Vapor Pressure
A. H2S because H2S is polar whereas CH4 is non-polar and therefore would be held together with London dispersion forces. B. H2O because while both are polar, H2O will form hydrogen bonds and H2S does not. C. HCl because it is polar and Cl2 is non-polar. D. NaI because it is ionic whereas NH3 is polar and ionic attractions are much stronger than polar attractions. E. SF4 because it is polar (distorted tetrahedron) whereas CH4 is non-polar. 2. D
Vapor Pressure Lesson Objectives •
The student will be able to describe the processes of evaporation and condensation.
•
The student will be able to describe vapor pressure equilibrium.
Introduction The phase of a substance is essentially the result of two forces acting on the molecules. The molecules of a substance are pulled together by intermolecular forces of attraction that were discussed in the previous section. Some of these intermolecular forces are weak and some are strong. The molecules of a substance also have kinetic energy so that the molecules are in constant random motion and are in almost constant collisions with each other. The motion and collisions of molecules push them away from each other. Without 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 and dominate 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 dominantly 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 increases or decreases, their molecular motion increases or decreases, and the substance may change phase. A substance in the solid phase (intermolecular forces dominate) can be heated until the molecular motion balances the intermolecular forces and the solid will melt to liquid. The liquid may be heated until the molecular motion completely overcomes the intermolecular forces and the liquid will vaporize to the gaseous state. When you open a jar of perfume, your nose detects the substance almost immediately. You can see that the substance is in liquid form and it is not boiling, yet some of that material obviously entered the gaseous state and reached your nose.
Evaporation The temperature of a beaker of water is a measure of the average kinetic energy of the molecules in the beaker. That does not mean that all the molecules in the beaker have exactly the same 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.
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Figure 13: Standard Distribution Curve (Created by: Richard Parsons, License: CC-BY-SA) Naturally occurring phenomena usually have most of the instances near the average and the number of instances become less as the value gets farther from the average.
Figure 14: The distribution of temperature among the molecules of a beaker of water. (Created by: Richard Parsons, License: CC-BY-SA) In the case of a beaker of water, some of the molecules will have an average temperature below the boiling point and some of the molecules will have a temperature above the boiling point (see Figure 13). The dashed yellow line is the average temperature of the molecules and would be the temperature shown on a thermomeo
ter inserted into the liquid. The red line represents the boiling point of water (100 C at 1.00 atm pressure) and the area under the curve to the right of the red line represents the molecules of water that are above the boiling point. In order for a molecule of liquid that is 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.
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Figure 15: Water boils only when a sufficient number of adjacent molecules are above the boiling point and can form bubbles of gaseous water. (Created by: Richard Parsons, License: CC-BY-SA) The only circumstance when there are enough molecules above the boiling point to form bubbles is when the average temperature is at the boiling point. For single molecules above the boiling point, they must wait until their random motion gets them to the surface and then the molecule can leave the liquid and enter into the gaseous phase. This process of molecules escaping to the gaseous phase from the surface of a liquid when the average temperature of the liquid is below the boiling point is called evaporation. The process of phase change is a little more complicated than just having the molecules reach the boiling point. Objects that attract each other and are separated have potential energy due to that attraction and separation. An object held above the earth is attracted to the earth by earth's gravity and has potential energy due to the attraction and separation. The amount of potential energy can be calculated by multiplying the force of attraction times the distance of separation. Two oppositely charged objects that are separated have potential energy. Objects with opposite magnetic poles that are separated have potential energy. A stretched rubber band has potential energy. Gaseous molecules that have a force of attraction between them but are separated have potential energy. Molecules in the liquid state and the same molecules in the gaseous state at the same temperature 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 potential energy that the liquid molecules do not. Molecules in the liquid state that are hot enough to exist in the gaseous state must absorb energy from their surroundings to provide that potential energy as they change phase. This potential energy is called the heat of vaporization and it is absorbed by evaporating or vaporizing molecules from the kinetic energy of the liquid. You are at least somewhat familiar with evaporation. You know that if you leave a saucer of water sitting out on the countertop, the water will slowly disappear – and yet, at no time is the temperature of the water ever at the boiling point. The water in an open container continues to evaporate until it is all in the vapor state. 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 molecules whose temperature was above the boiling point are gone, no more evaporation would occur. Here’s the reason evaporation continues. 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 and the molecules left behind have also contributed 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 and so when the liquid cools due to evaporation, the surroundings will give heat to the liquid thus raising its temperature back up equal to the surroundings thus producing more hot molecules. This process can continue in an open container until the liquid is all evaporated. Many years ago, when people lived without electricity, they figured out that if they placed the butter dish on the dinner table in a shallow container of water, evaporation would cool the water and therefore the butter dish, enough to keep the butter from melting to a liquid. They also knew that if you put a container of water or milk in a fabric sack, soaked the sack in water, and swung the sack around in the air, the evaporation of the water from the sack would cool it and cool the container of milk or water to make it nicer to drink. Many 534
hikers today use fabric canteen holders that they soak in water while hiking so that the water in the canteen will be cooler when they drink it. 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 liquids get closer to the boiling point, more of the molecules have temperatures above the boiling point and so evaporation is faster. 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 and those that hardly evaporate at all are called non-volatile.
