1
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    Dashed curve > curve BF (sublimation curve of metastable SR) >curve CF (vapour press. Curve of supercooled liquid sulphur) > curve FE (fusion curve of metastabl One triple point F 3 areas: Area ABFE (Metastabie SR) Area ABFCD (Sulphur vapours) 1290 atm Solid Rhombic (SR) 1 atm Solid Monoclinic c SMN Vapour (V) SR/L 165 Liquid (L) D 444.6 95.6 114 Temperature oc 120 Area DCFE (supercooled liquid sulphur) http://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-the-phase-1
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    1. 2. 3. 4. Phase Diagram for Two component system In two component system with P=l, the number of degrees of freedom are highest order is three. In two component system phase diagram may be represented by three dimensional diagram of P, composition and T. In this diagram two axes represents two variables while third variable is held constant. Phase Diagram may be constructed as : 1. P-T diagram keeping conc. Constant 2. P- Conc. Diagram T constant 3. T-C diagram keeping P constant.
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    Solid — Liquid Equilibria or condensed phase rule or reduced phase When P is kept constant, vapour phase of system is not considered. In this case system is said to be condensed and phase rule reduced to: F=C-P+I This is called condensed phase rule or reduced phase rule. T vs. Composition diagrams are shown to represents the solid- Liquid equilibria. Two component system is to be classified depending upon miscibility of two components in molten state and also on basis of solid phases that separates out on cooling.
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    Solid — Liquid Equilibria or condensed phase rule or reduced phase When two components that are completely miscible in liquid state are allowed to cool at low Temperature and components begin to separate out as solid in any of following three forms: 1. Components are not miscible in solid state and form eutectic mixture. Pb-Ag alloy, Cd- Bi alloy 2. Components form a stable solid compound which melts at constant temperature to give a liquid with same composition. Such compounds are said to have congruent melting points.: Zn-Mg system 3. Components form a solid compound which is unstable and decomposes below its mp to give a new solid phase and liquid that is different in composition from original compound. Such compounds have incongruent mp e.g. : Na-K system
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    Eutectic System Two component system in which both the components are completely miscible in liquid phase but do not react chemically is called a eutectic system e.g. Ag-Pb System Eutectic Temperature and composition: for a pure substance A, the freezing point is higher and upon increasing the conc. of B freezing point decreases to lowest value. This is called eutectic temperature and composition at this state is called eutectic composition. Eutectic Point: (easily melted) is defined as the lowest melting point attained by the mixture
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    Ag-Pb System It is a simple eutectic system in which silver and lead are completely soluble in liquid state. They do not react to form a any compound but on solidification they form an easy melting mixture.(eutectic system) Four phases that take part in equilibrium are: 1. solid silver 2. solid lead 3. solution of Lead & silver 4. Vapor Boiling point of Ag & Pb being high, so Gas phase is absent, so pressure has negligible effect. So S-L equilibrium without gas phase is known as condensed system.
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    961 303 100 % Ag Solid Ag + Liquid Solid Eutectic + solicL Ag Ag-Pb System Liquid rmelt Eutectic point 0 rni.xture 97.4 2.6 Ag Freezing Curve or 327 Solid Pb + liquid Solid Eutectic rnixture + solid PO 100 % % Com position http://www.ques10.com/p/7239/what-is-a-condensed-phase-systems-draw-the-phase-1/
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    Ag-Pb System Areas (Bivariant System) 1. Area above AOB: only molten mixture of Ag and Pb exist in this system 2. Areas enclosed by BOF: only molten mixture of Ag and Pb and solid Pb exist. 3. Areas enclosed by AOE: only molten mixture of Ag and Pb and solid Ag exist.
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    1, Curves of Ag-Pb System (Univariant System) Curve AO Since mp of silver is 961C, continuous addition of Pb lowers mp along Two phases exists in equilibrium along AO solid Ag and solution If more Pb is added, it separate out as solid
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    Curves of Ag-Pb System (Univariant System) 2. Curve BO Since mp of Pb is 327C, continuous addition of Ag lowers mp along BOO Two phases exists in equilibrium along BO solid Pb and solution System is univariant.
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    Ag-Pb System AO and BO meets at point at O, O is common to both the curves, solid Pb, solid Ag and their liquid solution coexist. At this point degrees of freedom is zero and it is non- variant. Point O is lowest T of 303C at which liquid exist. If liquid cooled below this temperature both Ag & Pb separates in solid form as 2.6% Ag and 97.6 % Pb. In an alloy of Ag and Pb, Ag melts at 303C which is lower than melting point of Ag and Pb called eutectic mixture.
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    Ag-Pb System Diagram is divided into two regions below the line EF: On the left of the line OD, crystalline Ag and eutectic mixture are stable On the right of the line OD crystalline Pb and eutectic mixture are stable.
