THE VIEW FROM ABOVE
One of the main reasons for the study of chemistry to be difficult has always been the difference in the way things seem to work from the point of view of the atom and the view from human being size. A human is usually between one and two meters tall. An atom is similarly usually between one and two Ångstroms in diameter. You might say that in any single length dimension there is a difference in size of about E10 (1010) between humans and atoms. What if there were a creature that was E10 larger than humans? How would it look to us and how would it see us? Let’s call such a large thing a vrumschk because I don’t know of anything else called a vrumschk. (If you know of anything called a vrumschk, or, even worse, someone with a name anything like it, PLEASE tell me so I can change it.) Your average vrumschk is 1.5 E 10 meters across. This distance is one light minute, so it takes a whole minute for light to go from one side to the other of a vrumschk. Vrumschks have a mass of less than the earth, so they are mostly in the form of what we would call a very low pressure gas. (You could quibble about that mass. Don’t bother.) Eight vrumschks would fit between the earth and the sun. A vrumschk would just barely be able to put its finger between the earth and the moon.
One vrumschk says to another, “Hey, Snerbert! Drift over here! You won’t believe this, but I am getting signals from this little round grain of crud. I would be willing to bet there is something living on that little speck.”
“You’ve been inhaling comet dust," says Snerbert, "There is no way to see anything that small because the frequency of electromagnetic radiation we can detect is far too large to make a picture of anything that small. Do you have any evidence that they exist?”
“I’ve been watching it for a few billion years and it has changed since that time. I have recently picked up signals in an extraordinary high frequency of electromagnetic radiation. Some are interpreted as vibration only and some can be changed into a picture. Something about Ricky Ricardo having to get back to the club before Lucy finds out about ……”
Likewise, we have evidence of the atoms even if we can’t see them directly. We know what they do under some conditions. We can get electromagnetic radiation from them, if not I Love Lucy programs. We have plenty of evidence of what goes on at the atomic level. Our best tool is our imagination. We construct models of the likely configuration of things on that level and test the idea against the other observations we can make of the materials.
The result of years of careful study of matter shows that the ‘micro’ world of atoms and subatomic particles is very different from the ‘macro’ world we live in. The way it was deduced has been a marvelous construction of head work and careful observation. It takes a bit of a leap of faith to take in the theory of how the micro world works until the mounting weight of evidence, as you see how more and more of it fits together, makes it seem a little more likely as you study chemistry.
KINETIC THEORY OF MATTER
The Kinetic Theory of Matter is the statement of how we believe atoms and molecules, particularly in gas form, behave and how it relates to the ways we have to look at the things around us. The Kinetic Theory is a good way to relate the 'micro world' with the 'macro world.'
A statement of the Kinetic Theory is:
- All matter is made of atoms, the smallest bit of each element. A particle of a gas could be an atom or a group of atoms.
- Atoms have an energy of motion that we feel as temperature. The motion of atoms or molecules can be in the form of linear motion of translation, the vibration of atoms or molecules against one another or pulling against a bond, and the rotation of individual atoms or groups of atoms.
- There is a temperature to which we can extrapolate, absolute zero, at which, theoretically, the motion of the atoms and molecules would stop.
- The pressure of a gas is due to the motion of the atoms or molecules of gas striking the object bearing that pressure. Against the side of the container and other particles of the gas, the collisions are elastic (with no friction).
- There is a very large distance between the particles of a gas compared to the size of the particles such that the size of the particle can be considered negligible.
Since light, electromagnetic radiation, is required to see an object and light hitting an object gives it energy, as soon as one is able to see an object at absolute zero, it is not at absolute zero anymore from the new energy. Any other means of detection would add energy to the material at absolute zero. An object at absolute zero would be as hard to keep as a lump of antimatter. What would you keep it in? Practically, we can cool something down to temperatures approaching absolute zero, but we cannot get to that theoretical point, nor can we achieve temperatures below that point. There is no such thing as a temperature below absolute zero.
The Kinetic Theory of Matter does not, and is not intended to, take into account the energy of atoms due to excitation of electrons as you might see in glowing neon in a neon light or the bright redness of molten iron. In fact, objects cooler than molten iron and less excited than electrified neon will give off electromagnetic radiation, but that is another story.