Condensation Liquids will usually evaporate to dryness in an open container. What happens, however, if the container is closed? When a lid is put on 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 collide with another molecule or a wall and condense (the gas to liquid phase change) back to liquid. Molecules at the boiling point can exist in either liquid phase or gaseous phase – the only difference between them is the amount of potential energy they hold.
Figure 15: Evaporation and condensation both occur in a closed container. (Created by: Richard Parsons, License: CC-BY-SA) For a liquid molecule with adequate temperature to exist in the gaseous phase, it is necessary for the molecule to gain the heat of vaporization. It does this by collision 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. That amount of potential energy is called the heat of vaporization when it is being gained and it is called the heat of condensation when it is being lost – but it is exactly the same amount of energy. 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 molecules evaporate is determined by the temperature, the surface area, and what substance is involved. Once the substance, the surface area, and the temperature are established, the rate of evaporation will be constant. The rate at which the gas condenses is determined by the partial pressure of the gas, the surface area, and what substance is involved. Once the substance and surface area is 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. In the section on evaporation, it was pointed out that as a liquid evaporates, the remaining liquid cools because the hottest molecules are leaving so the average decreases and the heat of vaporization is being 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
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those left behind, and the condensing molecules must give up the heat of condensation.
Vapor Pressure Equilibrium You can follow the progress of the two activities (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, there will be no condensation. 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 begins. Since the partial pressure of the water vapor is low, the rate of condensation will be low. Over time, more and more water evaporates and the partial pressure of the water vapor increases. Since the partial pressure increases, the rate of condensation 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 molecules of water going into the vapor phase and the number of molecules condensing back to liquid are exactly the same and 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. A condition called vapor pressure equilibrium has been established. As time goes on from this point, the amount of liquid cannot change, the amount of gas cannot change; neither the rate of evaporation nor the rate of condensation can change. Everything remains exactly the same, BUT the two activities continue. Evaporation continues and condensation continues at exactly the same rate. Each different liquid at each temperature will have an exact partial pressure of vapor that will be present when vapor pressure equilibrium is established. The pressure of the vapor in the space above the liquid is called the vapor pressure of that liquid at that temperature. Vapor Pressure of Water at Various Temperatures
Temperature in C
Vapor Pressure in Torr
0
4.6
10
9.2
20
17.5
30
31.8
40
55.3
50
92.5
60
149.4
70
233.7
80
355.1
90
525.8
100
760.0
o
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. The partial pressures of the gases will reach the equilibrium value – 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. You might have noticed a subtle switch in vocabulary sometimes referring to the substance in the gaseous state as a gas and sometimes as a vapor. Chemists have agreed that a substance in the gaseous phase at temperatures above the boiling point of its liquid should be called a gas and if the temperature of the substance is below the boiling point, it should be called a vapor. You should also 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 be 785 torr. The presence of the air in no way affects the vapor
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pressure.
Vapor Pressure Correction 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.
