Anastacia.kudinova s Condensed Phases: Solids and Liquids

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1 CK-12 FOUNDATION Anastacia.kudinova s Condensed Phases: Solids and Liquids Say Thanks to the Authors Click (No sign in required) Parsons

2 To access a customizable version of this book, as well as other interactive content, visit CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform. Copyright 2011 CK-12 Foundation, The names CK-12 and CK12 and associated logos and the terms FlexBook, and FlexBook Platform, (collectively CK-12 Marks ) are trademarks and service marks of CK-12 Foundation and are protected by federal, state and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution/Non-Commercial/Share Alike 3.0 Unported (CC-by-NC-SA) License ( as amended and updated by Creative Commons from time to time (the CC License ), which is incorporated herein by this reference. Complete terms can be found at Printed: November 15, 2011

3 Author Richard Parsons Contributor Anastacia Kudinova Editor Shonna Robinson i

4 Contents 1 Condensed Phases: Solids and Liquids Vapor Pressure and Boiling Heat and Changes of State Phase Diagrams ii

5 Chapter 1 Condensed Phases: Solids and Liquids 1.1 Vapor Pressure and Boiling The phase of a substance is essentially the result of two competing forces acting on the molecules. The molecules of a substance are pulled together by intermolecular forces of attraction, which could be either weak or strong. The molecules of a substance are also in constant random motion so that they are almost constantly colliding with each other. Without any intermolecular forces of attraction, the molecules of all substances would move away from each other, and there would be no condensed phases (liquids and solids). If the forces caused by molecular motion are much greater than the intermolecular forces of attraction, the molecules will separate and the substance will be in the gaseous state. If the intermolecular forces of attraction are stronger than the molecular motion, the molecules will be pulled into a closely packed pattern and the substance will be in the solid state. If there is some balance between molecular motion and intermolecular forces of attraction, the substance will be in the liquid state. When substances are heated (or cooled), their average kinetic energy will increase (or decrease) due to the increase (or decrease) in molecular motion and may result in a phase change. A substance in the solid phase can be heated until the molecular motion balances the intermolecular forces, causing the solid to melt into a liquid. The liquid may be heated until the molecular motion completely overcomes the intermolecular forces, causing the liquid to vaporize into the gaseous state. Evaporation and Condensation Evaporation The temperature in a beaker of water is a measure of the average kinetic energy of the molecules in the beaker. This does not mean that all the molecules in the beaker have the same amount of kinetic energy. Most of the molecules will be within a few degrees of the average, but a few molecules may be considerably hotter or colder than the average. The kinetic energy of the molecules in the breaker will have a distribution curve similar to a standard distribution curve for most naturally occurring phenomena. For most naturally occurring phenomena, most instances of the phenomena will occur near the average. Instances that occur 1

6 further away from the average are increasingly rare, as seen in the image below. In the case of a beaker of water, some of the molecules will have an average temperature below the boiling point, while some of the molecules will have a temperature above the boiling point (see figure below). The dashed yellow line is the average temperature of the molecules and would be the temperature shown on a thermometer inserted into the liquid. The red line represents the boiling point of water (100 C at 1.0 atm pressure), and the area under the curve to the right of the red line represents the number of molecules that are above the boiling point. In order for a molecule above the boiling temperature to escape from the liquid, it must either be on the surface, or it must be adjacent to many other molecules that are above the boiling point so that the molecules can form a bubble and rise to the surface. Water boils only when a sufficient number of adjacent molecules are above the boiling point and can form bubbles of gaseous water, as seen below. The process of molecules escaping from the surface of a liquid when the average temperature of the liquid is below the boiling point is called evaporation. 2

