section 4 â phase behaviour, pure component
21
SECTION 4 – PHASE BEHAVIOUR, PURE COMPONENT The Gibbs phase rule is one of the core concepts to this section. Although this rule is simple, it carries a great amount of explanation when trying to define a chemical system. The important thing is to be able to correctly define each term in the equation, and be able to interpret the outcome. The phase rule states: Degrees of Freedom = Components – Phases + 2 Where each term is defined as follows: Components is the number of independent chemical species. In a non-reactive system, this is the same thing as saying the number of different types of molecules present. Phases is the number of heterogeneous phases present. A phase is heterogeneous if it has a distinct phase boundary. This expands the definition of phase beyond the conventional solid-liquid-gas. There could exist multiple liquid phases, such as oil and water for example. However, you can only have a single gas phase. Degrees of freedom is the number of intensive variables needed to define the system. An alternative description is that it’s the number of variables you can change for the system. To understand this, we need to define intensive variables. Intensive variables are those that do not depend on the size of the system. Things like temperature, pressure, density, mole fraction, weight fraction, and molar volume are all intensive properties. Extensive variables are those that do depend on the size of the system. Things like volume, mass and moles would be considered extensive properties. It is important to note that the phase rule specifically applies to systems in equilibrium. For example, if you place an ice cube in a cup of water, you have to wait until they reach equilibrium before you can apply the phase rule. The power of the phase rule comes from the fact that it provides us with the degrees of freedom of a system. This gives us an idea of how many variables we can vary to maintain the number of components and phases we have present. As you will see in the next section, the degrees of freedom can be analogous to physical dimensions. The best way to understand the phase rule is through examples.
22 In the following chemical systems, define the number of components, the number of phases, then calculate the degrees of freedom and give an example of what properties can be used to define the system: a) b) c) d) e) f) g) h) i)
Pure water as it’s boiling Liquid nitrogen in a storage vessel Natural gas (methane, ethane and some propane) Tea (milk, sugar, water and tea) at room temperature Salt in water (before saturation is reached) Supersaturated mixture of salt and water A water-oil mixture at its bubble point (vapor-liquid equilibrium) A non-reactive system of ammonia, nitrogen and hydrogen A reactive system of ammonia, nitrogen and hydrogen
Question A B C D E F G H I
Phases
Components
Degrees of Freedom
23
Pressure-Temperature Diagrams Pressure – Temperature (PT) Diagrams are the simplest diagrams you can ever see in this course. There are a few important points and regions you should be able to identify, you should be able to interpret the diagram, and you should be able to move along the diagram. Let’s begin by looking at a PT diagram:
You’ll notice that it is typical to label pressure on the y-axis, and temperature on the x-axis. Most PT diagrams are generally the same shape. The two points you should be able to identify are: • •
Triple point – where all 3 phases coexist Critical point – after which liquid and vapor cannot be distinguished
The regions you should be able to label are: • • • •
Solid – existing at low temperature and high pressure Liquid – existing at higher temperature, and high pressure Vapor – existing at low pressures Supercritical region – existing at high temperature an high pressure, beyond the critical point Regions represent the existence of a single phase. Each line represents a 2 phase equilibrium, and the triple point is where all 3 phases coexist. Let’s return to the phase rule: For a pure component F = 3 – P. Phases 1 2 3
Degrees of Freedom 2 1 0
On graph Region Line Point
Physical dimension 2 1 0
24
We can see that the number of physical dimensions on the graph is identical to the degrees of freedom of the system. This is not a coincidence. In fact, we use physical dimension (an axis) to represent a degree of freedom. When we have more than 3 degrees of freedoms, graphs can get complex as we begin plotting 3 dimensional phase diagrams (which aren’t on your exams). Note that this concept only applies to PT diagrams. After being able to label the diagram and interpret the axis and lines, you will need to know have to navigate on the graph. Fortunately, this is an easy task on PT diagrams. If you need to change temperature at a constant pressure, you move horizontally, and vice versa. One short-coming of PT diagrams is that if we have two phases, we don’t know how much we have of each phase because it’s a single line.