Figure 16: Gas Collection Over Water. (Created by: Richard Parsons, License: CC-BY-SA) In Figure 16, 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 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 in the lab and the temperature in the lab and the volume of the jar to the water level, you can calculate how much gas you produced. (Plug P, V, T, 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, then it will contain the vapor pressure of water at this temperature. So the outside 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 o
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 o
o
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 H2 = 755 torr – 17.5 torr = 737 torr
Lesson Summary •
Molecules of liquid may evaporate from the surface of a liquid.
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When molecules of a liquid evaporate, the remaining liquid cools.
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Gas molecules in contact with their liquid may condense to liquid form. 537
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If a liquid is placed in a closed container, eventually vapor pressure equilibrium will be reached.
Review Questions 1. 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 o
o
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? (Intermediate) 2. Describe all the reasons that the remaining liquid cools as evaporation occurs.
(Challenging)
3. Describe all the reasons that the remaining gas gets hotter as condensation occurs.
(Challenging)
4.
The apparatus above can be used to determine the vapor pressure of benzene. With a vacuum in the top of the tube, the mercury rises to the height shown. When a small amount of liquid benzene is injected into the space at the top of the tube, it floats on the mercury. The benzene will evaporate and eventually reach vapor pressure equilibrium. The mercury in the tube will pushed down further by the pressure of the benzene vapor in the tube. Neglecting the effect of the liquid benzene, what would be the calculated vapor pressure of benzene? (Intermediate) o
5. Water vapor and hydrogen gas are sealed in a cylinder fitted with a piston at 60 C. The partial pressure of the hydrogen gas is 0.35 atm and the vapor pressure of the water is 0.20 atm at this temperature. The total pressure in the cylinder is 0.55 atm. If the piston is pushed down until the volume is half the original volume, what will be the pressure in the cylinder? (Challenging)
Vocabulary condensation
The process whereby a gas or vapor is changed to a liquid. equilibrium vapor pres- The pressure that is exerted, at a given temperature, sure by the vapor of a solid or liquid in equilibrium with the vapor. evaporation The escape of molecules from a liquid into the gaseous state at a temperature below the boiling point. heat of condensation The quantity of heat released when a unit mass of a vapor condenses to liquid at constant temperature. heat of vaporization The quantity of heat required to vaporize a unit mass of liquid at constant temperature.
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vapor
The gaseous phase of a substance that exists even though the temperature is below the boiling point of the substance.
Review Answers 1. (Total pressure) – (vapor pressure of water) = partial pressure of hydrogen 780. mm of Hg – 19 mm of Hg = 761 mm of Hg 2. Since the hotter molecules are evaporating, the average temperature of the ones left behind will be lower. Also, the molecules leaving the liquid and becoming gas absorb the necessary heat of vaporization from the other molecules in the liquid. 3. The molecules that are condensing are the cooler ones so the average temperature of the remaining gas will increase. Furthermore, the condensing molecules give up the heat of condensation to the surroundings which include the remaining gas. 4. The atmospheric pressure is 760. mm of Hg as demonstrated by the barometer on the left. The total pressure (mercury + benzene vapor pressure) in the tube on the right must therefore be equal to 760. mm of Hg. Since the mercury column in the tube on the right is 656 mm of Hg, the vapor pressure of benzene must be 104 mm of Hg. 5. The hydrogen gas is well above its boiling point and therefore, it will behave as a gas and follow the gas laws. Its new pressure will be double its original pressure or 0.70 atm. The water, however, it below its boiling point and will follow the rules of vapor pressure. As long as the temperature remains the same, the vapor pressure will remain the same. Therefore, when the piston is pushed down and the pressure of the water vapor increases, some of the water vapor will condense to liquid and only enough water vapor will remain to produce a vapor pressure of the same 0.20 atm. The total pressure in the cylinder will be 0.90 atm.
Boiling Point Lesson Objectives •
The student will know the relationship between boiling point, vapor pressure, and ambient pressure.
•
Given a vapor pressure table for water, and the ambient pressure, the student will be able to determine the boiling point of water for those conditions.