In the view at this level, it is useful to look at atoms as if they were close to the hard little balls that Dalton considered. With this very mechanical view of atoms and molecules, we are losing some important facts to get an instructive thought on matter.
Solids are materials in which the atoms or molecules are set in place. In ionic solids such as table salt crystals, the ions are connected to their neighbors by electrical attraction. Covalently linked crystals such as diamonds produce the hardest materials. In other solids, each unit may have its own spot in which it fits (as in sugar crystals) or it may be just a jumble of molecules as in glass that have decreased energy. Crystalline solids have characteristic angles and can be cleaved along lines defined by the aligning of atoms or molecules of the crystal. Amorphous (without crystal shape) solids can be like carbon black or linked as in plastics. The common point about solids is that the atoms or molecules are in place. The temperature that can be shown by solid materials is due to the movement in place of the atoms or molecules. They have no independent linear motion of translation because they are attached to one another. Solids can have molecular energy due to vibration and rotation. Picture a class of second graders glued to their seat. Each student can jump up and down and sideways and turn the chair around, but they can’t move out of place. Another useful mental picture is a junkyard for springs. The springs have all been tied to each other in one enormous mass. Each spring can twist and vibrate, but it can’t get loose from its neighbor.
It is now necessary to change from being able to see and understand each atom or molecule to our larger world. Solids show a definite shape and a definite volume. Unless forces are used that are not commonly found near the earth’s surface, solids can not be compressed.
Liquids are materials in which the atoms or molecules are as close to each other as solids, but the materials can slip over each other to change places. If you were only a few magnitudes larger than atoms, you might view liquids as B-B’s in a dump truck. Consider a large dump truck going fast down a very bumpy road. The B-B’s have some energy from the bumpy road. The top of the load is level. A few B-B’s are always in the process of getting enough energy to hop out of the dump truck. (This is a picture of vapor pressure of a liquid.) The B-B’s can be poured out of the dump truck. If there were a hole in the bottom of the dump truck, the B-B’s would leak out onto the ground. Like the B-B’s, liquids have no shape except for the shape of the container. B-B’s and liquids can not be compressed under common pressures. In a liquid the forces that hold the particles of liquid close to each other are greater than the forces due to motion that would force the particles away from each other.
The property of liquids of incompressibility is useful to us in hydraulic machines. A simple system of automobile hydraulic brakes are a good example of this. The brake pedal pushes a master cylinder. The travel (A description of distance (!) See Units and Measures.) of the brake petal is a few inches. The master cylinder pushes a small area of a liquid (hydraulic fluid) down a small tube (the brake lines) to the wheel cylinders. The wheel cylinders have a much larger area, but they go a shorter distance to push the brake pad against the drum or rotor, depending on what kind of brakes you have. The brake system cannot work correctly if there is any air (gas) in the system because the gas is compressible. Would anyone care to make a diagram of a hydraulic brake system to demonstrate this?
Gas, or vapor, is the most energetic phase of matter commonly found here on earth. The particles of gas, either atoms or molecules, have too much energy to settle down attached to each other or to come close to other particles to be attracted by them. Material in the vapor phase have no shape of their own, that is, they take on the shape of the container. Gases have no given volume. A certain amount of gas at a pressure of one atmosphere and a volume of ten liters could become five liters if the pressure was increased or would become more than ten liters if the pressure was decreased.. The gas expands to fill the container. The Gas Law that covers the calculations of the pressure, volume, and temperature of gases is in a later chapter.
How can you picture the materials as a gas? A pool table is only in two dimensions, but what if the balls kept moving and the pool table were in three dimensions? Such a pool table would be like a gas. The rails of the 3-D pool table would be the sides of the container. The billiard balls would bounce off each other in completely elastic collisions and would bounce off the sides of the table to produce a constant pressure. The real hallmark of the gas is that the motion of the particles is so great that the forces of attraction between the particles are not able to hold any of them together.
