section 5 â phase behaviour, binary mixtures
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SECTION 5 – PHASE BEHAVIOUR, BINARY MIXTURES In this section, we will review phase diagrams for binary mixtures, and the types of questions you could be asked in the exam. Recall from the phase rule that: Degrees of Freedom = Components – Phases + 2 Because we now have 2 components, a 1 phase region has 3 degrees of freedom. Since it’s near impossible to read and interpret 3D graphs on paper, we specify 1 degree of freedom, and graph the remaining 2 degrees of freedom. The most common diagram in this section is a Temperature-Composition (Tx) diagram. To have a 2-dimensinoal Tx diagram, we often specify the pressure of the system. This specification is either in the title of the graph, or is somewhere in the description of the question. The reason this is important is that specifying pressure takes up a degree of freedom, which would leave you with 2 degrees of freedom in a single phase region. If you’re asked about the degrees of freedom of the system, be sure to look for the pressure to see if it has been specified somewhere.
Temperature – Composition (Tx) Diagrams Tx diagrams is a general term for many different types of graphs you can expect to see. The actual shape of the graph will depend on two things: 1) Phases present: a. Liquid-vapor diagrams b. Solid-liquid diagrams 2) Miscibility a. Completely miscible b. Partially miscible c. Completely immiscible In the general case, the phases present do not change the shape of the graph, but only change the interpretation of the graph and the labelling of the regions. On any Tx diagrams, the x-axis represents a mass (weight) fraction or a mole fraction – take note of this difference. Because the axis represent a fraction, it only ranges from 0 to 1. At either end of the x-axis, you have a pure component, it is worth labelling which pure component exists at which end.
34 The y-axis represents temperature. Therefore, labelling regions on a Tx diagram should be intuitive. In a liquid-vapor diagram, vapor exists at higher temperature and liquid at lower temperatures. In solid-liquid diagrams, liquid exists at the higher temperature while the solid at the lower temperatures. In cases where the two components aren’t completely miscible, there will be multiple liquid or solid phases. In the case where you have multiple liquid phases, then one liquid phase will exist on the right side of the diagram, and one liquid phase will exist on the left side of the diagram. Below are a variety of Tx diagrams:
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36 Important points to know: •
The triple phase line – in partially miscible or completely immiscible systems • The bubble point/melting point of the pure component – occurs at x = 0 or x=1 • Maximum solubility of one component in another – occurs at the temperature of the triple phase line • Dew point curve, bubble point curve, saturated liquid curve, and saturated vapor curve all still apply as before • Azeotrope – occur on some completely miscible liquid-vapor diagrams, where the composition of the vapor is identical to the composition of the liquid • Hetero-azeotrope – occurs on partially miscible or immiscible liquid-vapor diagrams, where the composition of the vapor is identical to the composition of both liquids • Eutectic point – occurs on solid-liquid diagrams, and is the lowest melting point of the mixture Similar to Pv diagrams, if you’re interested in knowing compositions of each phase in a 2 phase region, you can navigate left or right to the boundary and read the composition of the phase there. Converting between mass fractions and mole fractions: Recall that both mass fractions and mole fractions are intensive properties, and hence do not depend on the mass or moles present in the system. We will consider an example of converting mass fractions to mole fractions, but the opposite would also work. Question: Consider a hydrocarbon mixture that is 20 mole % carbon, and 80 mole % hydrogen. What is the composition on a mass basis? Solution: Because we know mole fractions, we assume a total number of moles. Let’s assume total moles = 100. In that case, we have 20 moles of carbon, and 80 moles of hydrogen, which corresponds to 240 kg of carbon and 80 kg of hydrogen. Therefore, the mixture is 75 mass % carbon, and 25 mass % hydrogen. Lever Rule Returning to Tx diagrams, recall that the lever rule applies in 2 phase regions. This is different from components. When asked about components (composition) – that is something you read from the x-axis of the graph. When you’re asked about phases – that is something to use the lever rule for. Also recall that the lever rule gives a fraction. If the x-axis of the graph is in mole fractions, then the lever rule will give an answer in mole fraction.
