Phase Diagrams 101 - How do we read phase diagrams of multicomponent systems?
Lauth, Jakob Günter (SciFox)
PhysChemBasics#8 Phase Diagrams 101 The best way to discuss phase diagrams is to first look for the homogeneous and heterogeneous regeions, then label the binodals and draw in some tie lines. Finaly depict the invariant points and specify the processes that take place at these points. Ideal phase diagrams, whether melting or boiling phase diagrams, show neither maximum nor minimum for the binodals. Non-ideal mixtures may have maxima and minima, which are called azeotrope, peritectic or eutectic, depending on the type of diagram. Gibbs' phase triangle has proven useful for the illustration of 3-component mixtures. Again there may be binodals and tie lines in this diagram. A tie line not only tells us the composition of the phases in the heterogeneous region, but also - after applying the lever rule - their quantity ratio..
 The behavior of pure substances or mixtures is very often described graphically with face diagrams. How can we kind of translate these diagrams into real life? Hello and welcome to FisCAM Basics, our topic today, how to read face diagrams. In particular, what are binodals, tie lines, invariant points. Let's start with a mixture of alcohols as an example, which will guide us through this lecture. We mix one mole of liquid isopropyl alcohol, short IPA, and one mole of liquid isobutyl alcohol, short IBA and heat this mixture to 92 centigrade. This will lead to a total pressure of 100 kilopascals. If we analyze the gas phase above the liquid mixture, we see that it is 70% in IPA, while the liquid phase is only 50% IPA. What we just described is one possible state of the two component system IBA IPA, characterized by temperature, pressure and composition. As you may remember, Gibbs phase rule demands to set three and only three parameters to unambiguously describe a two component system. If we want to plot each and every possible state of a two component system, we may do so using a coordinate plane or rather a coordinate space with the axis temperature, pressure and composition. For our example, we end up with this representation. It is typical for the phase diagram of a two component system that the x-axis is kind of confined. The concentration of component B only goes from 0 to 100%. We can now choose any temperature pressure composition triple and the phase diagram will tell us how the system will look like. At first glance, many phase diagrams might look confusing, but here's a guideline for discussing phase diagrams. First of all, label the regions in the diagram which are homogeneous, which consist of a single phase, for example the liquid phase, region and the gas phase region. The remaining regions are then multi-phase. For example, we find the homogeneous liquid phase right here and the homogeneous gas phase right there. The dividing lines or dividing surfaces between homogeneous and heterogeneous regions are called binodals. In this diagram, we see two binodals, binodal surfaces to be exact. The two phase region liquid gas is separated from the liquid phase region by the boiling point line or rather surface and it is separated from the gaseous region by the dew point line or rather dew point surface. For the sake of clarity, most books use two D phase diagrams, rejections of this 3D phase diagram onto either the XT plane or the XP plane. The surface on top and on the front of this 3D diagram are examples. With these two D phase diagrams, the binodals reduce from surfaces to lines. For example, the yellow line is a boiling point curve, the blue line is a dew point curve. In the following, we want to discuss the 2D XT phase diagram of the IBA IPA system. That is the projection you find on top of this 3D diagram. We choose the pressure to be constant and standard value 100 kPa. The composition of the system is plotted on the X coordinate and temperature on the ordinate. On the X coordinate, you will find the pure IBA, the high boiler on the left end and pure IPA, the low boiler on the right end. The 2 binodals, boiling point curve and dew point curve intersect in two points. These are called invariant points. In this case, these are the boiling points of the pure components. The phase diagram may answer many questions on the behavior of mixtures. We will discuss some of them now. First question. At what temperature will the aforementioned 5050 IBA IPA mixture start to boil? To enter this, we draw a so-called aithopleath, a line on which the composition of the mixture is constant, a line on which the composition of the mixture is constant at X equals 0.5 into the diagram and C, where this line intersects with the boiling point