Introduction If you want hard-boiled eggs at home, you can probably put the eggs in boiling water for about eight minutes to accomplish it. If you go camping in the Rocky Mountains at an altitude of 10,000 feet, you will find that an egg placed in boiling water for eight minutes is not hard boiled. In fact, even after twelve minutes in boiling water, the egg may still be a little too runny for your tastes.
Normal Boiling Point 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 water and remaining at the same size rises to the top of the water and the gas escapes 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 and it would not have existed. 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.
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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 but only when that vapor pressure equals the surrounding atmospheric pressure can the water form bubbles in the process we call boiling. A liquid cannot boil until its vapor pressure is equal to the pressure on the surface of the liquid. The actual definition of boiling point is that 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 o
volatile than water such as chloroform will boil at 61.3 C. This is because the vapor pressure of chloroform o
o
is 1.00 atm at 61.3 C. The vapor pressure of ethanol reaches 1.00 atm at a temperature of 78.4 C and therefore, that is the normal boiling point of ethanol.
Boiling Points Change with Changes in Pressure Since liquids boil when their vapor pressure becomes equal to surrounding pressure, then if the surrounding pressure is lower, liquids will boil at lower temperatures. At higher altitudes, atmospheric pressure is lower. o
o
In cities whose altitude is around 5,000 feet, water boils at 95 C instead of at 100 C and at 10,000 feet, o
water boils around 90 C. The water boils in normal fashion but its temperature is lower and therefore, cooking in boiling water takes a longer time. In situations where boiling is used to purify water or sterilize equipment, the lower temperature of boiling water requires concern. 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.
Figure 17: A beaker of water under a bell jar with lowered pressure. (Created by: Richard Parsons, License: CC-BY-SA) o
At room temperature, 20 C, the vapor pressure of water is 17.5 mm of Hg so if the pressure in the bell jar o
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 o
is at 100 C, with steam coming off and so on, but the water can be removed from the bell jar and poured o
on your hand and the temperature is only 20 C. When you look up the boiling point of a liquid, the reference will be to the normal boiling point which means the boiling point when the surrounding pressure is 1.00 atm. 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. It’s fairly unusual to find atmospheric pressures greater than 1.00 atm except during storms, but it’s easy enough to raise the surrounding pressure in a laboratory situation. If we use a strong container with a lid that screws on very tight, we can boil water in the container and as water vaporizes and the temperature of both the air and the water vapor increase, the gas pressure in the container will increase. As the pressure in the container ino
creases, the boiling point of the water increases. The vapor pressure of liquid water at 120 C is 2.0 atm. Therefore, if we can raise the pressure inside a sealed container to 2.0 atm, water will not boil in the container 540
o
until its temperature is 120 C. This is the concept that is used in pressure cookers and rice cookers. The cooking pot has a lid that can be sealed tightly and a valve in the lid that will open slightly when the pressure inside the container reaches 2.0 atm. Water and whatever food you wish to cook is placed inside the pressure cooker and it is set on the stove. The pressure and therefore the boiling point of water increases inside the container until the pressure reaches 2.0 atm. If the pressure goes beyond 2.0 atm, the little valve opens and lets out some gas so that the pressure remains at 2.0 atm. The valve can be opened and closed any number o
of times to keep the inside pressure at 2.0 atm. The temperature of the boiling water inside will be 120 C under these conditions and the food will cook in as little as one-third the normal time.
Lesson Summary •
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.
Review Questions 1. What happens to the boiling point of a liquid if the pressure exerted on the surface of the liquid is increased? (Beginning) 2. How can you make water boil without heating it?
(Intermediate)
Vocabulary boiling point normal boiling point
The temperature at which the vapor pressure of a liquid equals the surrounding pressure. The temperature at which the vapor pressure of a liquid equals 1.00 atmosphere.
Review Answers 1. The boiling point will increase because the vapor pressure of the water must be higher (to equal surrounding pressure) for the water to boil. 2. Water will boil when its vapor pressure equals the surrounding pressure so you can boil it by lowering pressure instead of raising temperature.
Heat of Vaporization Lesson Objectives •
The student will be able to calculate energy changes during phase changes.