A WALK UP THE PHASE CHANGE GRAPH
On a piece of graph paper with the long side toward you, draw a graph with units of calories on the bottom from zero to nine hundred or a thousand calories and with temperature on the side, starting with minus twenty on the bottom and going up to about a hundred and twenty.
Let’s start with ice at minus twenty degrees Celsius and zero calories of heat added. That is cold for a home refrigerator. Most home refrigerators don’t cool ice to below minus twenty. Usually a home freezer can get down to minus forty. The ice cube you take out of a freezer that cold will attract humidity out of the air and freeze it to the ice cube. It looks as if the ice cube is growing hair. This does not happen in completely dry air, but really dry air is not comfortable for people. The ice cube increases its temperature by cooling the surroundings. The surroundings lose the calories while the ice cube gains the same number of calories. Materials of different temperature will exchange heat until the two materials are the same temperature. It takes energy to separate temperatures, which is why it takes energy to run a refrigerator or an air conditioner.
The ice cube takes up about one half of a calorie for each gram of ice for each degree temperature increase. You can plot a slanted line from zero calories and minus twenty degrees Celsius to ten calories and zero degrees Celsius. This melting point of ice, zero degrees Celsius, is the end of the line for that process. The slope of the line indicates the specific heat of the ice, that is, the amount of heat that is necessary to increase the temperature of that material in that phase. Q is the heat in calories ice gains as it increases in temperature. m is the mass of ice in grams. c is the specific heat of ice, about 0.5 calorie per gram degree. T is the temperature of the ice. (T2 - T1) or T, pronounced 'delta tee' is the change in temperature as the ice accepts heat.
Q = m c T is the equation that relates temperature change, specific heat, mass and heat of a material not changing phase, but changing temperature. Notice that the formula is the same for a downward change in temperature, but that the Q becomes negative for the ice as the temperature drops.
Once the ice cube reaches zero Celsius, there is a phase change. The ice changes from solid to liquid at the melting point. The same temperature is also the freezing point. To get the process of melting right, we are going to have to mix the materials well enough and do the heat changes slowly enough so that there are only very small changes of temperature throughout the container. The first drop of water from the ice cube has a temperature of zero degrees Celsius. The rest of the ice cube has the same temperature. As half of the ice has melted, the temperature of the water is zero degrees Celsius and so is the temperature of the ice. As the last little piece of ice is in the cup, the temperature of it is zero degrees Celsius and so is the water around it. THE PHASE CHANGE HAPPENS WITH NO CHANGE OF TEMPERATURE. The energy of the heat goes to increasing the molecular energy of motion of the water molecules.
As the ice melts, it takes about eighty calories (of heat) per gram (of ice) for the ice to melt. Continue the graph from the top of the line for the increase in temperature of ice for eighty degrees AT THE SAME TEMPERATURE. Go straight across the graph to show no change in temperature in a phase change. Q is the heat in calories gained by the ice. m is the mass of ice in grams. Hf is the “heat of fusion” of water, a measure of the amount of heat required to change the phase of one gram of ice (or water). (Draw your line from zero degrees Celsius and ten calories to the point zero degrees Celsius and ninety calories.)
Q = m Hf is the math formula for the phase change. Why is there no figure in this formula for a change in temperature?
When all the ice has melted, we have water at zero degrees Celsius. You know you can put water on a stove to accept more heat. As you increase the amount of heat the water accepts, the water increases in temperature by the slope of one calorie per gram degree. There is a considerable difference between the specific heat of water as a solid and water as a liquid. This is mainly due to the hydrogen bonding of water.
At the end of the eighty calorie straight line at zero degrees, begin the line for the warming of water as a liquid. The line goes up one hundred calories and goes up to one hundred degrees Celsius. You have seen this before. The water in the kettle increases in temperature as the heat from the stove is added to it. (Draw the line from zero degrees Celsius and ninety calories to 100 degrees C and 190 calories.)
The mathematical formula for the heating of water as a liquid is the same Q = m c (T2 - T2) as for the heating of ice. This time, thought, the specific heat of water as a liquid, c, is one calorie per gram degree.