7 The phase change process is a little more complicated than just having the molecules reach the boiling point. Gaseous molecules have a force of attraction between them due to the separation between the molecules. Recall two oppositely charged objects that are separated have potential energy, and the amount of potential energy can be calculated by multiplying the force of attraction times the distance of separation. At the same temperature, the same molecules in the liquid state and the gaseous state do not have the same total energy. If they are at the same temperature, they have the same kinetic energy, but the gaseous molecules have additional potential energy that the liquid molecules do not have. As a result, molecules in the liquid state hot enough to exist in the gaseous state must absorb energy from their surroundings to gain the potential energy needed to change phase. This potential energy is called the heat of vaporization. If a saucer of water is sitting out on the countertop, the water will slowly disappear yet, at no time is the temperature of the water ever at the boiling point. When molecules of a liquid are evaporating, it is clear that it is the hottest molecules that are evaporating. It might seem that once the hottest molecules are gone, evaporation would no longer continue. This is not true, as the water in an open container continues to evaporate until it is all in the vapor state. When a substance is a vapor, the substance is in the gaseous phase even though the substance is at a temperature below its boiling point. Note that a substance in the gaseous phase at temperatures above the boiling point of its liquid is called a gas, not vapor. Evaporation continues because the temperature of the liquid is the average temperature of all the molecules. When the hottest molecules evaporate, the average temperature of those molecules left behind is lower, so the molecules left behind also contribute to the heat of vaporization to the evaporating molecules. The process of evaporation causes the remaining liquid to cool significantly. Heat flows from warmer objects to colder objects, so when the liquid cools due to evaporation, the surroundings will give heat to the liquid. The temperature of the liquid is raised so that it matches the temperature of the surroundings, thus producing more hot molecules. This process can continue in an open container until the liquid is all evaporated. The rate of evaporation is related to the strength of the intermolecular forces of attraction, to the surface area of the liquid, and to the temperature of the liquid. As the temperature of a liquid gets closer to the boiling point, more of the molecules will have temperatures above the boiling point, resulting in faster evaporation. Substances with weak intermolecular forces of attraction evaporate more quickly than those with strong intermolecular forces of attraction. Substances that evaporate readily are called volatile, while those that hardly evaporate at all are called non-volatile. Condensation Liquids in an open container will usually evaporate completely. What happens, however, if the container is closed? When a lid is placed over the container, the molecules that have evaporated are now kept in the space above the liquid. This makes it possible for a gaseous molecule to condense back to a liquid after colliding with another molecule or a wall, as seen in the figure below. This process where a gas or vapor is 3

8 changed into a liquid is called condensation. Molecules at the boiling point can exist in either the liquid phase or gaseous phase the only difference between them is the amount of potential energy they hold. See below figure. For a liquid molecule with adequate temperature to exist in the gaseous phase, it needs to gain the heat of vaporization. It does this by colliding with adjacent molecules. For a gaseous molecule to return to the liquid phase, it must give up the same amount of potential energy that it gained. This amount of potential energy is called the heat of vaporization when it is being gained and the heat of condensation when it is being lost, but the amount of energy gained or lost is the same amount. As more and more molecules evaporate in a closed container, the partial pressure of the gas in the space above the liquid increases. The rate at which the gas condenses is determined by the partial pressure of the gas, the surface area, and the substance involved. Once these factors are established, the rate of condensation will only vary depending on the partial pressure of the gas. As the partial pressure of the gas in the space above the liquid increases, the rate of condensation will increase. It was pointed out that as a liquid evaporates, the remaining liquid cools because the hottest molecules are leaving, so the average temperature decreases and the heat of vaporization is absorbed from the remaining molecules. For similar reasons, when a gas is undergoing condensation, the temperature of the remaining gas increases because the coolest molecules are condensing, thus raising the average of those left behind. The condensing molecules must then give up the heat of condensation. Vapor Pressure You can follow the progress of evaporation and condensation in a thought experiment. Suppose we place some liquid water in an Erlenmeyer flask and seal it. No water has evaporated yet, so the partial pressure of water vapor in the space above the liquid is zero. As a result, no condensation is taking place. As the water evaporates (at a constant rate since the temperature and surface area are constant), the partial pressure of the water vapor increases. Now that some vapor exists, condensation can begin. Since the partial pressure of the water vapor is low, the rate of condensation will be low. Over time, more and more water evaporates, causing the partial pressure of the water vapor to increase. Since the partial pressure has increased, the rate of condensation also increases. Eventually, the rate of condensation will become high enough that it is equal to the rate of evaporation. Once this happens, the rate of water molecules entering the vapor phase and the rate of water molecules condensing back into liquid are exactly the same, so the partial pressure no longer increases. When the partial pressure of the water vapor becomes constant, the rate of condensation is constant and is exactly equal to the rate of evaporation. As a result, the pressure exerted by the vapor of a solid or 4