37 BYC Concept Clarifier Use the following solid-liquid equilibrium diagram for a mixture of A and B to answer the following questions
6kg of solid B is placed in a container. 14kg of solid A is added to the container at room temperature. The container is slowly heated. a) At what temperature would liquid appear? b) At what temperature will the entire mixture be a liquid? The container is then cooled slowly. c) At what temperature will the mixture begin to crystalize? The mixture is then brought to 450°C d) What is the mass percent of B in the mixture? e) What is the mass percent of liquid in the mixture? f) What is the mass percent of B in the liquid phase?
38 Tip: Keep in mind that solids do not mix. If you start with a mixture of two separate solids, they must first be melted and mixed before you can locate them on the phase diagram. Addition of Components One common type of question is: How much of component A needs to be added before a second phase appears? The solution to these questions entails a similar methodology every time, and can best be demonstrated by an example. Refer to the previous question, at point F: The mixture is 30 mass% B and held at 450°C. Determine the minimum amount (in kg) of B that should be added to make the entire mixture a liquid. Is there a maximum amount?
Constructing Binary Phase Diagrams You may be required to construct binary phase diagrams from data you’re provided. There is no set method to do this, but the process tends to be similar across questions. 1) 2) 3) 4) 5)
Begin by taking note of the type of diagram you have. Label the pure component melting/boiling points Label points of maximum solubility Draw the triple phase line (if applicable) Label any azeotropes or eutectic points
This is best demonstrated through an example.
39 BYC Concept Clarifier You know the following information about a binary mixture of X and Y: • • • • •
There is a eutectic at 900°C with 35% X in Y (mole percent) X has a maximum solubility of 5% in Y (mole percent) Y has a maximum solubility of 10% in X (mole percent) Pure X melts at 1300°C and pure Y melts at 1000°C At 700°C: o X has a solubility of 1% in Y o Y has a solubility of 3% in X Use this information to sketch the solid-liquid Tx diagram for X in Y (mole percent)
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Exam questions The most common types of questions would ask you • • • • • • •
Label regions on a phase diagram Apply the phase rule to the system Locate a system on a phase diagram and be able to navigate on the diagram with changing conditions Determine the amount of you each phase present in a two phase region Convert between mass and mole fractions Maximum solubility Adding/removing a component to change the number of phases
And you can expect to be given: • •
Equilibrium data – phase diagram Molar mass if necessary
Make sure to: • • •
Label all regions on the graph, even if the question doesn’t ask for it Distinguish between phase and component Apply the lever rule correctly and only in 2 phase regions
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Practice Questions
1) Use the above solid-liquid equilibrium diagram to answer the following questions: a) What is the melting temperature of tin? b) What is the maximum solubility of lead in tin? c) What is the composition of a 10kg mixture that is 50% liquid, 50% solid α, at 250°C? d) The mixture in part(b) is heated. At what point does the last piece of solid melt? What is the composition of the last crystal? e) The mixture is then cooled back to 200°C. Determine the minimum and maximum amounts of tin that can be added to only have liquid present. f) Assuming you added the minimum amount of Tin in part (d), you then heat the mixture to 300°C. How much lead can be added before solid begins to form? What is the composition of the first solid crystal?
42 2) Use the following information for a system of A and B at 300kPa: i) MA = 60 kg/kmol ii) MB = 80 kg/kmol iii) Melting point of pure A is 500°C iv) Melting point of pure B is 300°C v) Maximum solubility of B in A is 10 mol% vi) Maximum solubility of A in B is 0% vii) At 200°C, there is a eutectic point with 45 mol% B viii)The solubility of B in A at 100°C is 3% ix) At 250°C, there is: a. A liquidus point with 27.5 mol% A b. A solidus point with 95 mol% A c. A liquidus point with 22.5 mol% B a) Sketch and label the diagram based on the above information
b) A mixture consists of 10kg of B and 15kg of A at 100°C. Determine the phases present, their compositions and moles c) The mixture is then heated to 250°C. Determine the phases present, their compositions and moles.