curve. Intersection is at 365 k. This is obviously the temperature at which the mixture will start to boil. The phase diagram also tells us at what temperature a 5050 gazius mixture of IBA and IPA will start to condense, start to dew. We only have to draw the aithopleath from above and mark the intersection with a dew point curve. Obviously, at 371 k, the first liquid droplets condense from a gazius 5050 mixture. Remember, the boiling point curve always refers to the composition of the liquid mixture. The dew point curve always refers to the composition of gazius mixtures. Back to the liquid 5050 mixture. This mixture starts to boil at 365 k. Now, what's the composition of the vapors, the gas phase above this boiling mixture? Well, here we have to ask the tie line or the conode. A tie line or conode is a straight line in the two-phase region of a phase diagram, which connects the compositions of the phases at equilibrium. Every horizontal line in the two-phase regions is in fact a tie line. Tie lines are always both isobars and isotherms. Let's draw a tie line through the two-phase region starting at intersection IBA boiling point curve. The intersection of the tie line with a dew point curve is at 0.7. That's the composition of the gas phase. The gas phase over a 5050 liquid mixture is therefore enriched with low boiler. Similarly, we can use the phase diagram to determine that the liquid that results from a 5050 gas phase mixture is enriched with a high boiler. The tie line tells us that the first drops of liquid are about 20% in IPA. With the phase diagram, we can discuss any temperature and composition of the two-component system. For example, if we heat a 5050 mixture to 370 kV, we are in the two-phase region, which means that this mixture is not stable as a homogeneous phase, but it decomposes along the tie line into a liquid phase and a gaseous phase. The intersection of the tie line with the binodals tells us the composition of these phases. The liquid phase is 40% and the gas phase is 55% in IPA. If we want to determine the amount of substance in the liquid and the gas phase, we need the so-called lever rule. The tie line is sort of a lever, the mixture being the fulcrum. The liver arm A, the distance from the fulcrum to the left end of the tie line, multiplied by the amount of the liquid phase, is equal to the lever arm B, the distance from the fulcrum to the right end of the tie line. The distance from the fulcrum to the right end of the tie line, multiplied by the amount of the gas phase. In our case, A is about twice the size as B, which means that we have twice as much gas phase as liquid phase. The example just discussed, isoputyl alcohol isopropyl alcohol corresponds to an ideal mixture. With non-ideal mixtures, there may be maxima or minima in the phase diagram. For example, with the ethanol water system, the boiling point curve and the dew point curve intersect three times. Not only on both sides of the phase diagram, but also in a minimum. This minimum is called an azirthrope. So we have in fact three invariant points in this diagram. The boiling point of pure water at constant 100 centigrade, the boiling point of pure ethanol at constant 78.3 centigrade, and the boiling point of the azeotrope at constant 78.2 centigrade. At invariant points, phase transitions occur at a constant temperature. Moreover, the compositions of both phases in equilibrium are the same. Thus an azeotrope is a constant boiling point mixture and boils and condenses like a pure substance. It cannot be separated into its compounds by distillation. This also is a phase diagram of an ideal two-component system. However, it is not a boiling phase diagram, but a melting phase diagram. The binodals here are called solidest line and liquidest line, and they tell us at what temperature a solid phase melts, or at what temperature a liquid phase solidifies. As with any ideal phase diagram, we have only two invariant points, namely the phase transformations of the pure substances, in this case the melting point of silver and the melting point of gold. Here is another phase diagram, more precisely a melting phase diagram, of a non-ideal mixture, the system being silver and copper. There are three invariant points, the melting point of pure silver, the melting point of pure copper, and a minimum. The minimum is called the eutectic. It represents a mixture with the lowest melting point of the system, and again it melts and solidifies like a pure substance at a constant temperature. A liquid eutectic mixture solidifies on cooling into two solid phases, which do not form a homogeneous solution, but a heterogeneous mixture. Here we see the phase diagram of the water NACL system. It's a bit