9 liquid in equilibrium with the vapor is known as the equilibrium vapor pressure. As time goes on from this point, neither the amount of liquid or the amount of gas can change; consequently, neither the rate of evaporation nor the rate of condensation can change. Everything remains exactly the same, and evaporation and condensation will continue at exactly the same rate. As seen in Table 1.1, a liquid will establish an equilibrium vapor pressure at all temperatures. The pressure of the vapor in the space above the liquid is called the vapor pressure of that liquid at that temperature. Table 1.1: Vapor Pressure of Water at Various Temperatures Temperature in C Vapor Pressure in Torr Volatile liquids would have higher vapor pressures than water at the same temperature, and non-volatile liquids would have lower vapor pressures at the same temperature. The amount of volume for the space above the liquid makes no difference. If the space is small, it will take little gas to produce the pressure, and if the space is large, it will take much more gas to produce the pressure. As long as you introduce enough liquid into the container so that vapor pressure equilibrium will be reached, then the precise vapor pressure will be attained. Note that the equilibrium vapor pressure of a liquid is the same regardless of whether or not another gas is present in the space above the liquid. If the space above liquid water contains air at 760 torr and the liquid water evaporates until its equilibrium vapor pressure (25 torr) is reached, then the total pressure in the space above the liquid will be785 torr. The presence of the air in no way affects the vapor pressure. When gaseous substances are produced from chemical reactions and collected in the laboratory, they are usually collected over water. The collection over water technique is inexpensive and allows gaseous substances to be collected without having air mixed in. The process involves filling a collecting jar with water and inverting the jar in a pan of water without letting any water out or air in, as illustrated below. In the sketch above, the picture on the far left represents the collecting jar full of water and inverted in a pan of water. A tube runs from the reaction vessel where the gas is produced and is tucked under the edge of the collecting jar. As the gas is produced and comes out the end of the tube, it bubbles up through the 5

10 water and pushes the water out of the jar. When the water in the collecting jar and the pan are exactly level, as in the picture at the far right, the pressure inside the collecting jar and the atmospheric pressure in the lab are equal. Using the pressure and temperature in the lab, as well as the volume of the jar to the water level, you can calculate how much gas you produced. (Plug P and R into PV = nrt and solve for n). It turns out, however, that you must make a correction before you plug in the pressure value. Since the collecting jar is a closed container and it has liquid water in the bottom of it, it will contain the vapor pressure of water at this temperature. Consequently, the pressure in the lab tells you the pressure inside the collecting jar, but it doesn t tell you how much of that pressure is due to the gas collected and how much is due to water vapor. You must get a table of the vapor pressure of water at each temperature and look up the vapor pressure of water at the temperature of your lab and then subtract that pressure from the total pressure in the collecting jar. The result will be the actual pressure of the gas collected. Example: Some hydrogen gas was collected over water in the lab on a day that the atmospheric pressure was 755 torr and the lab temperature was 20 C. Hydrogen gas was collected in the collecting jar until the water levels inside and outside the jar was equal. What was the partial pressure of the hydrogen in the collecting jar? Solution: The total pressure in the collecting jar is 755 torr and is equal to the sum of the partial pressure of hydrogen in the jar and the vapor pressure of water at 20 C. From the table, the vapor pressure of water at 20 C is 17.5 torr. Partial pressure of H 2 = 755 torr 17.5 torr = 737 torr The Boiling Point of a Liquid Imagine you are boiling water in a place where the atmospheric pressure is 1.00 atm. In the boiling water, a large bubble forms near the surface of the liquid. The bubble remains the same size as it rises to the top of the water, where the gas can escape into the air. If the pressure of the gas inside that bubble had been less than 1.00 atm, the outside pressure of the atmosphere would have crushed the bubble. If the pressure of the gas inside that bubble had been greater than 1.00 atm, the bubble would have expanded to a larger size, instead of remaining at the same size. The fact that the bubble remained at the same size indicates that the gas pressure inside that bubble was the same as the atmospheric pressure. When you are heating water in an effort to boil it, gas bubbles cannot form until the water can produce a vapor pressure equal to the surrounding air pressure. The hotter the water gets, the higher its vapor pressure becomes. The liquid cannot boil, however, until its vapor pressure is equal to the pressure on the surface of the liquid. The boiling point is the temperature at which the vapor pressure of the liquid equals the surrounding pressure. If you are measuring boiling points at the normal sea level atmospheric pressure of 1.00 atm, a liquid more volatile than water such as chloroform will boil at 61.3 C. This is because the vapor pressure of chloroform is 1.00 atm at 61.3 C. The vapor pressure of ethanol reaches 1.00 atm at a temperature of 78.4 C, so this is the normal boiling point of ethanol. Since liquids boil when their vapor pressures become equal to the surrounding pressure, if the surrounding pressure is lower, the liquids will boil at lower temperatures. At higher altitudes, atmospheric pressure is lower. In cities whose altitude is around 5, 000 feet, water boils at 95 C instead of at 100 C, and at 10, 000 feet, water boils around 90 C. The water boils in normal fashion, but its temperature is lower. As a result, cooking in boiling water takes a longer time at higher altitudes. If a container of water is placed in a bell jar and a vacuum pump attached so that the air pressure around the water can be greatly reduced, water may be made to boil at very low temperatures. At room 6