The boiling point of water is one hundred degrees Celsius at one atmosphere pressure. At this temperature we are going to have another phase change. Just as with the change from solid to liquid, the phase change will occur with no change in temperature. The temperature at which the phase change happens, though depends upon the gas pressure on the liquid. At one standard atmosphere the boiling point of water is one hundred degrees. This is just another way of saying that the vapor pressure of water at one hundred degrees is one atmosphere. The boiling point of a liquid is the temperature at which the vapor pressure equals the ambient pressure. (Ambient pressure is the pressure around the material. Ambient pressure in open containers is the atmospheric pressure.) An open pot of water boiling on the stove will be one hundred degrees when the water begins to boil. Regardless of how rapidly the water boils, it can not reach temperatures above the boiling point. The last few drops of water at a boil will be at one hundred degrees.
It takes 540 calories per gram to change liquid water into water vapor by boiling at one atmosphere pressure. This is an incredibly large heat of vaporization (Hv). From the top of the line for heating liquid water to the boiling point, extend the line straight across (no change in temperature) for 540 calories. (Draw the line from 100 degrees C and 190 calories to 100 degrees C and 730 (!) calories.) The graph is a good way to see that the process of boiling water takes almost two and a half times the energy needed to bring the water up to temperature from minus twenty degrees. The formula for the boiling away of water is similar to the formula for melting ice, but Hv, the heat of vaporization substitutes for Hf, the heat of fusion. Q = m Hv
The number of 540 calories per gram to vaporize water seems high. It is. You can confirm this for yourself by the following quick-and-dirty experiment. Measure the temperature of a pot of water at about room temperature. Put the pot with water in it on a gas cooking eye or onto a hot electric eye. Time (in seconds) how long it takes the water to come to a boil (with the top on the pot most of the time). With the top off the pot, time how long it takes to boil out all the water. Make sure the heating device is producing the same amount of heat all through the experiment. Take the pot off the eye immediately after the water boils out and cool the pot (under a stream of running water). If you started at twenty degrees Celsius, it takes eighty calories per gram to get to the boiling point (at sea level). You can proportionate the times and find how much heat it takes to boil out the same amount of water that you brought to a boil. This experiment is not really accurate due to the heat capacity of the pot, the uncontrolled evaporation of the water, and the lack of accurate heating, but it can give you the vital information that the heat of vaporization of water is very large.
Once water is in the form of steam, it must be contained in order to be heated further. In a pressure cooker or boiler or other pressure device the temperature of the gas can be increased with the addition of heat. The formula again is: Q = m c (T2 - T1) and c, the specific heat is about one half of a calorie per gram degree.
There are a few things like free element iodine and carbon dioxide that go directly from a solid to a gas at normal atmospheric pressures. There are a number of materials that undergo chemical reactions at some temperature before they change phase, but most other materials go through the same type of phase changes as water, but with the numbers for melting point, boiling point, c, Hf, Hv, etc. that are properties of that material.
THE 'HEAT CURVE' FOR WATER
If you followed the instructions in the 'walk up the phase change pathway,' here is what you should have drawn. Leg 'A' is the warming of ice. Leg 'B' is the melting of ice. Leg 'C' is the warming of water. Leg 'D' is the boiling of water to steam. Leg 'E' is the warming of steam.
Live steam is the name given to water vapor at temperatures over the boiling point of water. The amount of energy required to change water into live steam can be reclaimed in the process of condensing the steam onto an object. Live steam is useful in pressing clothes, cleaning masonry or rugs, and very quick heating of water. The high efficiency of steam engines for trains and automobiles and the power they can produce is a testament to the great amount of energy in live steam. Live steam is extremely dangerous unless you have been given some training in how to use it. Many industrial accidents come from people using this primitive but powerful technology without proper training. High pressure boilers are used to make this readily accessible from many places in a site. In a hospital, for instance, the steam may be used to cook, to heat water, or to sterilize in different parts of the hospital. Not enough of the people using this powerful tool understand how dangerous it can be.