more complicated because in addition to H2O and NACL, we have another homogeneous solid phase, the halide. Halide, chemical formula NACL.2H2O, is only stable up to approximately 0 centigrade, and then decomposes into solid NACL and liquid brine. Discussing this diagram we follow our usual path. First of all, we search for and label the homogeneous regions. Those are the liquid phase, the brine, solid H2O, ice, solid halide, and solid NACL. All other regions are heterogeneous. We can draw in the binodals, for example the liquid lines and two important tie lines. The tie line that describes the decomposition of halide and the tie line that goes through the eutectic. The decomposition of halide at 0 centigrade is somewhat equivalent to the behavior of a eutectic melt, but in the opposite way. A homogeneous solid melts on heating into two phases. A heterogeneous mixture of a liquid with a different composition and another solid. This is called a peritectic. If we want to describe this recomponent system, we can depict any possible mixture in an equilateral triangle. The so-called Gibbs phase triangle. The corners of the triangle represent the pure components, the edges of the triangle represent two component mixtures, and the area inside of the triangle relates to three component mixtures. When discussing the phase triangle, you have to keep in mind that the composition axes are not perpendicular to each other, but form a 60 degree angle. The composition of the red dot marked here corresponds to 20% of component C, 20% of component B, and 60% component A. Homogeneous and heterogeneous regions may also occur in the phase triangle diagram, and so are binodals. Here's a diagram of this resolvance chloroform, water, and acetic acid. The system is heterogeneous below the binodal and homogeneous above. If we start with a 50-50 chloroform water mixture, we are in the heterogeneous region at 0.1. If we then gradually add more and more acetic acid, we come to the points 2, 3, and 4. We may draw tie lines through points 2 and 3, which tell us which phases are actually present. In point 2, for example, we have an organic phase of the alpha-2 composition and an aqueous phase of beta-2 composition. We may specify the exact composition of the phases alpha-2 and beta-2. Oxilirate-ry angles have been proven useful here, and we can also specify the quantitative ratio of the phases alpha-2 and beta-2 by application of the lever rule. Lever arm A is larger than lever arm B. This means that phase beta-2 is in excess. Let us summarize. The best way to discuss phase diagrams is that you look first for the homogeneous and heterogeneous regions. Then label the binodals and draw in some tie lines. Finally, depict the invariant points and specify the processes that take place at these points. Ideal phase diagrams, whether boiling or melting phase diagrams, show neither maximum nor minimum for the binodals. Non-ideal mixtures may have maxima and minima, which are called a zeotrope, peritectic, or eutectic, depending on the type of diagram. The Gibbs phase triangle has proven useful for the illustration of the recomponent mixtures. Again, there may be binodals and tie lines in this diagram. A tie line not only tells us the composition of the phases in the heterogeneous region, but also their quantity ratio we have to apply the lever rule. More information about the topic you will find in the book and in the lecture. Thanks for watching.
 The behavior of pure substances or mixtures is very often described graphically with face diagrams.  How can we kind of translate these diagrams into real life?  Hello and welcome to FisCAM Basics, our topic today, how to read face diagrams.  In particular, what are binodals, tie lines, invariant points.  Let's start with a mixture of alcohols as an example, which will guide us through this lecture.  We mix one mole of liquid isopropyl alcohol, short IPA, and one mole of liquid isobutyl alcohol,  short IBA and heat this mixture to 92 centigrade.  This will lead to a total pressure of 100 kilopascals.  If we analyze the gas phase above the liquid mixture, we see that it is 70% in IPA,  while the liquid phase is only 50% IPA.  What we just described is one possible state of the two component system IBA IPA,  characterized by temperature, pressure and composition.  As you may remember, Gibbs phase rule demands to set three and only three parameters  to unambiguously describe a two component system.  If we want to plot each and every possible state of a two component system,  we may do so using a coordinate plane or rather a coordinate space with the axis temperature,  pressure and composition.  For our example, we end up with this representation.  