11 temperature, 20 C, the vapor pressure of water is 17.5 mm of Hg, so if the pressure in the bell jar is reduced to 17.5 mm of Hg, water will boil at 20 C. The appearance of the boiling water is the same as it is at 100 C, but the water can be removed from the bell jar and poured on your hand without burning. If the surrounding pressure is less than 1.00 atm, the boiling points of liquids will be lower. Conversely, if the surrounding pressure is greater than 1.00 atm, the boiling points of liquids will be higher. If we use a strong container with a lid that screws on very tightly, as we boil water in the container, the gas pressure in the container will increase. As the pressure in the container increases, the boiling point of the water increases. The vapor pressure of liquid water at 120 C is 2.00 atm. Therefore, if we can raise the pressure inside a sealed container to 2.00 atm, water will not boil in the container until its temperature is 120 C. This is the concept that is used in pressure cookers and rice cookers. The cooking pot has a tightly sealing lid and a valve in the lid. The valve will open slightly when the pressure inside the container reaches 2.00 atm, helping to maintain the inside pressure at 2.00 atm. The pressure and the boiling point of water will therefore increase inside the container until the pressure reaches 2.00 atm. The temperature of the boiling water inside will be 120 C. Under these conditions, any food placed inside the pressure cooker will cook in as little as one-third the normal time. Lesson Summary Molecules of liquid may evaporate from the surface of a liquid. When molecules of a liquid evaporate, the remaining liquid cools. Gas molecules in contact with their liquid may condense to liquid form. If a liquid is placed in a closed container, eventually vapor pressure equilibrium will be reached. The boiling point of a liquid is the temperature at which the vapor pressure of the liquid becomes equal to the surrounding pressure. The normal boiling of a liquid is the temperature at which the vapor pressure of the liquid becomes equal to 1.00 atmosphere. Further Reading / Supplemental Links The following website provides more information about vapor pressure

12 This video is a ChemStudy film called Gas Pressure and Molecular Collisions. The film is somewhat dated but the information is accurate. Review Questions 1. In the following groups of substances, pick the one that has the requested property and justify your answer. (a) highest boiling point: HCl, Ar, F 2 (b) highest melting point: H 2 O, NaCl, HF (c) lowest vapor pressure at 20 C: Cl 2,Br 2, I 2 2. A flask half-filled with water is sealed with a stopper. The space above the water contains hydrogen gas and water vapor in vapor pressure equilibrium with the liquid water. The total pressure of the two gases is 780. mm of Hg at 20. C. The vapor pressure of water at 20. C is 19 mm of Hg. What is the partial pressure of the hydrogen gas in the flask? 3. Describe all the reasons that the remaining liquid cools as evaporation occurs. 4. Describe all the reasons that the remaining gas gets hotter as condensation occurs. 5. A flask half-filled with water is sealed with a stopper. The space above the water contains hydrogen gas and water vapor in vapor pressure equilibrium with the liquid water. The total pressure of the two gases is 780. mm of Hg at 20. C. The vapor pressure of water at 20. C is 19 mm of Hg. What is the partial pressure of the hydrogen gas in the flask? 1.2 Heat and Changes of State Lesson Objectives The student will: calculate the energy changes during phase changes. explain the slopes of the various parts in heating and cooling curves. explain why it is necessary for a solid to absorb heat during melting even though no temperature change is occurring. calculate, given appropriate thermodynamic data, the heat required to raise temperatures of a given substance with no phase change. calculate, given appropriate thermodynamic data, the heat required to melt specific samples of solids with no temperature change. calculate, given appropriate thermodynamic data, the heat required to produce both a phase change and temperature change for a given sample of solid. Vocabulary freezing freezing point fusion heat of fusion melting melting point specific heat 8