Just as the humidity in the air is not visible to the human eye, neither is live steam. You might think of a rapidly boiling kettle and remember the white plume coming out of the spout. That’s not live steam. Look closer to the spout of the kettle. There is a short space just past the spout where there is none of the white fluffy material. THAT is the live steam. If you put your finger into the white fluffy material, it will get hot and wet. If you put your finger into the clear space just after the end of the spout, it will burn you very quickly. The white fluffy material is just a cloud with warm water droplets in it. The water in the cloud has already lost the heat of vaporization back to the air. Not that we are accustomed to doing so, but the live steam area is the place to put an envelope you might want to steam open.
Steam engines use live steam. The fire uses energy to heat up a boiler. The boiler is under pressure as the steam builds up in the boiler. The pressure of the steam is used to drive a reciprocating steam engine or a steam turbine. The use of steam for transportation is very efficient and the engines burn any combustible fuel. Some of the reasons we don't have very many steam automobiles are, (1) there is some popular fear about a boiler in a car, (2) it takes some time to heat up the boiler so the car can go, and (3) the increased weight and instability of the car from carrying around a large container of water.
COOKING IN WATER
A lot of cooking is done in water. Boiling, poaching, and steaming have as lot of history in cooking. (After all, cooking is just some practical chemistry.) Cooking is just a matter of applying heat. The way the heat is applied, though, has a lot to do with how efficiently the heat is transferred, how evenly the heat is transferred, what other tastes and materials are taken on by the food in the process of heating, and how the amount of cooking is regulated. Boiling is a good way to efficiently transfer heat at a good, consistent temperature. It is easy to regulate how well an egg is to be cooked by timing the boiling of it. Boiling temperature varies with the altitude of the cooking and to a lesser extent with the small variations of the atmospheric pressure with the changes in weather. In Atlanta, Georgia with an elevation of one thousand feet above sea level, the boiling point of water averages about ninety-nine degrees Celsius, one degree lower than in Miami, Florida at sea level. In Denver, Colorado, the ‘mile high city,’ there is an even lower boiling point of water to an average of about ninety-five degrees Celsius. Since the cooking temperature is lower, the cooking time must be increased to get the same results.
Could you speed up cooking by keeping the heat all the way up on the stove? No, in an open pot cooking goes just as fast at a slow boil as at a vigorously rolling boil. Get the pot boiling and turn down the heat just enough to keep the pot boiling.
Could you speed up the cooking by increasing the pressure? Yes, pressure cookers work by increasing the pressure inside the cooker to increase the boiling temperature of water. Cooking with a pressure cooker requires enough water in the pot to increase the pressure by boiling water and trapping the vapor pressurized in a vessel. * * * * PRESSURE COOKERS CAN BE DANGEROUS. * * * * Follow the instructions carefully if you use a pressure cooker.
You know that carbon dioxide is a gas at room temperatures. You may have seen 'dry ice,' solid carbon dioxide. The dry ice appears to go directly from the solid state to the vapor phase. What happened to liquid carbon dioxide?
There is no such thing as liquid carbon dioxide at only one atmosphere of pressure. If you increase the pressure to about 23 atmospheres at -40 degrees, you can see some liquid carbon dioxide.
What is the difference between chemistry and physics? In a physics course, the study of the phases of matter is a subchapter of the chapter on thermodynamics. Here in Chemtutor we will do something of a Sluffover and Passoff job on thermodynamics just to give you a taste of the idea.
The word "thermodynamics" means the "movement of heat." That sounds somewhat silly if you define heat as, "the way we feel the movement of molecules." Perhaps a more useful definition of thermodynamics is, "the flow or transfer of heat." The symbol, "Q" is used for this flow of heat energy.
The First Law of Thermodynamics can be stated something like this: " Heat is a form of energy. Types of energy can be transferred from one type to another, and it is possible to account for all of the energy to show no loss or gain of energy from the transfer." This law is apparently violated by the famous Einstein equation, E = m c2, in which E is energy, m is mass and c is the velocity of light. This is the equation that shows that an incredibly small mass disappears when a nuclear reaction occurs and an incredibly large amount of energy is made. Einstein's equation does not violate the first law, but just shows us the difficult idea that mass and energy are just two different forms of the same thing. Mass is just a very concentrated form of energy. It is pretty difficult to get energy from mass. (And even more difficult to get mass from energy!)