It is typical for the phase diagram of a two component system that the x-axis is kind of confined.  The concentration of component B only goes from 0 to 100%.  We can now choose any temperature pressure composition triple and the phase diagram will tell us how the system will look like.  At first glance, many phase diagrams might look confusing, but here's a guideline for discussing phase diagrams.  First of all, label the regions in the diagram which are homogeneous,  which consist of a single phase, for example the liquid phase,  region and the gas phase region. The remaining regions are then multi-phase.  For example, we find the homogeneous liquid phase right here and the homogeneous gas phase right there.  The dividing lines or dividing surfaces between homogeneous and heterogeneous regions are called  binodals. In this diagram, we see two binodals,  binodal surfaces to be exact. The two phase region liquid gas is separated from the  liquid phase region by the boiling point line or rather surface and it is separated from the gaseous region  by the dew point line or rather dew point surface.  For the sake of clarity, most books use two D phase diagrams,  rejections of this 3D phase diagram onto either the XT plane or the XP plane.  The surface on top and on the front of this 3D diagram are examples.  With these two D phase diagrams, the binodals reduce from surfaces to lines.  For example, the yellow line is a boiling point curve, the blue line is a dew point curve.  In the following, we want to discuss the 2D XT phase diagram of the IBA IPA system.  That is the projection you find on top of this 3D diagram.  We choose the pressure to be constant and standard value 100 kPa.  The composition of the system is plotted on the X coordinate and temperature on the ordinate.  On the X coordinate, you will find the pure IBA, the high boiler on the left end and pure IPA,  the low boiler on the right end.  The 2 binodals, boiling point curve and dew point curve intersect in two points.  These are called invariant points.  In this case, these are the boiling points of the pure components.  The phase diagram may answer many questions on the behavior of mixtures.  We will discuss some of them now.  First question.  At what temperature will the aforementioned 5050 IBA IPA mixture start to boil?  To enter this, we draw a so-called aithopleath, a line on which the composition of the mixture is constant,  a line on which the composition of the mixture is constant at X equals 0.5 into the diagram  and C, where this line intersects with the boiling point curve.  Intersection is at 365 k.  This is obviously the temperature at which the mixture will start to boil.  The phase diagram also tells us at what temperature a 5050 gazius mixture of IBA  and IPA will start to condense, start to dew.  We only have to draw the aithopleath from above and mark the intersection with a dew point curve.  Obviously, at 371 k, the first liquid droplets condense from a gazius 5050 mixture.  Remember, the boiling point curve always refers to the composition of the liquid mixture.  The dew point curve always refers to the composition of gazius mixtures.  Back to the liquid 5050 mixture.  This mixture starts to boil at 365 k.  Now, what's the composition of the vapors, the gas phase above this boiling mixture?  Well, here we have to ask the tie line or the conode.  A tie line or conode is a straight line in the two-phase region of a phase diagram,  which connects the compositions of the phases at equilibrium.  Every horizontal line in the two-phase regions is in fact a tie line.  Tie lines are always both isobars and isotherms.  Let's draw a tie line through the two-phase region starting at intersection IBA boiling point curve.  The intersection of the tie line with a dew point curve is at 0.7.  That's the composition of the gas phase.  The gas phase over a 5050 liquid mixture is therefore enriched with low boiler.  Similarly, we can use the phase diagram to determine that the liquid that results from a 5050 gas phase mixture  is enriched with a high boiler.  The tie line tells us that the first drops of liquid are about 20% in IPA.  With the phase diagram, we can discuss any temperature and composition of the two-component system.  For example, if we heat a 5050 mixture to 370 kV, we are in the two-phase region,  which means that this mixture is not stable as a homogeneous phase,  but it decomposes along the tie line into a liquid phase and a gaseous phase.  The intersection of the tie line with the binodals tells us the composition of these phases.  The liquid phase is 40% and the gas phase is 55% in IPA.  If we want to determine the amount of substance in the liquid and the gas phase, we need the so-called lever rule.  