13 Introduction In order to vaporize a liquid, heat must be added to raise the kinetic energy (temperature) to the boiling point. Upon reaching the phase change temperature, additional heat is still needed to provide the potential energy to separate the molecules into gaseous form. The melting point of a substance, like its boiling point, is directly related to the strength of the forces of attraction between molecules. Low melting points are typical of substances whose forces of attraction are very weak, such as hydrogen gas whose melting point is 259 C. High melting points are associated with substances whose forces of attraction are very strong, such as elemental carbon whose melting point is greater than 3500 C. Heating and Melting Curves The addition of heat before, during, and after a phase transition can be analyzed with the help of a heating curve. In the heating curve below, a sample of water at 20 C and 1.00 atm pressure is heated at a constant rate. Between the temperatures of 20 C and 0 C, all the heat added is absorbed as kinetic energy, causing the temperature of the solid to increase. Upon reaching the melting point, even though heat is still being added at the same rate, the temperature does not increase. All the heat added during this time goes into providing the potential energy needed to melt the solid; this energy represents the heat of melting. During this flat line period, an observer would see the water changing from solid to liquid. Both the water in solid form and the water in liquid form would be at exactly 0 C. Adding more heat causes the water to melt faster, but the temperature does not increase until all of the solid has been converted to liquid. If the liquid is cooled, it follows this same curve in reverse. As it is cooled, the same flat line appears while the heat of fusion is removed before the temperature may go down again. 9

14 Once all the water is in the liquid form, the heat is again absorbed as kinetic energy. Between the temperatures of 0 C and 100 C, the heat added causes the temperature increases. Upon reaching the boiling point, the temperature again does not increase even though heat is added. All the heat added to the sample during the time that the slope of the line is zero goes into potential energy. This energy represents the heat of vaporization and is used to separate the liquid molecules into the gaseous form. During this flat line period, an observer would see that the water was changing into gas, but both the liquid part and the gaseous part would be at exactly 100 C. Adding more heat causes the water to boil faster, but its temperature will never exceed 100 C. Once all the water is in the gaseous form, the heat can again go into raising the kinetic energy and temperature of the gas. When the gas is cooled, it follows this same curve in reverse. As it is cooled, the same flat line appears while the heat of condensation is removed before the temperature may drop. This video contains a lecture covering the energy involved in phase changes (7c): (6:28). Figure 1.1: State of Matter and Melting Boiling Point Graph (Watch Youtube Video) Specific Heat Thermodynamic data (melting point, boiling point, heat of melting, heat of vaporization) for almost all the elements and for thousands of compounds are available in various reference books and on the internet. One useful piece of thermodynamic data is the specific heat. Symbolized by the letter C, the specific heat for a substance is the amount of heat required to raise 1.00 gram of the substance by 1.00 C. For liquid water, the specific heat is 4.18 J/g C. Example: How much heat is required to raise the temperature of 25 grams of water from 15 C to 55 C? Solution: Q = mc T = (25 g)(4.18 J/g C)(40. C) = 4180 J = 4.18 kj Melting and Freezing Points Solids, like liquids, have a vapor pressure. Like liquids, the vapor pressure of a solid increases with temperature. At 100 C, the vapor pressure of liquid water is 760 mm of Hg. As the temperature decreases to 0 C, the vapor pressure decreases (non-linearly) to 4.6 mm of Hg. The vapor pressure of a solid is generally very low because the forces of attraction in solids are strong. 10