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    System with congruent melting point Congruent melting : occurs during melting of a compound when the composition of the liquid that forms is the same as the composition of the solid. It can be contrasted with incongruent melting A binary system is said to be possess a congruent melting point when it melts at sharp temperature to give a liquid of the same composition as that of solid. This generally happens in two-component systems. e.g. Zn-Mg System
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    Zn-Mg System 59•o-c 41 CC liquid melt azo•c Zn + MgZnz ZIT — 100% DMgZnz + liquid melt Meet liquid congruent meetir.g point Mg Mg Zn cMgzna = 650•c Mg liquid melt Eutectic points 2 345•c 100% Fig. 2.3 Phase diagram ofZn-Mg systern [Congruent rmelting point systeml https://www.google.co.in/search?q=ppt+on+phase+diagram+of++Zn-Mg+system&source
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    Zn-Mg System Zn-Mg System is a two component system and having congruent melting point. In this system zinc and magnesium, which melt at 4190C and 6500C. Both metals enter into chemical combination and form an intermetallic compound MgZn2 and melts at 5900C to give a liquid of the same composition. Hence, 5900C is the congruent melting point of the system. In the reduced form, the system has the following four phases: Solid magnesium, solid zinc, Solid MgZn2 Liquid solution of Zn and Mg.
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    1. 2. Zn-Mg System On applying the reduced phase rule Therefore, at point D constitutes a non-variant system. Point E (Eutectic point): Point E represents the eutectic point of the system at a temperature of 3450C which is the least melting point of Mg-MgZn2 system. Here, also three phases existing together in equilibrium at point E are solid Mg, solid MgZn2 and liquid MgZn2. The system is non-variant.
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    3. Zn-Mg System Point C (Eutectic point): This point also represents the eutectic point (3800C) which is the least melting point of Zn-MgZn2 system. At this point, the three phases—solid Zn, solid MgZn2 and liquid MgZn2 exist together in equilibrium. Hence, point C represents a non-variant system.
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    Areas of Zn-Mg System The area above the curve BCDEA constitutes a single phase system. i.e. liquid melt consisting of a liquid solution of zinc and magnesium. The system is bivariant. Other areas of the Zn-Mg system consists of two phases and they are univariant systems.
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    Curves of Zn-Mg System Table 2.3: Some salient features of the Zn-Mg system Curve/ area/ paint Curve BC (Freezing CUfVé of Zn) Curve AE {Freezing CUfVé of Mg) CUfVé CO Corve OE CUfVe COE Area BCOEA Phases in equilibrium Zn & Melt {Containing Zn & Melt (Containing Zn MgZnz & melt {Containing MgZnz & melt (Containing MgZna & melt Liquid {Melt of Znv Mg & No- af phase(P) 02 02 02 02 02 01 Degree of the freedom (F) 01 {Univatiant} 01 (Univariant} 01 {Univariant} 01 {Univariant} 01 {Univariant) 02(Bivariant) https://www.google.co.in/search?q=ppt+on+phase+diagram+of++Zn-Mg+system&source
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    Areas of Zn-Mg System Area BCE Area OCG Area DEH Area AE] Area below line FCC Area below line HEI Point C (Eutectic} Point E (Eutectic) Zn & Melt{Containing MgZn2 & Melt{Containing MgZn2 & Melt{Containing Mg & melt toontaining Mg + Zn & MgZr'i2 (both solid) & MgZnz Zn, MgZnz & Melt{Containing MgZnz & Melt(Containin.g 02 02 02 02 03 03 01 {Univariant} 01{Univariant} 01 {Univariant} 01 {Univariant} 01 {Univariant} 01 {Univariant} O(invariant) O(invariant) https://www.google.co.in/search?q=ppt+on+phase+diagram+of++Zn-Mg+system&source
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    Applications of Phase Rule ' Safety Plugs , Solder ' Freeze Drying : Technique of dehydration of food in pharmaceutical industry
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    Thermal Analysis Thermal analysis is a branch of materials science where the properties of materials are studied as they change with temperature, Several methods are commonly used — these are distinguished from one another by the property which is measured.
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    Thermal Analysis Depending upon the variables being measured as a function of temperature or 1. 2. 3. 4. 5. time: Thermal Gravimetric Analysis (TG): Weight Loss due to decomposition Differential Thermal Analysis (DTA): Temperature change between a substance and inert reference is calculated as a function of temperature. Differential scanning colorimetry (DSC): Enthalpy required to record zero temperature difference between a substance and reference material. Dilatometry : changes in size or dimension of substance are measured. Evolved gas analysis: volatile product evolved are analysed.
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    Bibliography NPTEL LECTURES: https://www.youtube.com/watch?v=k RErdKwaAg NPTEL LECTURES: https://www.youtube.com/watch?v=c01bqam9zm8
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    FaQs What do you mean by polymerization? 1. How will you distinguish between addition and 2. condensation polymerization? Write short notes on : a. PVC 3. b. Nylon 4. Write applications of polymers. 5. Explain vulcanization of rubber.

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