Pressure – Specific Volume (Pv) Diagrams Similar to PT diagrams, Pv diagrams allow you to identify which phases are present given a pressure and specific volume. Pv diagrams are slightly more complex however, because they also incorporate temperature and 2 phase regions. Let’s begin by looking at a typical Pv diagram:
25 Important points to know: • •
Critical point – after which liquid and vapor cannot be distinguished. This point is at the peak of the dome The triple point actually becomes a line, and is known as the triple phase line. It exists at the base of the dome
Important regions to know: • • • • •
•
A solid exists at the lowest specific volume (highest density) A liquid exists at the intermediate specific volumes A vapor exists a higher specific volume, and lower pressures There are 3 regions called 2 phase regions where two phases coexist For the liquid-vapor envelope: o The left side is the bubble point curve, or saturated liquid o The right side is the dew point curve, or saturated vapor o The entire envelope is known as the saturation curve A gas exists at high temperature (to be defined shortly)
Previous exam question: How many degrees of freedom are present at the critical point?
26 Once you’re able to label the diagram, you can add what is known as isotherms. Isotherms represent lines where the temperature is equal along the lines. A few important properties of isotherms: • • • •
Every point along the isotherm is at the same temperature Higher isotherms are at higher temperatures Isotherms are horizontal in 2 phase regions, and downward sloping in single phase regions The critical isotherm is the isotherm that passes through the critical point A gas exists at temperatures that are higher than the critical isotherm
Pv diagrams are most commonly used on liquid-vapor systems, so you’ll often just see what is known as the liquid vapor envelope. If you don’t clearly see a solid region, you can assume it’s not there – but if you get this on a test, you can ask your professor to confirm. Everything still works the same way, except the diagram is a little more simplified and looks as follows:
Navigating a Pv diagram is relatively straight forward. When moving isobarically, you move left to right. When moving isothermally, you follow the isotherm you’re on. If your system is closed in a rigid container, then both mass and volume are fixed, and so is specific volume – so you’ll be moving vertically. Pv diagrams overcome the shortcoming of PT diagrams in that they can provide information about how much of each phase is present and they can provide information about each phase. If you’re in a 2 phase region, and you want information about either phase, then simply move horizontally to the region’s boundary to get that information. For example, if you’re in the liquid-vapor envelope and you want to know the specific volume of the liquid, you move horizontally towards the liquid side (left) until you reach the boundary, then you read the specific volume at that point.
27
Lever Rule The lever rule is very simple conceptually, and can provide us with a lot of information. Unfortunately, there are small details in applying the lever rule where many students make mistakes. The lever rule is to be used in a 2 phase region to get phase information. This point is crucial in applying the lever rule, and you’ll see why in the next section. There are two important things to remember when applying the lever rule: 1) The lever rule gives you a ratio. This ratio will depend on the method you used to calculate it 2) You need to look at the side opposite of the phase you’re interested in Because the lever rule can be applied in any two phase region, we will consider how it applies to the liquid-vapor envelope, and the equations can be modified to fit other regions. In the liquid-vapor region, the vapor rule states: 𝑚𝑙 𝑣𝑣 − 𝑣𝑚 = 𝑚𝑚 𝑣𝑣 − 𝑣𝑙 or 𝑚𝑣 𝑣𝑚 − 𝑣𝑙 = 𝑚𝑚 𝑣𝑣 − 𝑣𝑙 Recall from the previous section that the specific volume of liquid and vapor can be acquired from the boundary of the 2 phase region, and the specific volume of the mixture would probably be given in the question or calculated in previous parts of the question. First, notice that because we’re using specific volume (m3/kg) to calculate the ratio, we will be getting a mass ratio. If we were to use molar volume (m3/kmol), then we would get a molar ratio. This isn’t too important when dealing with pure component systems, but it is a common mistake when dealing with binary mixtures. Second, notice how when calculating the liquid fraction, we use the vapor and mixture specific volumes, and when calculating the vapor fraction, we use the liquid and mixture specific volumes. This can be visualized best by drawing the isotherm from the Pv diagram into a single line, and using that to calculate the ratio.