15 For example, at 83 C, the vapor pressure of ice is mm of Hg. As ice is heated, its vapor pressure increases. At 0 C, the vapor pressure of ice is 4.6 mm of Hg, which also happens to be the vapor pressure of water at 0 C. In fact, for all substances, their solids and liquids have the same vapor pressure at the melting point. The melting point of a solid is defined as the temperature at which the vapor pressure of the solid and liquid are the same. Therefore, the melting point of the solid and the freezing point of the liquid are exactly the same temperature. Heat of Fusion Melting, the phase change from solid to liquid, has many similarities to vaporization. The solid must reach its melting point before the molecules can enter the liquid phase. The molecules in liquid phase, however, are farther apart than the molecules in the solid phase. Since the molecules attract each other, increasing the distance between them requires work. The work done in separating the molecules is stored in the molecules as potential energy in the liquid phase. This is the same process that occurs when the heat of vaporization must be added to liquid molecules to get them into the gaseous phase. In the case of melting, this potential energy is called the heat of fusion, or the heat of melting. The word fusion is used several times in science with different meanings. You need to note the context in order to determine which meaning is intended. In this case, fusion refers to the change from the liquid to solid phase. When a solid melts, the heat of fusion must be added, and when a liquid freezes (fuses) back to solid, the heat of fusion is given off. The heat of fusion for water is 334 joules/gram. Example: How much heat must be added to 25 g of ice at 0 C to convert it to liquid water at 0 C? Solution: Q = (mass)( H FUS ION ) = (25 g)(334 J/g) = 8350 J = 8.4 kj Heat of Vaporization The difference between the liquid phase and the gas phase of a substance is essentially the distance between the molecules. Since the molecules attract each other and are separated by a greater distance in the gaseous phase than in the liquid phase, the molecules in the gaseous phase possess more potential energy than in the liquid phase. When a substance changes from the liquid phase to the gaseous phase, work must be done on the molecules to pull them away from each other. The work done separating the molecules is stored in the molecular structure as potential energy. If the molecules are allowed to condense back into the liquid phase, the potential energy is released exactly the same amount that was needed to separate the molecules. This potential energy stored in molecules in the gaseous phase is called the heat of vaporization. The heat of vaporization ( H VAP ) for water is 540 calories/gram, which is 2.26 kj/g at the normal boiling point. Because of the strength of the polar attractions holding water molecules together in the liquid form, water has a fairly high heat of vaporization. Other examples of polar molecules are ammonia, NH 3, and ethanol, C 2 H 5 OH, which have heats of vaporization of 1.38 kj/g and 0.84 kj/g, respectively. Example: How much heat in kj is necessary to vaporize 100. grams of ammonia at its boiling point? Solution: Q = (mass)( H VAP ) = (100. g)(1.38 kj/g) = 138 kj The boiling point of ammonia is 33 C. It is very important to understand that the ammonia is at the boiling point before and after the heat of vaporization is added. All the energy involved in the heat of 11

16 vaporization is absorbed by the substance as potential energy; none of it goes into kinetic energy, so the temperature cannot change. To test your understanding of this point, determine which would produce a more severe burn: spilling boiling water at 100 C on your skin or being burned by gaseous water at 100 C. At first it may seem that they would do the same damage since they are both at the same temperature, but in fact, the gaseous water would do more damage. The gaseous water would release a tremendous amount of heat (heat of vaporization) to your skin as it condenses to water before burning your skin as 100 C water. Example: How much heat is required to raise the temperature of 25 grams of liquid water from 25 C to gaseous water at 100. C? Solution: In this problem, you have to calculate the heat needed to raise the temperature of the liquid water from 25 C to 100. C and then the heat of vaporization for the 25 g of water. Heating: Q = mc T = (25 g)(4.18 J/g C)(75 C) = 7838 J = 7.8 kj Vaporizing: Q = mh VAP = (25 g)(2.26 kj/g) = 56.5 kj Q T = 7.8 kj kj = 64.3 kj Example: A 2, 000. grams mass of water in a calorimeter has its temperature raised by 3.00 C while an exothermic chemical reaction is occurring. How much heat, in joules, is transferred to the water by the heat of reaction? Solution: The heat is calculated by determining the heat absorbed by the water. This amount of heat is the product of three factors: 1) the mass of the water, 2) the specific heat of water, and 3) the change in temperature of the water. Q = (mass of water)(c water )( T) = (2000. g)(4.18 J/g C)(3.00 C) = 25, 080 J = 25.1 kj Example: A 1, 000. gram mass of water whose temperature was 50. C lost 33, 400 J of heat over a 5-minute period. What was the temperature of the water after the heat loss? Solution: Q = (mass)(c_w)( T) = heat (mass)(c w ) 33,400 J (1000. g)(4.18 J/g C) = = 8.00 C If the original temperature was 50. C and the temperature decreased by 8 C, then the final temperature would be 42 C. Example: Use the thermodynamic data given to calculate the total amount of energy necessary to raise 25 grams of ice at 20. C to gaseous water at 120. C. Data: 12