The tie line is sort of a lever, the mixture being the fulcrum.  The liver arm A, the distance from the fulcrum to the left end of the tie line,  multiplied by the amount of the liquid phase, is equal to the lever arm B,  the distance from the fulcrum to the right end of the tie line.  The distance from the fulcrum to the right end of the tie line, multiplied by the amount of the gas phase.  In our case, A is about twice the size as B, which means that we have twice as much gas phase as liquid phase.  The example just discussed, isoputyl alcohol isopropyl alcohol corresponds to an ideal mixture.  With non-ideal mixtures, there may be maxima or minima in the phase diagram.  For example, with the ethanol water system, the boiling point curve and the dew point curve intersect three times.  Not only on both sides of the phase diagram, but also in a minimum.  This minimum is called an azirthrope.  So we have in fact three invariant points in this diagram.  The boiling point of pure water at constant 100 centigrade,  the boiling point of pure ethanol at constant 78.3 centigrade,  and the boiling point of the azeotrope at constant 78.2 centigrade.  At invariant points, phase transitions occur at a constant temperature.  Moreover, the compositions of both phases in equilibrium are the same.  Thus an azeotrope is a constant boiling point mixture and boils and condenses like a pure substance.  It cannot be separated into its compounds by distillation.  This also is a phase diagram of an ideal two-component system.  However, it is not a boiling phase diagram, but a melting phase diagram.  The binodals here are called solidest line and liquidest line,  and they tell us at what temperature a solid phase melts,  or at what temperature a liquid phase solidifies.  As with any ideal phase diagram, we have only two invariant points,  namely the phase transformations of the pure substances,  in this case the melting point of silver and the melting point of gold.  Here is another phase diagram, more precisely a melting phase diagram, of a non-ideal mixture,  the system being silver and copper.  There are three invariant points, the melting point of pure silver, the melting point of pure copper, and a minimum.  The minimum is called the eutectic.  It represents a mixture with the lowest melting point of the system,  and again it melts and solidifies like a pure substance at a constant temperature.  A liquid eutectic mixture solidifies on cooling into two solid phases,  which do not form a homogeneous solution, but a heterogeneous mixture.  Here we see the phase diagram of the water NACL system.  It's a bit more complicated because in addition to H2O and NACL,  we have another homogeneous solid phase, the halide.  Halide, chemical formula NACL.2H2O, is only stable up to approximately 0 centigrade,  and then decomposes into solid NACL and liquid brine.  Discussing this diagram we follow our usual path.  First of all, we search for and label the homogeneous regions.  Those are the liquid phase, the brine, solid H2O, ice, solid halide, and solid NACL.  All other regions are heterogeneous.  We can draw in the binodals, for example the liquid lines and two important tie lines.  The tie line that describes the decomposition of halide and the tie line that goes through the eutectic.  The decomposition of halide at 0 centigrade is somewhat equivalent to the behavior of a eutectic melt,  but in the opposite way.  A homogeneous solid melts on heating into two phases.  A heterogeneous mixture of a liquid with a different composition and another solid.  This is called a peritectic.  If we want to describe this recomponent system, we can depict any possible mixture in an equilateral triangle.  The so-called Gibbs phase triangle.  The corners of the triangle represent the pure components,  the edges of the triangle represent two component mixtures,  and the area inside of the triangle relates to three component mixtures.  When discussing the phase triangle, you have to keep in mind that the composition axes are not perpendicular to each other,  but form a 60 degree angle.  The composition of the red dot marked here corresponds to 20% of component C,  20% of component B, and 60% component A.  Homogeneous and heterogeneous regions may also occur in the phase triangle diagram,  and so are binodals.  Here's a diagram of this resolvance chloroform, water, and acetic acid.  The system is heterogeneous below the binodal and homogeneous above.  If we start with a 50-50 chloroform water mixture, we are in the heterogeneous region at 0.1.  If we then gradually add more and more acetic acid, we come to the points 2, 3, and 4.  We may draw tie lines through points 2 and 3, which tell us which phases are actually present.  