28 BYC Concept Clarifier A new chemical has been synthesized, and tested in the lab to determine the follow Pv diagram:
29 a) As the safety engineer in the company, your role is to determine whether this substance can be safely used in the following conditions. The lab technicians want to hear your reasoning as well, to improve the compound. i) The substance will be stored in gas storage vessels at 5MPa at room temperature ii) The substance is to be used in creating a more complex liquid solution that is to be stored at 10MPa and 30°C without vaporizing iii) The substance is to be used in a gas phase reaction that occurs at 5MPa and 10°C
b) Over what range of pressures will the substance remain a liquid when held at a temperature of 30°C? c) By what factor does this substance expand when vaporized at 20°C? d) What is the boiling temperature of this substance at 7MPa? e) How much of this substance can be stored in a 0.1m3 vessel at 20°C without condensation? f) What is the vapor pressure of this substance at 10°C? g) 20kg of this substance are stored in a 0.1m3 vessel at 20°C. i) What is the mass of liquid present? ii) What is the mass ratio of liquid to vapor at these conditions? iii) What is the vapor density? h) 5 kg of this substance are stored in a 0.05m3 vessel at 30°C. i) What is the volume fraction occupied by the vapor? ii) What is the density of the liquid iii) You allow the liquid to isothermally drain from the system, until only the vapor remains. You then cool the mixture to 20°C. What is the mass of liquid in this system? i) 10kg of this substance is stored in a 0.05m3 vessel at 30°C. This substance is heated until a phase change is observed. i) What is the new phase? ii) What is the temperature? iii) Without changing the volume of the vessel, how much substance should be added/removed to completely change the phase to liquid/vapor (whichever phase that isn’t currently present)
30
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
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 Apply the lever rule correctly
31
Practice Questions 1) Use the following vapor-liquid equilibrium data for ammonia to answer the following questions: T (K)
Specific volume V (cm3/g) bubble point dew point (triple point) 1.67 121.3 1.88 40.87 2.29 14.5 4.26 4.26
P (MPa)
195.4 300 340 380 405.6
0.006 1.06 3.08 7.15 11.29
Determine which phases are present at the following temperature/pressure/volume conditions for 1 kg of pure ammonia. If more than one phase is present, determine the mass of each phase. T (K) 200 380 300 450 340 406 180
P
Volume (cm3)
Phase(s) Present
5.0 kPa 16000 40000 12.0 MPa 3.08 MPa
10000
3.10 MPa 5.00 MPa 700 kPa
a) Estimate the vapor pressure of ammonia at 360K b) Estimate the boiling point of ammonia at 1000kPa.
Mass of each phase (g)
Density of each phase (g/cc)
32 2) Use the following data to answer the following questions:
a) b) c) d)
e) f)
g)
h)
What are the critical properties of this substance? How many degrees of freedom are present at the critical point? Explain. What are the properties of the triple point for this substance? We place 10 kg of this substance in a variable height 0.1m x 0.5m x 0.3m vessel (w x l x h) at a temperature of 130°C. i. What phases are present in the vessel? ii. What is the pressure inside the vessel? The pressure in the vessel is raised to 1000kPa. What is the temperature in the vessel? The material is then cooled to 100°C. i. What phases are present in the vessel? ii. What is the mass of each phase? iii. What is the density of each phase? iv. What is the volume fraction of each phase? The material is then expanded and heated back to 120°C until the first bubble forms a. What is the density of the first bubble? b. What is the pressure of the system? c. What is the new height of the vessel? Lastly, the vessel is heated to 140°C, and more of the substance is removed at a constant volume until the first bubble forms. a. What is the pressure of the system? b. What is the density of the liquid droplet? c. How much substance was removed?