SECTION 5 – PHASE BEHAVIOUR, BINARY MIXTURES In this section, we will review phase diagrams for binary mixtures, and the types of questions you could be asked in the exam. Recall from the phase rule that: Degrees of Freedom = Components – Phases + 2 Because we now have 2 components, a 1 phase region has 3 degrees of freedom. Since it’s near impossible to read and interpret 3D graphs on paper, we specify 1 degree of freedom, and graph the remaining 2 degrees of freedom. The most common diagram in this section is a Temperature-Composition (Tx) diagram. To have a 2-dimensinoal Tx diagram, we often specify the pressure of the system. This specification is either in the title of the graph, or is somewhere in the description of the question. The reason this is important is that specifying pressure takes up a degree of freedom, which would leave you with 2 degrees of freedom in a single phase region. If you’re asked about the degrees of freedom of the system, be sure to look for the pressure to see if it has been specified somewhere.
Temperature – Composition (Tx) Diagrams Tx diagrams is a general term for many different types of graphs you can expect to see. The actual shape of the graph will depend on two things: 1) Phases present: a. Liquid-vapor diagrams b. Solid-liquid diagrams 2) Miscibility a. Completely miscible b. Partially miscible c. Completely immiscible In the general case, the phases present do not change the shape of the graph, but only change the interpretation of the graph and the labelling of the regions. On any Tx diagrams, the x-axis represents a mass (weight) fraction or a mole fraction – take note of this difference. Because the axis represent a fraction, it only ranges from 0 to 1. At either end of the x-axis, you have a pure component, it is worth labelling which pure component exists at which end.
34 The y-axis represents temperature. Therefore, labelling regions on a Tx diagram should be intuitive. In a liquid-vapor diagram, vapor exists at higher temperature and liquid at lower temperatures. In solid-liquid diagrams, liquid exists at the higher temperature while the solid at the lower temperatures. In cases where the two components aren’t completely miscible, there will be multiple liquid or solid phases. In the case where you have multiple liquid phases, then one liquid phase will exist on the right side of the diagram, and one liquid phase will exist on the left side of the diagram. Below are a variety of Tx diagrams:
35
36 Important points to know: •
The triple phase line – in partially miscible or completely immiscible systems • The bubble point/melting point of the pure component – occurs at x = 0 or x=1 • Maximum solubility of one component in another – occurs at the temperature of the triple phase line • Dew point curve, bubble point curve, saturated liquid curve, and saturated vapor curve all still apply as before • Azeotrope – occur on some completely miscible liquid-vapor diagrams, where the composition of the vapor is identical to the composition of the liquid • Hetero-azeotrope – occurs on partially miscible or immiscible liquid-vapor diagrams, where the composition of the vapor is identical to the composition of both liquids • Eutectic point – occurs on solid-liquid diagrams, and is the lowest melting point of the mixture Similar to Pv diagrams, if you’re interested in knowing compositions of each phase in a 2 phase region, you can navigate left or right to the boundary and read the composition of the phase there. Converting between mass fractions and mole fractions: Recall that both mass fractions and mole fractions are intensive properties, and hence do not depend on the mass or moles present in the system. We will consider an example of converting mass fractions to mole fractions, but the opposite would also work. Question: Consider a hydrocarbon mixture that is 20 mole % carbon, and 80 mole % hydrogen. What is the composition on a mass basis? Solution: Because we know mole fractions, we assume a total number of moles. Let’s assume total moles = 100. In that case, we have 20 moles of carbon, and 80 moles of hydrogen, which corresponds to 240 kg of carbon and 80 kg of hydrogen. Therefore, the mixture is 75 mass % carbon, and 25 mass % hydrogen. Lever Rule Returning to Tx diagrams, recall that the lever rule applies in 2 phase regions. This is different from components. When asked about components (composition) – that is something you read from the x-axis of the graph. When you’re asked about phases – that is something to use the lever rule for. Also recall that the lever rule gives a fraction. If the x-axis of the graph is in mole fractions, then the lever rule will give an answer in mole fraction.