In point 2, for example, we have an organic phase of the alpha-2 composition  and an aqueous phase of beta-2 composition.  We may specify the exact composition of the phases alpha-2 and beta-2.  Oxilirate-ry angles have been proven useful here, and we can also specify the quantitative ratio  of the phases alpha-2 and beta-2 by application of the lever rule.  Lever arm A is larger than lever arm B. This means that phase beta-2 is in excess.  Let us summarize.  The best way to discuss phase diagrams is that you look first for the homogeneous and heterogeneous regions.  Then label the binodals and draw in some tie lines.  Finally, depict the invariant points and specify the processes that take place at these points.  Ideal phase diagrams, whether boiling or melting phase diagrams, show neither maximum nor minimum  for the binodals.  Non-ideal mixtures may have maxima and minima, which are called a zeotrope, peritectic, or eutectic,  depending on the type of diagram.  The Gibbs phase triangle has proven useful for the illustration of the recomponent mixtures.  Again, there may be binodals and tie lines in this diagram.  A tie line not only tells us the composition of the phases in the heterogeneous region,  but also their quantity ratio we have to apply the lever rule.  More information about the topic you will find in the book and in the lecture.  Thanks for watching.
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The behavior of pure substances or mixtures is very often described graphically with face diagrams. How can we kind of translate these diagrams into real life? Hello and welcome to FisCAM Basics, our topic today, how to read face diagrams. In particular, what are binodals, tie lines, invariant points. Let's start with a mixture of alcohols as an example, which will guide us through this lecture. We mix one mole of liquid isopropyl alcohol, short IPA, and one mole of liquid isobutyl alcohol, short IBA and heat this mixture to 92 centigrade. This will lead to a total pressure of 100 kilopascals. If we analyze the gas phase above the liquid mixture, we see that it is 70% in IPA, while the liquid phase is only 50% IPA. What we just described is one possible state of the two component system IBA IPA, characterized by temperature, pressure and composition. As you may remember, Gibbs phase rule demands to set three and only three parameters to unambiguously describe a two component system. If we want to plot each and every possible state of a two component system, we may do so using a coordinate plane or rather a coordinate space with the axis temperature, pressure and composition. For our example, we end up with this representation. It is typical for the phase diagram of a two component system that the x-axis is kind of confined. The concentration of component B only goes from 0 to 100%. We can now choose any temperature pressure composition triple and the phase diagram will tell us how the system will look like. At first glance, many phase diagrams might look confusing, but here's a guideline for discussing phase diagrams. First of all, label the regions in the diagram which are homogeneous, which consist of a single phase, for example the liquid phase, region and the gas phase region. The remaining regions are then multi-phase. For example, we find the homogeneous liquid phase right here and the homogeneous gas phase right there. The dividing lines or dividing surfaces between homogeneous and heterogeneous regions are called binodals. In this diagram, we see two binodals, binodal surfaces to be exact. The two phase region liquid gas is separated from the liquid phase region by the boiling point line or rather surface and it is separated from the gaseous region by the dew point line or rather dew point surface. For the sake of clarity, most books use two D phase diagrams, rejections of this 3D phase diagram onto either the XT plane or the XP plane. The surface on top and on the front of this 3D diagram are examples. With these two D phase diagrams, the binodals reduce from surfaces to lines. For example, the yellow line is a boiling point curve, the blue line is a dew point curve. In the following, we want to discuss the 2D XT phase diagram of the IBA IPA system. That is the projection you find on top of this 3D diagram. We choose the pressure to be constant and standard value 100 kPa. The composition of the system is plotted on the X coordinate and temperature on the ordinate. On the X coordinate, you will find the pure IBA, the high boiler on the left end and pure IPA, the low boiler on the right end. The 2 binodals, boiling point curve and dew point curve intersect in two points. These are called invariant points. In this