Incongruent melting

Transcription

Ladies and Gentlemen, I´d like to welcome you to our course "Physical Chemistry". My name is Dr. Lauth and today's topic is: How to read binary phase diagrams? How to read phase diagrams of mixtures? e.g. this boiling-point curve of the two components IBA (isobutanol) and IPA (isopropanol). On the abscissa concentration of the mixture is plotted. On the left hand side there´s pure IBA, on the right hand side, there´s pure IPA, in between all possible mixtures. (described with the mole fraction x sub B). On the ordinate temperature is plotted between 80 degrees and 110 degrees. A phase diagram tells us what phases are present at a particular combination of state variables. In order to orient ourselves in this diagram, we look first of all at the homogeneous phases. If we choose a composition x and temperature T, so get to a point in the phase diagram in the above right, we have a homogeneous gaseous mixture. If we choose a point in the lower left, we have a homogeneous liquid mixture. The boundaries of the homogeneous regions are called binodals. Binodals fence off the homogeneous areas to the heterogeneous areas in a phase diagram, and often have specific names: The binodal which marks off the region of the homogeneous fluid to higher temperatures is called bubble point curve (boiling point line); the binodal, which marks off the region of the gas phase to low temperatures is called the dew point curve. Between bubble point curve and dew point curve is a two-phase region. If we plot a point in this area, the system is unstable in an homogeneous state, but will decomposes into two phases - but more on that later. Bubble point curve and dew point curve meet in two points, two so-called invariant points in the phase diagram. At these points the system has no degree of freedom according to Gibbs phase rule (F = C-P +2). Firstly, this is the boiling point of pure IPA. Here liquid and gaseous IPA coexist at exactly 82 degrees Celsius (C = 1, P = 2, F = 1 (p)). On the other side we find the boiling point of pure IBA. Here liquid and gaseous IBA coexist at 108 degrees Celsius. Binodals without any maximum and minimum are typical for phase transitions of ideal mixtures. (a mixture of components A and B being chemically very similar.) We want to discuss heating of a 50:50 mixture using this diagram: If we mix 1 mole of IPA and 1 mole , say , at 80 degrees Celsius, we get a point in the diagram, which is located right here (on the abscissa at 0.5) - So we have a homogeneous liquid phase. We heat the liquid - this means we move up on a vertical. (a so-called isopleth - here marked in green) at about 92 degrees Celsius, the isopleth intersects the bubbling point curve - That is, the mixture begins to boil. The composition of the gas phase above the boiling liquid 50:50 mixture, we may determine using the so called tie line. A tie line is an equilibrium line, an isotherm in a two-phase region. We can draw any number of tie lines in the two-phase region. Each horizontal line between bubbling and dew point curve is a tie line. A tie line connects two phases in equilibrium. In our case it connects the 50 percent liquid phase to the 70 % gas phase. The gas phase is thus enriched in the lower boiling component. A 50:50 mixture of IPA and IBA at 92 ° C begins to boil and the gaseous phase that results from the liquid phase is approximately 70 percent. We want to discuss another issue using the liquid gas phase diagram of IBA / IPA. If we mix 65 percent IPA with 35 percent IBA and heat the mixture to 91.5 degrees Celsius, we´ll end up at a point in the two-phase area of the diagram between bubbling point curve and dew point curve. Here a homogeneous system is not stable but disintegrates along the tie line into a liquid phase and a gas phase. The stoichiometry of the decomposition follows the so-called lever rule. We draw the tie line (in yellow) through the point, we find that it intersects the bubbling point curve x=0.5, and intersects the dew point curve at 0.72. The system is homogeneous unstable and decomposes into a liquid phase with 50 percent IPA (read on the bubbling point curve) and a gas phase with 72 percent IPA (read on the dew point curve). Consider the tie line as a lever, with the initial state point as the fulcrum. The lever arm a(to the liquid side) is approximately twice as long as the lever arm b, which means the amount of gas phase is twice as large as the amount of liquid phase. Using the liquid gas phase diagram of nitrogen and oxygen we may discuss the cooling of air. At 82 Kelvins, the air is still homogeneous gaseous -- with a composition of about 79 percent nitrogen - At 81 Kelvins liquid phase condenses, which is 50% nitrogen. Only at 79 Kelvins, the air is completely condensed. During condensation (or evaporation) of an ideal mixture neither temperature nor composition of the phases are constant. Liquid gas phase diagrams with tie lines and binodals describe the exact course of condensing (or evaporation). In ideal mixtures, the gas phase is always enriched in the lower boiling component. Thus we are able to separate the mixture by distillation. In principle an ideal mixture may be completely separated into the pure components by multiple distillation. This process may be plotted in the phase diagram as a stairs shaped line. Now for non-ideal mixtures. The (non-ideal) mixture of water and formic acid shows a phase diagram with a maximum. The peak is also called an azeotrope. At this point, bubbling point curve and dew point curve intersect for a third time: The azeotrope forms a third invariant point. It boils and condenses exactly as a pure substance. Therefore, it´s not possible to separate a non-ideal mixture into the pure components by distillation. The (non-ideal) mixture of water and ethanol shows a phase diagram with minimum azeotrope. A liquid mixture of 95.6% ethanol will boil at a constant temperature of 78.2 ° C into a gas phase, which is also 95.6% ethanol. Accordingly, you cannot distillate pure ethanol form ethanol / water mixture . Here you can see a phase diagram of the system hexane / nitrobenzene below the