37 BYC Concept Clarifier Use the following solid-liquid equilibrium diagram for a mixture of A and B to answer the following questions
6kg of solid B is placed in a container. 14kg of solid A is added to the container at room temperature. The container is slowly heated. a) At what temperature would liquid appear? b) At what temperature will the entire mixture be a liquid? The container is then cooled slowly. c) At what temperature will the mixture begin to crystalize? The mixture is then brought to 450°C d) What is the mass percent of B in the mixture? e) What is the mass percent of liquid in the mixture? f) What is the mass percent of B in the liquid phase?
38 Tip: Keep in mind that solids do not mix. If you start with a mixture of two separate solids, they must first be melted and mixed before you can locate them on the phase diagram. Addition of Components One common type of question is: How much of component A needs to be added before a second phase appears? The solution to these questions entails a similar methodology every time, and can best be demonstrated by an example. Refer to the previous question, at point F: The mixture is 30 mass% B and held at 450°C. Determine the minimum amount (in kg) of B that should be added to make the entire mixture a liquid. Is there a maximum amount?
Constructing Binary Phase Diagrams You may be required to construct binary phase diagrams from data you’re provided. There is no set method to do this, but the process tends to be similar across questions. 1) 2) 3) 4) 5)
Begin by taking note of the type of diagram you have. Label the pure component melting/boiling points Label points of maximum solubility Draw the triple phase line (if applicable) Label any azeotropes or eutectic points
This is best demonstrated through an example.
39 BYC Concept Clarifier You know the following information about a binary mixture of X and Y: • • • • •
There is a eutectic at 900°C with 35% X in Y (mole percent) X has a maximum solubility of 5% in Y (mole percent) Y has a maximum solubility of 10% in X (mole percent) Pure X melts at 1300°C and pure Y melts at 1000°C At 700°C: o X has a solubility of 1% in Y o Y has a solubility of 3% in X Use this information to sketch the solid-liquid Tx diagram for X in Y (mole percent)
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Exam questions The most common types of questions would ask you • • • • • • •
Label regions on a phase diagram Apply the phase rule to the system Locate a system on a phase diagram and be able to navigate on the diagram with changing conditions Determine the amount of you each phase present in a two phase region Convert between mass and mole fractions Maximum solubility Adding/removing a component to change the number of phases
And you can expect to be given: • •
Equilibrium data – phase diagram Molar mass if necessary
Make sure to: • • •
Label all regions on the graph, even if the question doesn’t ask for it Distinguish between phase and component Apply the lever rule correctly and only in 2 phase regions
41
Practice Questions
1) Use the above solid-liquid equilibrium diagram to answer the following questions: a) What is the melting temperature of tin? b) What is the maximum solubility of lead in tin? c) What is the composition of a 10kg mixture that is 50% liquid, 50% solid α, at 250°C? d) The mixture in part(b) is heated. At what point does the last piece of solid melt? What is the composition of the last crystal? e) The mixture is then cooled back to 200°C. Determine the minimum and maximum amounts of tin that can be added to only have liquid present. f) Assuming you added the minimum amount of Tin in part (d), you then heat the mixture to 300°C. How much lead can be added before solid begins to form? What is the composition of the first solid crystal?
42 2) Use the following information for a system of A and B at 300kPa: i) MA = 60 kg/kmol ii) MB = 80 kg/kmol iii) Melting point of pure A is 500°C iv) Melting point of pure B is 300°C v) Maximum solubility of B in A is 10 mol% vi) Maximum solubility of A in B is 0% vii) At 200°C, there is a eutectic point with 45 mol% B viii)The solubility of B in A at 100°C is 3% ix) At 250°C, there is: a. A liquidus point with 27.5 mol% A b. A solidus point with 95 mol% A c. A liquidus point with 22.5 mol% B a) Sketch and label the diagram based on the above information
b) A mixture consists of 10kg of B and 15kg of A at 100°C. Determine the phases present, their compositions and moles c) The mixture is then heated to 250°C. Determine the phases present, their compositions and moles.