17 Melting point of ice = 0 C Boiling point of water = 100 C H VAP for water = 2260 J/g H FUS ION for water = 334 J/g C ice = 2.11 J/g C C water = 4.18 J/g C C water vapor = 1.84 J/g C Solution There will be five steps in the solution process. 1. We must calculate the heat required to raise the temperature of the ice from 20. C to 0 C. Raising the temperature of ice, Q = mc T = (25 g)(2.11 J/g C)(20 C) = 1055 J 2. We must calculate the heat required to provide the heat of melting in order to change ice at 0 C to water at 0 C. Melting ice to liquid, Q = (mass)( H FUS ION ) = (25 g)(334 J/g) = 8350 J 3. We must calculate the heat required to raise the temperature of the liquid water from 0 C to 100 C. Raising the temperature of liquid, Q = mc T = (25 g)(4.18 J/g C)(100 C) = J 4. We must calculate the heat required to provide the heat of vaporization to change liquid water at 100 C to gaseous water at 100 C. Vaporizing liquid to gas, Q = (mass)( H VAP ) = (25 g)(2260 J/g) = J 5. Finally, we must calculate the heat required to raise the temperature of the gaseous water from 100 C to 120 C. Raising the temperature of gas, Q = mc T = (25 g)(1.84 J/g C)(200 C) = 9200 J The sum of all five steps is 85, 555 J = 86 kj The cooling process would be the exact reverse of the heating process. If water in the gaseous phase is cooled, each 1.84 joules of heat removed would lower the temperature of 1.00 g of gas by 1.00 C. When the gaseous water reaches the boiling point (also the condensation point), each gram of gaseous water that condenses to liquid will release 2260 joules of heat. Once all the water is in the liquid form, the removal of each 4.18 joules of heat by cooling will cause the temperature of 1.00 g of water to cool by 1.00 C. At the freezing point (also the melting point) 334 joules of heat must be removed to convert each gram of liquid water to ice. When the entire sample of water is in the form of ice, 2.26 joules of heat must be removed to cool each gram by 1.00 C. 13

18 1.3 Phase Diagrams A phase diagram is a convenient way of representing the phase of a substance as a function of temperature and pressure. Phase diagrams are produced by altering the temperature of a pure substance at constant pressure in a closed system. This process is repeated at many different pressures, and the resultant phases charted. Generic Phase Diagrams The phase diagram seen below is a generic phase diagram that would be produced by many pure substances. Differences in the diagram would be in the specific thermodynamic points, such as the melting point and boiling point, and in the slopes of the curved lines. The pink area in the diagram represents the solid state, the purple area represents the liquid state, and the yellow area represents the gaseous state. Following a constant pressure line, such as line X, shows that the phase of the substance at different temperatures at this pressure. Since the line crosses from solid into liquid at point A, this temperature would be the melting point of the substance. Continuing along the line, we see it crosses from liquid to gas at the point corresponding with temperature C. This is the boiling point of the substance at pressure X. The line between the pink and purple areas represent the various melting points at different pressures, while the line separating the purple area from the yellow area represents the boiling point at various pressures. At the melting points, both solid and liquid can exist at the same time as the phase changes occurs. Similarly, at the boiling points, the substance may exist in both liquid and gas phase at the same time. There is one point on the diagram where all three phases may exist at one time. This point is called the triple point. The pressure at this point is called the triple point pressure, and the temperature at this 14

19 point is called the triple point temperature. There is also a line separating the pink area from the yellow area. This line represents the phase change in which a solid changes directly to a gas without passing through the liquid phase. This phase change is known as sublimation. All substances undergo sublimation at the appropriate pressures. We do not see sublimation often because the pressures are frequently quite low. One example of sublimation that we can observe at normal atmosphere (1.00 atm) is carbon dioxide, CO 2, in its solid form, which is also known as dry ice. If you have seen dry ice, you would notice that the substance goes from the solid phase to the gaseous phase at room conditions without passing through a liquid phase. In the phase diagram for dry ice, we would see that the triple point is above normal atmospheric pressure, so at standard conditions, carbon dioxide undergoes sublimation. The figure above shows the same generic phase diagram we looked at earlier. Two points have been added to the diagram, labeled A and B. You should note that the substance at point A can be caused to go through a phase change from solid to gas (sublimation) in two different ways. The substance could be heated at constant pressure, or the substance could undergo a lowering of pressure at constant temperature. Both of these procedures would cause the solid to undergo sublimation. Point B is similar except that the substance begins as a liquid. The liquid at point B could be caused to under a phase change into a gas by either heating the liquid at constant pressure or by lowering the pressure at constant temperature. You might also note that the substance at the triple point will become a solid if the pressure is increased and will become a gas if the pressure is decreased. The Phase Diagram for Water The phase diagram for water has one very interesting difference from the generic phase diagram. Please note that this diagram is not drawn to scale. If the distance between 1.0 atm and 218 atm was drawn to scale, the difference between 1.0 atm and atm would be invisible. The diagram is drawn just to show specific points of interest. 15