case, these are the boiling points of the pure components. The phase diagram may answer many questions on the behavior of mixtures. We will discuss some of them now. First question. At what temperature will the aforementioned 5050 IBA IPA mixture start to boil? To enter this, we draw a so-called aithopleath, a line on which the composition of the mixture is constant, a line on which the composition of the mixture is constant at X equals 0.5 into the diagram and C, where this line intersects with the boiling point curve. Intersection is at 365 k. This is obviously the temperature at which the mixture will start to boil. The phase diagram also tells us at what temperature a 5050 gazius mixture of IBA and IPA will start to condense, start to dew. We only have to draw the aithopleath from above and mark the intersection with a dew point curve. Obviously, at 371 k, the first liquid droplets condense from a gazius 5050 mixture. Remember, the boiling point curve always refers to the composition of the liquid mixture. The dew point curve always refers to the composition of gazius mixtures. Back to the liquid 5050 mixture. This mixture starts to boil at 365 k. Now, what's the composition of the vapors, the gas phase above this boiling mixture? Well, here we have to ask the tie line or the conode. A tie line or conode is a straight line in the two-phase region of a phase diagram, which connects the compositions of the phases at equilibrium. Every horizontal line in the two-phase regions is in fact a tie line. Tie lines are always both isobars and isotherms. Let's draw a tie line through the two-phase region starting at intersection IBA boiling point curve. The intersection of the tie line with a dew point curve is at 0.7. That's the composition of the gas phase. The gas phase over a 5050 liquid mixture is therefore enriched with low boiler. Similarly, we can use the phase diagram to determine that the liquid that results from a 5050 gas phase mixture is enriched with a high boiler. The tie line tells us that the first drops of liquid are about 20% in IPA. With the phase diagram, we can discuss any temperature and composition of the two-component system. For example, if we heat a 5050 mixture to 370 kV, we are in the two-phase region, which means that this mixture is not stable as a homogeneous phase, but it decomposes along the tie line into a liquid phase and a gaseous phase. The intersection of the tie line with the binodals tells us the composition of these phases. The liquid phase is 40% and the gas phase is 55% in IPA. If we want to determine the amount of substance in the liquid and the gas phase, we need the so-called lever rule. The tie line is sort of a lever, the mixture being the fulcrum. The liver arm A, the distance from the fulcrum to the left end of the tie line, multiplied by the amount of the liquid phase, is equal to the lever arm B, the distance from the fulcrum to the right end of the tie line. The distance from the fulcrum to the right end of the tie line, multiplied by the amount of the gas phase. In our case, A is about twice the size as B, which means that we have twice as much gas phase as liquid phase. The example just discussed, isoputyl alcohol isopropyl alcohol corresponds to an ideal mixture. With non-ideal mixtures, there may be maxima or minima in the phase diagram. For example, with the ethanol water system, the boiling point curve and the dew point curve intersect three times. Not only on both sides of the phase diagram, but also in a minimum. This minimum is called an azirthrope. So we have in fact three invariant points in this diagram. The boiling point of pure water at constant 100 centigrade, the boiling point of pure ethanol at constant 78.3 centigrade, and the boiling point of the azeotrope at constant 78.2 centigrade. At invariant points, phase transitions occur at a constant temperature. Moreover, the compositions of both phases in equilibrium are the same. Thus an azeotrope is a constant boiling point mixture and boils and condenses like a pure substance. It cannot be separated into its compounds by distillation. This also is a phase diagram of an ideal two-component system. However, it is not a boiling phase diagram, but a melting phase diagram. The binodals here are called solidest line and liquidest line, and they tell us at what temperature a solid phase melts, or at what temperature a liquid phase solidifies. As with any ideal phase diagram, we have only two invariant points, namely the phase transformations of the pure substances, in this case the melting point of silver and the melting point of gold. Here is another phase diagram, more precisely a melting phase diagram, of a non-ideal mixture, the system being silver