boiling point. We may discuss this phase diagram in a similar way as liquid gas phase diagram. We find a binodal, which separates the homogeneous region from the heterogeneous region . above the binodal, the mixture is homogeneous; below the binodal, it consists of two separated liquid phases. In this heterogeneous region, we can arbitrarily draw tie lines. If we prepare a 40:60 nitrobenzene / hexane mixture at 25 ° C ( room temperature) the system is in the state (1). The mixture is homogeneous -- it´s a single phase. If we cool this mixture, the isopleth intersects the binodal at about 20 ° C (state (2)). The mixture then splits up into two liquid phases. At 15 ° C we find state (3). A nitrobenzene-rich liquid phase I and a hexane-rich liquid phase II coexist. The ratio of the two liquid phases can be calculated using the lever rule. Now for solid liquid phase transitions. This is the solid-liquid phase diagram of an ideal mixture (copper / nickel) It looks just like an "ideal" liquid gas phase diagram and we can discuss it in the same way. We find two homogeneous regions, the liquid at high temperatures and the solid at a low temperatures. There are two binodals and these are referred to as solidus and liquidus. The binodals intersect only in two points, namely, the melting points of the pure components. In the two-phase region (between the liquidus and solidus), we can arbitrarily draw tie lines. With the help of tie lines and binodals, we may discuss the solidification of a 60-percent melt. We find, that during solidification of an ideal mixture neither phase composition nor temperature remain constant. This is a typical solid liquid phase diagram of a non-ideal mixture (lithium chloride / potassium chloride). While the two components are perfectly miscible in the liquid phase, however, they form only few mixed crystals (solid solution) in the solid state. Let´s first look for the homogeneous areas in the diagram: we find liquid phase (melt) at high temperature, marked off to lower temperatures by a typical V-shaped liquidus. We find two solid homogeneous regions: potassium chloride mixed crystals (marked in red) and lithium chloride mixed crystals (black featured here) . These homogeneous solid areas may be so narrow that they are almost indistinguishable from the ordinates. All other areas in the diagram are heterogeneous. In the triangular area to the left molten and solid potassium chloride (mixed crystals) coexist. In the triangular area to the right molten and solid lithium chloride mixed crystals coexist. The rectangular area consists of a heterogeneous mixture of solid potassium chloride and solid lithium chloride crystals. As expected, the melting points of the pure components are invariant points (intersections of binodals). And there is another invariant point at the minimum of the liquidus. We call this invariant point eutectic. At this point, molten liquid, solid potassium chloride mixed crystals and solid lithium chloride mixed crystals coexist at a constant temperature of 359 degrees Celsius. Like a pure substance, this mixture melts and solidifies at constant temperature. We want to discuss the solidification of an under-eutectic melt in a schematic solid-liquid phase diagram. We cool the melt (initial state 1), that is we are moving out along an isopleth down to low temperatures. At state (2) we intersect the liquidus. Potassium chloride crystals precipitate from the melt. As we cool down further, the potassium chloride crystals grow, the melt accumulates in lithium chloride and moves along the liquidus to the eutectic. In state (3) large potassium chloride crystals are present in a melt with eutectic composition. Now temperature remains constant until the eutectic mixture has completely solidified. At the final state (4) we find large potassium chloride crystals in a solid eutectic matrix. This matrix is heterogeneous: it consists of an intimate mixture of potassium chloride and lithium chloride crystals. At a eutectic, liquid phase is no longer stable below a certain temperature and decomposes into two solid phases. Conversely at a so called peritectic, a solid phase is no longer stable above a certain temperature and decomposes into another solid phase and a liquid phase with a different composition (this is also called incongruent melting). With congruent melting of a solid compound to a , we find a dystectic, a solid compound formed of two components melts to homogeneous liquid phase with the same composition. We can tell a eutectic by the V-shaped structure of the liquidus, we can tell a peritectic by a kink in the liquidus and the roof-shaped or T-shaped structure of the solidus. If these structures occur and only solid phases are involved, we speak of a eutectoid or by a peritectoid We have here a section of the iron / iron-carbide phase diagram. We want to discuss this diagram. We find a liquid homogeneous area (melt) up here. We find four solid homogeneous regions: Solid alpha-iron bottom left, solid gamma iron (the somewhat broader area here) and delta-iron top left. And we have solid cementite (iron carbide) - that is the right boundary. All other areas in the phase diagram are heterogeneous; We can see several invariant points: - the eutectic at this point (V-shaped liquidus), below this temperature the melt is no longer stable, but decomposes into gamma-iron and cementite. - of the eutectoid at this point (V-shaped solidus): Below this temperature gamma-iron is no longer stable but disintegrates into alpha-iron and cementite. Gamma-iron does not only have a floor temperature, but also a ceiling temperature: That´s where the peritectic is located. Gamma-iron decomposes into delta-iron and melt. Furthermore, there´s a dystectic at this point: cementite melts congruently to the corresponding melt. If you want to discuss a phase diagram, first find the homogeneous areas, then search for then the binodals and designate them as bubbling point curve, dew point curve, liquidus, solidus. Finally determine the invariant points and characterize them as eutectic, peritectic, ect., recording the corresponding phase equilibria. Thank you for watching.