SECTION 4 – PHASE BEHAVIOUR, PURE COMPONENT The Gibbs phase rule is one of the core concepts to this section. Although this rule is simple, it carries a great amount of explanation when trying to define a chemical system. The important thing is to be able to correctly define each term in the equation, and be able to interpret the outcome. The phase rule states: Degrees of Freedom = Components – Phases + 2 Where each term is defined as follows: Components is the number of independent chemical species. In a non-reactive system, this is the same thing as saying the number of different types of molecules present. Phases is the number of heterogeneous phases present. A phase is heterogeneous if it has a distinct phase boundary. This expands the definition of phase beyond the conventional solid-liquid-gas. There could exist multiple liquid phases, such as oil and water for example. However, you can only have a single gas phase. Degrees of freedom is the number of intensive variables needed to define the system. An alternative description is that it’s the number of variables you can change for the system. To understand this, we need to define intensive variables. Intensive variables are those that do not depend on the size of the system. Things like temperature, pressure, density, mole fraction, weight fraction, and molar volume are all intensive properties. Extensive variables are those that do depend on the size of the system. Things like volume, mass and moles would be considered extensive properties. It is important to note that the phase rule specifically applies to systems in equilibrium. For example, if you place an ice cube in a cup of water, you have to wait until they reach equilibrium before you can apply the phase rule. The power of the phase rule comes from the fact that it provides us with the degrees of freedom of a system. This gives us an idea of how many variables we can vary to maintain the number of components and phases we have present. As you will see in the next section, the degrees of freedom can be analogous to physical dimensions. The best way to understand the phase rule is through examples.
22 In the following chemical systems, define the number of components, the number of phases, then calculate the degrees of freedom and give an example of what properties can be used to define the system: a) b) c) d) e) f) g) h) i)
Pure water as it’s boiling Liquid nitrogen in a storage vessel Natural gas (methane, ethane and some propane) Tea (milk, sugar, water and tea) at room temperature Salt in water (before saturation is reached) Supersaturated mixture of salt and water A water-oil mixture at its bubble point (vapor-liquid equilibrium) A non-reactive system of ammonia, nitrogen and hydrogen A reactive system of ammonia, nitrogen and hydrogen
Question A B C D E F G H I
Phases
Components
Degrees of Freedom
23
Pressure-Temperature Diagrams Pressure – Temperature (PT) Diagrams are the simplest diagrams you can ever see in this course. There are a few important points and regions you should be able to identify, you should be able to interpret the diagram, and you should be able to move along the diagram. Let’s begin by looking at a PT diagram:
You’ll notice that it is typical to label pressure on the y-axis, and temperature on the x-axis. Most PT diagrams are generally the same shape. The two points you should be able to identify are: • •
Triple point – where all 3 phases coexist Critical point – after which liquid and vapor cannot be distinguished
The regions you should be able to label are: • • • •
Solid – existing at low temperature and high pressure Liquid – existing at higher temperature, and high pressure Vapor – existing at low pressures Supercritical region – existing at high temperature an high pressure, beyond the critical point Regions represent the existence of a single phase. Each line represents a 2 phase equilibrium, and the triple point is where all 3 phases coexist. Let’s return to the phase rule: For a pure component F = 3 – P. Phases 1 2 3
Degrees of Freedom 2 1 0
On graph Region Line Point
Physical dimension 2 1 0
24
We can see that the number of physical dimensions on the graph is identical to the degrees of freedom of the system. This is not a coincidence. In fact, we use physical dimension (an axis) to represent a degree of freedom. When we have more than 3 degrees of freedoms, graphs can get complex as we begin plotting 3 dimensional phase diagrams (which aren’t on your exams). Note that this concept only applies to PT diagrams. After being able to label the diagram and interpret the axis and lines, you will need to know have to navigate on the graph. Fortunately, this is an easy task on PT diagrams. If you need to change temperature at a constant pressure, you move horizontally, and vice versa. One short-coming of PT diagrams is that if we have two phases, we don’t know how much we have of each phase because it’s a single line.