and copper. There are three invariant points, the melting point of pure silver, the melting point of pure copper, and a minimum. The minimum is called the eutectic. It represents a mixture with the lowest melting point of the system, and again it melts and solidifies like a pure substance at a constant temperature. A liquid eutectic mixture solidifies on cooling into two solid phases, which do not form a homogeneous solution, but a heterogeneous mixture. Here we see the phase diagram of the water NACL system. It's a bit more complicated because in addition to H2O and NACL, we have another homogeneous solid phase, the halide. Halide, chemical formula NACL.2H2O, is only stable up to approximately 0 centigrade, and then decomposes into solid NACL and liquid brine. Discussing this diagram we follow our usual path. First of all, we search for and label the homogeneous regions. Those are the liquid phase, the brine, solid H2O, ice, solid halide, and solid NACL. All other regions are heterogeneous. We can draw in the binodals, for example the liquid lines and two important tie lines. The tie line that describes the decomposition of halide and the tie line that goes through the eutectic. The decomposition of halide at 0 centigrade is somewhat equivalent to the behavior of a eutectic melt, but in the opposite way. A homogeneous solid melts on heating into two phases. A heterogeneous mixture of a liquid with a different composition and another solid. This is called a peritectic. If we want to describe this recomponent system, we can depict any possible mixture in an equilateral triangle. The so-called Gibbs phase triangle. The corners of the triangle represent the pure components, the edges of the triangle represent two component mixtures, and the area inside of the triangle relates to three component mixtures. When discussing the phase triangle, you have to keep in mind that the composition axes are not perpendicular to each other, but form a 60 degree angle. The composition of the red dot marked here corresponds to 20% of component C, 20% of component B, and 60% component A. Homogeneous and heterogeneous regions may also occur in the phase triangle diagram, and so are binodals. Here's a diagram of this resolvance chloroform, water, and acetic acid. The system is heterogeneous below the binodal and homogeneous above. If we start with a 50-50 chloroform water mixture, we are in the heterogeneous region at 0.1. If we then gradually add more and more acetic acid, we come to the points 2, 3, and 4. We may draw tie lines through points 2 and 3, which tell us which phases are actually present. In point 2, for example, we have an organic phase of the alpha-2 composition and an aqueous phase of beta-2 composition. We may specify the exact composition of the phases alpha-2 and beta-2. Oxilirate-ry angles have been proven useful here, and we can also specify the quantitative ratio of the phases alpha-2 and beta-2 by application of the lever rule. Lever arm A is larger than lever arm B. This means that phase beta-2 is in excess. Let us summarize. The best way to discuss phase diagrams is that you look first for the homogeneous and heterogeneous regions. Then label the binodals and draw in some tie lines. Finally, depict the invariant points and specify the processes that take place at these points. Ideal phase diagrams, whether boiling or melting phase diagrams, show neither maximum nor minimum for the binodals. Non-ideal mixtures may have maxima and minima, which are called a zeotrope, peritectic, or eutectic, depending on the type of diagram. The Gibbs phase triangle has proven useful for the illustration of the recomponent mixtures. Again, there may be binodals and tie lines in this diagram. A tie line not only tells us the composition of the phases in the heterogeneous region, but also their quantity ratio we have to apply the lever rule. More information about the topic you will find in the book and in the lecture. Thanks for watching.
summarize. The best way to discuss phase diagrams is that you look first for the homogeneous and and draw in some tie lines. Finally, depict the invariant points and specify the processes that take place at these points. Ideal phase diagrams, whether boiling or melting phase diagrams, show neither maximum nor minimum for the binodals. Non-ideal mixtures may have maxima and minima, which are called a zeotrope, peritectic, or eutectic, depending on the type of diagram. The Gibbs phase triangle has proven useful for the illustration of the recomponent mixtures. Again, there may be binodals and tie lines in this diagram. A tie line not only tells us the composition of the phases in the heterogeneous region, but also their quantity ratio we have to