20 The primary difference in the shape of this diagram and the generic diagram is that the solid-liquid equilibrium line has a negative slope. A positive slope indicates that as pressure increases, the melting point increases. In other words, more pressure on the surface would require a higher temperature to overcome that extra pressure to melt the substance. The negative slope of this line in the water diagram indicates that as the pressure increases, the melting point of water decreases. The reason this occurs is because the increased pressure breaks some of the hydrogen bonds in the water, so less thermal energy is needed to melt ice at higher pressures. This property of water is evidenced in various situations. We all think of ice as being a very slippery substance, but the surface of ice is no different from the surface of many other solids. The reason that we slip on ice is because when you stand on ice, the pressure of your weight causes the ice to melt, which causes the surface to be slippery. Another example of this is in the track of the blade left by an ice skate. If you look closely at the track, you ll see that the track is filled with liquid. If you follow the line at a pressure of 1.0 atm for water, you see that the temperatures at the melting and boiling points are what we expected. The triple point for water is at atm and C, which also means that the pressure and temperature at which ice water sublimates to water vapor are very low. There are commercial processes that make use of the sublimation of water. Foods that are referred to as freeze dried have the surrounding pressure and temperature reduced to a point below the triple point. The food is then heated while a vacuum pump removes vapor to keep the pressure below the triple point pressure. This causes the water in the food to sublimate, which is drawn off by the pump. The end result is that all the water will be removed from the food. As the temperature of liquid is raised, the amount of pressure that is required to keep the substance in liquid form also increases. Liquids will eventually reach a temperature at which no amount of pressure will keep it in the liquid form. The substance at that temperature will vaporize regardless of the amount of pressure on it. The highest temperature a liquid reaches and can still be maintained as a liquid is called the critical temperature. The pressure that is required at the critical temperature to force the substance to stay in liquid form is called the critical pressure. The critical temperature and pressure for water is 374 Cand 218 atm. 16

21 Review Questions 1. Use the thermodynamic data given in the following table (Table 1.2) to answer problems 1-5. Table 1.2: Thermodynamic Data of Various Substances Water Cesium, Cs Silver, Ag Melting Point 0 C 29 C 962 C Boiling Point 100. C 690. C 2162 C H fusion 334 J/g 16.3 J/g 105 J/g H vaporization 2260 J/g 669 J/g 2362 J/g Specific Heat, C, for 2.01 J/g C J/g C J/g C Gas Specific Heat, C, for 4.18 J/g C J/g C J/g C Liquid Specific Heat, C, for Solid 2.09 J/g C J/g C J/g C (a) How many joules are required to melt 100. grams of silver at its normal melting point with no temperature change? (b) How many joules are required to boil 150. grams of cesium at its normal boiling point with no temperature change? (c) How many joules are required to heat 200. g of liquid water from 25 C to steam at 125 C under normal pressure? (d) How many joules are required raise the temperature of 1.00 gram of water from 269 C (the current temperature of space) to C (the estimated temperature of space immediately after the Big Bang)? (e) How many joules are required to raise the temperature of g of cesium from 200. C to C? (f) Why does the boiling point of water increase with increasing surrounding pressure? (g) Why must heat be absorbed to melt a solid even though both the solid and the liquid are at the same temperature? Use the image below for problems

22 (h) What is happening to the water in section B? (i) What is happening to the water in section A? (j) Why are the slopes of the lines in sections A, C, and E different?consider the phase diagram below. Name the phases that may be present at each lettered point in the diagram. Use the phase diagram for water below to answer the remaining questions. 18

23 2. What is the state of water at 2.0 atm and 50. C? 3. What phase change will occur if the temperature is lowered from 80. C to 5 C at 1.0 atm? 4. You have ice at 10 C and 1.0 atm. What could you do in order to cause the ice to sublime? All images, unless otherwise stated, are created by the CK-12 Foundation and are under the Creative Commons license CC-BY-NC-SA. 19