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The student will be able to explain the slopes of various parts of heating and cooling curves.
Introduction In order to vaporize a liquid, heat must be added to raise the kinetic energy (temperature) to the phase change temperature and then more heat must be added to provide the necessary potential energy to separate
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Vapor Pressure Lesson Objectives •
The student will be able to describe the processes of evaporation and condensation.
•
The student will be able to describe vapor pressure equilibrium.
Introduction The phase of a substance is essentially the result of two forces acting on the molecules. The molecules of a substance are pulled together by intermolecular forces of attraction that were discussed in the previous section. Some of these intermolecular forces are weak and some are strong. The molecules of a substance also have kinetic energy so that the molecules are in constant random motion and are in almost constant collisions with each other. The motion and collisions of molecules push them away from each other. Without 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 and dominate 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 dominantly 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 increases or decreases, their molecular motion increases or decreases, and the substance may change phase. A substance in the solid phase (intermolecular forces dominate) can be heated until the molecular motion balances the intermolecular forces and the solid will melt to liquid. The liquid may be heated until the molecular motion completely overcomes the intermolecular forces and the liquid will vaporize to the gaseous state. When you open a jar of perfume, your nose detects the substance almost immediately. You can see that the substance is in liquid form and it is not boiling, yet some of that material obviously entered the gaseous state and reached your nose.
Evaporation The temperature of a beaker of water is a measure of the average kinetic energy of the molecules in the beaker. That does not mean that all the molecules in the beaker have exactly the same 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.
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Figure 13: Standard Distribution Curve (Created by: Richard Parsons, License: CC-BY-SA) Naturally occurring phenomena usually have most of the instances near the average and the number of instances become less as the value gets farther from the average.
Figure 14: The distribution of temperature among the molecules of a beaker of water. (Created by: Richard Parsons, License: CC-BY-SA) In the case of a beaker of water, some of the molecules will have an average temperature below the boiling point and some of the molecules will have a temperature above the boiling point (see Figure 13). The dashed yellow line is the average temperature of the molecules and would be the temperature shown on a thermomeo
ter inserted into the liquid. The red line represents the boiling point of water (100 C at 1.00 atm pressure) and the area under the curve to the right of the red line represents the molecules of water that are above the boiling point. In order for a molecule of liquid that is 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.
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Figure 15: Water boils only when a sufficient number of adjacent molecules are above the boiling point and can form bubbles of gaseous water. (Created by: Richard Parsons, License: CC-BY-SA) The only circumstance when there are enough molecules above the boiling point to form bubbles is when the average temperature is at the boiling point. For single molecules above the boiling point, they must wait until their random motion gets them to the surface and then the molecule can leave the liquid and enter into the gaseous phase. This process of molecules escaping to the gaseous phase from the surface of a liquid when the average temperature of the liquid is below the boiling point is called evaporation. The process of phase change is a little more complicated than just having the molecules reach the boiling point. Objects that attract each other and are separated have potential energy due to that attraction and separation. An object held above the earth is attracted to the earth by earth's gravity and has potential energy due to the attraction and separation. The amount of potential energy can be calculated by multiplying the force of attraction times the distance of separation. Two oppositely charged objects that are separated have potential energy. Objects with opposite magnetic poles that are separated have potential energy. A stretched rubber band has potential energy. Gaseous molecules that have a force of attraction between them but are separated have potential energy. Molecules in the liquid state and the same molecules in the gaseous state at the same temperature 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 potential energy that the liquid molecules do not. Molecules in the liquid state that are hot enough to exist in the gaseous state must absorb energy from their surroundings to provide that potential energy as they change phase. This potential energy is called the heat of vaporization and it is absorbed by evaporating or vaporizing molecules from the kinetic energy of the liquid. You are at least somewhat familiar with evaporation. You know that if you leave a saucer of water sitting out on the countertop, the water will slowly disappear – and yet, at no time is the temperature of the water ever at the boiling point. The water in an open container continues to evaporate until it is all in the vapor state. 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 molecules whose temperature was above the boiling point are gone, no more evaporation would occur. Here’s the reason evaporation continues. 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 and the molecules left behind have also contributed 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 and so when the liquid cools due to evaporation, the surroundings will give heat to the liquid thus raising its temperature back up equal to the surroundings thus producing more hot molecules. This process can continue in an open container until the liquid is all evaporated. Many years ago, when people lived without electricity, they figured out that if they placed the butter dish on the dinner table in a shallow container of water, evaporation would cool the water and therefore the butter dish, enough to keep the butter from melting to a liquid. They also knew that if you put a container of water or milk in a fabric sack, soaked the sack in water, and swung the sack around in the air, the evaporation of the water from the sack would cool it and cool the container of milk or water to make it nicer to drink. Many 534
hikers today use fabric canteen holders that they soak in water while hiking so that the water in the canteen will be cooler when they drink it. 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 liquids get closer to the boiling point, more of the molecules have temperatures above the boiling point and so evaporation is faster. 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 and those that hardly evaporate at all are called non-volatile.