Pressure – Specific Volume (Pv) Diagrams Similar to PT diagrams, Pv diagrams allow you to identify which phases are present given a pressure and specific volume. Pv diagrams are slightly more complex however, because they also incorporate temperature and 2 phase regions. Let’s begin by looking at a typical Pv diagram:
25 Important points to know: • •
Critical point – after which liquid and vapor cannot be distinguished. This point is at the peak of the dome The triple point actually becomes a line, and is known as the triple phase line. It exists at the base of the dome
Important regions to know: • • • • •
•
A solid exists at the lowest specific volume (highest density) A liquid exists at the intermediate specific volumes A vapor exists a higher specific volume, and lower pressures There are 3 regions called 2 phase regions where two phases coexist For the liquid-vapor envelope: o The left side is the bubble point curve, or saturated liquid o The right side is the dew point curve, or saturated vapor o The entire envelope is known as the saturation curve A gas exists at high temperature (to be defined shortly)
Previous exam question: How many degrees of freedom are present at the critical point?
26 Once you’re able to label the diagram, you can add what is known as isotherms. Isotherms represent lines where the temperature is equal along the lines. A few important properties of isotherms: • • • •
Every point along the isotherm is at the same temperature Higher isotherms are at higher temperatures Isotherms are horizontal in 2 phase regions, and downward sloping in single phase regions The critical isotherm is the isotherm that passes through the critical point A gas exists at temperatures that are higher than the critical isotherm
Pv diagrams are most commonly used on liquid-vapor systems, so you’ll often just see what is known as the liquid vapor envelope. If you don’t clearly see a solid region, you can assume it’s not there – but if you get this on a test, you can ask your professor to confirm. Everything still works the same way, except the diagram is a little more simplified and looks as follows:
Navigating a Pv diagram is relatively straight forward. When moving isobarically, you move left to right. When moving isothermally, you follow the isotherm you’re on. If your system is closed in a rigid container, then both mass and volume are fixed, and so is specific volume – so you’ll be moving vertically. Pv diagrams overcome the shortcoming of PT diagrams in that they can provide information about how much of each phase is present and they can provide information about each phase. If you’re in a 2 phase region, and you want information about either phase, then simply move horizontally to the region’s boundary to get that information. For example, if you’re in the liquid-vapor envelope and you want to know the specific volume of the liquid, you move horizontally towards the liquid side (left) until you reach the boundary, then you read the specific volume at that point.
27
Lever Rule The lever rule is very simple conceptually, and can provide us with a lot of information. Unfortunately, there are small details in applying the lever rule where many students make mistakes. The lever rule is to be used in a 2 phase region to get phase information. This point is crucial in applying the lever rule, and you’ll see why in the next section. There are two important things to remember when applying the lever rule: 1) The lever rule gives you a ratio. This ratio will depend on the method you used to calculate it 2) You need to look at the side opposite of the phase you’re interested in Because the lever rule can be applied in any two phase region, we will consider how it applies to the liquid-vapor envelope, and the equations can be modified to fit other regions. In the liquid-vapor region, the vapor rule states: 𝑚𝑙 𝑣𝑣 − 𝑣𝑚 = 𝑚𝑚 𝑣𝑣 − 𝑣𝑙 or 𝑚𝑣 𝑣𝑚 − 𝑣𝑙 = 𝑚𝑚 𝑣𝑣 − 𝑣𝑙 Recall from the previous section that the specific volume of liquid and vapor can be acquired from the boundary of the 2 phase region, and the specific volume of the mixture would probably be given in the question or calculated in previous parts of the question. First, notice that because we’re using specific volume (m3/kg) to calculate the ratio, we will be getting a mass ratio. If we were to use molar volume (m3/kmol), then we would get a molar ratio. This isn’t too important when dealing with pure component systems, but it is a common mistake when dealing with binary mixtures. Second, notice how when calculating the liquid fraction, we use the vapor and mixture specific volumes, and when calculating the vapor fraction, we use the liquid and mixture specific volumes. This can be visualized best by drawing the isotherm from the Pv diagram into a single line, and using that to calculate the ratio.