The Second Law of Thermodynamics is a bit more complex. There are several ways to express it and several parts to it. "Usable work from a heat engine is available from a difference in temperature rather than any amount of material at the same temperature." and When two materials are combined, the temperature of both of them will become the same, a weighted average based on the specific heat and mass of the two materials coming together.
The Third Law of Thermodynamics describes material under a very specialized condition. It shows that it is impossible to bring and keep a material to absolute zero temperature, since absolute zero is the condition wherein a material has absolutely no motion of the atoms or molecules.
If a scientist looks at you without the trace of a smile and talks about the fourth law of thermodynamics, you know to avoid playing poker with that individual. There is no such thing, but in jest many a scientist has talked about Murphy's Law as being a Fourth Law of Thermodynamics, when actually it is a special case of the Second Law. Murphy's Law says, "If anything can go wrong, it will," and other humorous ways to explain perversity. The chemistry corollary to this is that, "All reactions tend toward maximum gunk. Buttered toast always lands butter - side - down," is a manifestation of Murphy's Law.
HEAT CURVE MATH
You should know the following facts about water by rote: x
The specific heat, c, of ice (solid water) is about 0.5 cal/gram degree.x
The specific heat, c, of liquid water is 1 cal/gram degreex
The specific heat, c, of water vapor (gaseous water) is about 0.5 cal/gram degreex
The heat of fusion, Hf, of water is 80 calories per gram.
The heat of vaporization, HV, of water is 540 calories per gram at 100 ºC.x
The melting point (and freezing point) of water is 0 ºC.x
The boiling point of water at one atmosphere pressure is 100 ºC.x
In most of the chemistry courses numbers for any other materials should be made available to you in the form of a table or chart so you can work the problems.
The only two formulas you need to know are; Q = m c T for changes of temperature with the change of heat (no phase change) and Q = m Hv or Q = m Hf for changes of phase.
- 1. How much heat is needed to warm 25 grams of water from 10ºC to 20ºC?
- How much heat is needed to warm 25 grams of water from -10ºC to 20ºC?
- What is the specific heat of copper metal if 200 cal increases the temperature of 40.9 g of it from 21 ºC to 73 ºC?
- How much heat is needed to increase the temperature of 12 grams of gold from 20 ºC to 95 ºC?
- What is the temperature of 40 grams of water at 45 ºC added to 60 grams of water at 95 ºC?
- What mass of live steam at 100 ºC is needed to heat 27.5 kg of water from 20 ºC to 100 ºC?
- A 641 gram iron horse shoe at 1100 ºC is dunked into a bucket containing 12.8 kg of water at 22 ºC. Assume that no steam was lost. (All of the steam leaves its heat of vaporization and its mass to the water in the bucket.) The horse shoe is taken out at 100 ºC, just after it has quit boiling the water around it. What is the new temperature of the water?
TABLE OF HEAT PROPERTIES OF SELECTED MATERIALS
Most of the numbers in this table are rounded to two significant digits. These numbers may be somewhat different a different temperatures, but that has been overlooked in this table.
|MATERIAL||SPECIFIC HEAT 20ºC||HEAT OF FUSION @mp||HEAT OF VAP. @bp|
|water||1.0 cal/g deg||80 cal/g||540 cal/g|
|aluminum||0.22 cal/g deg||94 cal/g||2510 cal/g2|
|ammonia||1.1 cal/gdeg||108 cal/g||327 cal/g|
|copper||0.094 cal/gdeg||49 cal/g||1130 cal/g1|
|gold||0.032 cal/gdeg||16 cal/g||377 cal/g2|
|iron||0.12 cal/gdeg||1510 cal/g2||84.52cal/g2|
|lead||0.032 cal/gdeg||5.5 cal/g||205 cal/g1|
|mercury||0.033 cal/gdeg||2.8 cal/g||71 cal/g|
|silver||0.056 cal/gdeg||26 cal/g||558 cal/g 1|
ANSWERS TO PROBLEMS
|1. 250 cal||2. 2625 cal||3. 0.094 cal/g deg||4. 28.8 cal|
|5. 75 ºC||6. 4074 grams||7. 26.0 ºC|
- David Wilner
- Dr. Lane Whitesell
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