Condensation Liquids will usually evaporate to dryness in an open container. What happens, however, if the container is closed? When a lid is put on 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 collide with another molecule or a wall and condense (the gas to liquid phase change) back to liquid. Molecules at the boiling point can exist in either liquid phase or gaseous phase – the only difference between them is the amount of potential energy they hold.
Figure 15: Evaporation and condensation both occur in a closed container. (Created by: Richard Parsons, License: CC-BY-SA) For a liquid molecule with adequate temperature to exist in the gaseous phase, it is necessary for the molecule to gain the heat of vaporization. It does this by collision 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. That amount of potential energy is called the heat of vaporization when it is being gained and it is called the heat of condensation when it is being lost – but it is exactly the same amount of energy. 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 molecules evaporate is determined by the temperature, the surface area, and what substance is involved. Once the substance, the surface area, and the temperature are established, the rate of evaporation will be constant. The rate at which the gas condenses is determined by the partial pressure of the gas, the surface area, and what substance is involved. Once the substance and surface area is 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. In the section on evaporation, it was pointed out that as a liquid evaporates, the remaining liquid cools because the hottest molecules are leaving so the average decreases and the heat of vaporization is being 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
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those left behind, and the condensing molecules must give up the heat of condensation.
Vapor Pressure Equilibrium You can follow the progress of the two activities (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, there will be no condensation. 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 begins. Since the partial pressure of the water vapor is low, the rate of condensation will be low. Over time, more and more water evaporates and the partial pressure of the water vapor increases. Since the partial pressure increases, the rate of condensation 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 molecules of water going into the vapor phase and the number of molecules condensing back to liquid are exactly the same and 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. A condition called vapor pressure equilibrium has been established. As time goes on from this point, the amount of liquid cannot change, the amount of gas cannot change; neither the rate of evaporation nor the rate of condensation can change. Everything remains exactly the same, BUT the two activities continue. Evaporation continues and condensation continues at exactly the same rate. Each different liquid at each temperature will have an exact partial pressure of vapor that will be present when vapor pressure equilibrium is established. The pressure of the vapor in the space above the liquid is called the vapor pressure of that liquid at that temperature. Vapor Pressure of Water at Various Temperatures
Temperature in C
Vapor Pressure in Torr
0
4.6
10
9.2
20
17.5
30
31.8
40
55.3
50
92.5
60
149.4
70
233.7
80
355.1
90
525.8
100
760.0
o
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. The partial pressures of the gases will reach the equilibrium value – 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. You might have noticed a subtle switch in vocabulary sometimes referring to the substance in the gaseous state as a gas and sometimes as a vapor. Chemists have agreed that a substance in the gaseous phase at temperatures above the boiling point of its liquid should be called a gas and if the temperature of the substance is below the boiling point, it should be called a vapor. You should also 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 be 785 torr. The presence of the air in no way affects the vapor
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pressure.
Vapor Pressure Correction 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.
Figure 16: Gas Collection Over Water. (Created by: Richard Parsons, License: CC-BY-SA) In Figure 16, 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 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 in the lab and the temperature in the lab and the volume of the jar to the water level, you can calculate how much gas you produced. (Plug P, V, T, 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, then it will contain the vapor pressure of water at this temperature. So the outside 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 o
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 o
o
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 H2 = 755 torr – 17.5 torr = 737 torr
Lesson Summary •
Molecules of liquid may evaporate from the surface of a liquid.