28 BYC Concept Clarifier A new chemical has been synthesized, and tested in the lab to determine the follow Pv diagram:
29 a) As the safety engineer in the company, your role is to determine whether this substance can be safely used in the following conditions. The lab technicians want to hear your reasoning as well, to improve the compound. i) The substance will be stored in gas storage vessels at 5MPa at room temperature ii) The substance is to be used in creating a more complex liquid solution that is to be stored at 10MPa and 30°C without vaporizing iii) The substance is to be used in a gas phase reaction that occurs at 5MPa and 10°C
b) Over what range of pressures will the substance remain a liquid when held at a temperature of 30°C? c) By what factor does this substance expand when vaporized at 20°C? d) What is the boiling temperature of this substance at 7MPa? e) How much of this substance can be stored in a 0.1m3 vessel at 20°C without condensation? f) What is the vapor pressure of this substance at 10°C? g) 20kg of this substance are stored in a 0.1m3 vessel at 20°C. i) What is the mass of liquid present? ii) What is the mass ratio of liquid to vapor at these conditions? iii) What is the vapor density? h) 5 kg of this substance are stored in a 0.05m3 vessel at 30°C. i) What is the volume fraction occupied by the vapor? ii) What is the density of the liquid iii) You allow the liquid to isothermally drain from the system, until only the vapor remains. You then cool the mixture to 20°C. What is the mass of liquid in this system? i) 10kg of this substance is stored in a 0.05m3 vessel at 30°C. This substance is heated until a phase change is observed. i) What is the new phase? ii) What is the temperature? iii) Without changing the volume of the vessel, how much substance should be added/removed to completely change the phase to liquid/vapor (whichever phase that isn’t currently present)
30
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
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 Apply the lever rule correctly
31
Practice Questions 1) Use the following vapor-liquid equilibrium data for ammonia to answer the following questions: T (K)
Specific volume V (cm3/g) bubble point dew point (triple point) 1.67 121.3 1.88 40.87 2.29 14.5 4.26 4.26
P (MPa)
195.4 300 340 380 405.6
0.006 1.06 3.08 7.15 11.29
Determine which phases are present at the following temperature/pressure/volume conditions for 1 kg of pure ammonia. If more than one phase is present, determine the mass of each phase. T (K) 200 380 300 450 340 406 180
P
Volume (cm3)
Phase(s) Present
5.0 kPa 16000 40000 12.0 MPa 3.08 MPa
10000
3.10 MPa 5.00 MPa 700 kPa
a) Estimate the vapor pressure of ammonia at 360K b) Estimate the boiling point of ammonia at 1000kPa.
Mass of each phase (g)
Density of each phase (g/cc)
32 2) Use the following data to answer the following questions:
a) b) c) d)
e) f)
g)
h)
What are the critical properties of this substance? How many degrees of freedom are present at the critical point? Explain. What are the properties of the triple point for this substance? We place 10 kg of this substance in a variable height 0.1m x 0.5m x 0.3m vessel (w x l x h) at a temperature of 130°C. i. What phases are present in the vessel? ii. What is the pressure inside the vessel? The pressure in the vessel is raised to 1000kPa. What is the temperature in the vessel? The material is then cooled to 100°C. i. What phases are present in the vessel? ii. What is the mass of each phase? iii. What is the density of each phase? iv. What is the volume fraction of each phase? The material is then expanded and heated back to 120°C until the first bubble forms a. What is the density of the first bubble? b. What is the pressure of the system? c. What is the new height of the vessel? Lastly, the vessel is heated to 140°C, and more of the substance is removed at a constant volume until the first bubble forms. a. What is the pressure of the system? b. What is the density of the liquid droplet? c. How much substance was removed?