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When molecules of a liquid evaporate, the remaining liquid cools.
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Gas molecules in contact with their liquid may condense to liquid form. 537
•
If a liquid is placed in a closed container, eventually vapor pressure equilibrium will be reached.
Review Questions 1. 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 o
o
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? (Intermediate) 2. Describe all the reasons that the remaining liquid cools as evaporation occurs.
(Challenging)
3. Describe all the reasons that the remaining gas gets hotter as condensation occurs.
(Challenging)
4.
The apparatus above can be used to determine the vapor pressure of benzene. With a vacuum in the top of the tube, the mercury rises to the height shown. When a small amount of liquid benzene is injected into the space at the top of the tube, it floats on the mercury. The benzene will evaporate and eventually reach vapor pressure equilibrium. The mercury in the tube will pushed down further by the pressure of the benzene vapor in the tube. Neglecting the effect of the liquid benzene, what would be the calculated vapor pressure of benzene? (Intermediate) o
5. Water vapor and hydrogen gas are sealed in a cylinder fitted with a piston at 60 C. The partial pressure of the hydrogen gas is 0.35 atm and the vapor pressure of the water is 0.20 atm at this temperature. The total pressure in the cylinder is 0.55 atm. If the piston is pushed down until the volume is half the original volume, what will be the pressure in the cylinder? (Challenging)
Vocabulary condensation
The process whereby a gas or vapor is changed to a liquid. equilibrium vapor pres- The pressure that is exerted, at a given temperature, sure by the vapor of a solid or liquid in equilibrium with the vapor. evaporation The escape of molecules from a liquid into the gaseous state at a temperature below the boiling point. heat of condensation The quantity of heat released when a unit mass of a vapor condenses to liquid at constant temperature. heat of vaporization The quantity of heat required to vaporize a unit mass of liquid at constant temperature.
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vapor
The gaseous phase of a substance that exists even though the temperature is below the boiling point of the substance.
Review Answers 1. (Total pressure) – (vapor pressure of water) = partial pressure of hydrogen 780. mm of Hg – 19 mm of Hg = 761 mm of Hg 2. Since the hotter molecules are evaporating, the average temperature of the ones left behind will be lower. Also, the molecules leaving the liquid and becoming gas absorb the necessary heat of vaporization from the other molecules in the liquid. 3. The molecules that are condensing are the cooler ones so the average temperature of the remaining gas will increase. Furthermore, the condensing molecules give up the heat of condensation to the surroundings which include the remaining gas. 4. The atmospheric pressure is 760. mm of Hg as demonstrated by the barometer on the left. The total pressure (mercury + benzene vapor pressure) in the tube on the right must therefore be equal to 760. mm of Hg. Since the mercury column in the tube on the right is 656 mm of Hg, the vapor pressure of benzene must be 104 mm of Hg. 5. The hydrogen gas is well above its boiling point and therefore, it will behave as a gas and follow the gas laws. Its new pressure will be double its original pressure or 0.70 atm. The water, however, it below its boiling point and will follow the rules of vapor pressure. As long as the temperature remains the same, the vapor pressure will remain the same. Therefore, when the piston is pushed down and the pressure of the water vapor increases, some of the water vapor will condense to liquid and only enough water vapor will remain to produce a vapor pressure of the same 0.20 atm. The total pressure in the cylinder will be 0.90 atm.
Boiling Point Lesson Objectives •
The student will know the relationship between boiling point, vapor pressure, and ambient pressure.
•
Given a vapor pressure table for water, and the ambient pressure, the student will be able to determine the boiling point of water for those conditions.
Introduction If you want hard-boiled eggs at home, you can probably put the eggs in boiling water for about eight minutes to accomplish it. If you go camping in the Rocky Mountains at an altitude of 10,000 feet, you will find that an egg placed in boiling water for eight minutes is not hard boiled. In fact, even after twelve minutes in boiling water, the egg may still be a little too runny for your tastes.
Normal Boiling Point 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 water and remaining at the same size rises to the top of the water and the gas escapes 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 and it would not have existed. 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.
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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 but only when that vapor pressure equals the surrounding atmospheric pressure can the water form bubbles in the process we call boiling. A liquid cannot boil until its vapor pressure is equal to the pressure on the surface of the liquid. The actual definition of boiling point is that 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 o
volatile than water such as chloroform will boil at 61.3 C. This is because the vapor pressure of chloroform o
o
is 1.00 atm at 61.3 C. The vapor pressure of ethanol reaches 1.00 atm at a temperature of 78.4 C and therefore, that is the normal boiling point of ethanol.
Boiling Points Change with Changes in Pressure Since liquids boil when their vapor pressure becomes equal to surrounding pressure, then if the surrounding pressure is lower, liquids will boil at lower temperatures. At higher altitudes, atmospheric pressure is lower. o
o
In cities whose altitude is around 5,000 feet, water boils at 95 C instead of at 100 C and at 10,000 feet, o
water boils around 90 C. The water boils in normal fashion but its temperature is lower and therefore, cooking in boiling water takes a longer time. In situations where boiling is used to purify water or sterilize equipment, the lower temperature of boiling water requires concern. 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.
Figure 17: A beaker of water under a bell jar with lowered pressure. (Created by: Richard Parsons, License: CC-BY-SA) o
At room temperature, 20 C, the vapor pressure of water is 17.5 mm of Hg so if the pressure in the bell jar o
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 o
is at 100 C, with steam coming off and so on, but the water can be removed from the bell jar and poured o
on your hand and the temperature is only 20 C. When you look up the boiling point of a liquid, the reference will be to the normal boiling point which means the boiling point when the surrounding pressure is 1.00 atm. 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. It’s fairly unusual to find atmospheric pressures greater than 1.00 atm except during storms, but it’s easy enough to raise the surrounding pressure in a laboratory situation. If we use a strong container with a lid that screws on very tight, we can boil water in the container and as water vaporizes and the temperature of both the air and the water vapor increase, the gas pressure in the container will increase. As the pressure in the container ino
creases, the boiling point of the water increases. The vapor pressure of liquid water at 120 C is 2.0 atm. Therefore, if we can raise the pressure inside a sealed container to 2.0 atm, water will not boil in the container 540
o
until its temperature is 120 C. This is the concept that is used in pressure cookers and rice cookers. The cooking pot has a lid that can be sealed tightly and a valve in the lid that will open slightly when the pressure inside the container reaches 2.0 atm. Water and whatever food you wish to cook is placed inside the pressure cooker and it is set on the stove. The pressure and therefore the boiling point of water increases inside the container until the pressure reaches 2.0 atm. If the pressure goes beyond 2.0 atm, the little valve opens and lets out some gas so that the pressure remains at 2.0 atm. The valve can be opened and closed any number o
of times to keep the inside pressure at 2.0 atm. The temperature of the boiling water inside will be 120 C under these conditions and the food will cook in as little as one-third the normal time.
Lesson Summary •
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.
Review Questions 1. What happens to the boiling point of a liquid if the pressure exerted on the surface of the liquid is increased? (Beginning) 2. How can you make water boil without heating it?
(Intermediate)
Vocabulary boiling point normal boiling point
The temperature at which the vapor pressure of a liquid equals the surrounding pressure. The temperature at which the vapor pressure of a liquid equals 1.00 atmosphere.
Review Answers 1. The boiling point will increase because the vapor pressure of the water must be higher (to equal surrounding pressure) for the water to boil. 2. Water will boil when its vapor pressure equals the surrounding pressure so you can boil it by lowering pressure instead of raising temperature.
Heat of Vaporization Lesson Objectives •
The student will be able to calculate energy changes during phase changes.
•
The student will be able to explain the slopes of various parts of heating and cooling curves.
Introduction In order to vaporize a liquid, heat must be added to raise the kinetic energy (temperature) to the phase change temperature and then more heat must be added to provide the necessary potential energy to separate
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