The number of elements that appear ordinarily in the form of a gas is relatively small: oxygen, hydrogen, fluorine, and chlorine in the halogen "family"; and a handful of others, most notably the noble gases in Group 8 of the periodic table. Yet many substances can exist in the form of a gas, depending on the relative attraction and motion of molecules in that substance. A simple example, of course, is water, or H2O, which, though it appears as a liquid at room temperature, begins to vaporize and turn into steam at 212°F (100°C). In general, gases respond more dramatically to changes in pressure and temperature than do most other types of matter, and this allows scientists to predict gas behaviors under certain conditions. These predictions can explain mundane occurrences, such as the fact that an open can of soda will soon lose its fizz, but they also apply to more dramatic, life-and-death situations.
HOW IT WORKS
Molecular Motion and Phases of Matter
On Earth, three principal phases or states of matter exist: solid, liquid, and gas. The differences between these three are, on the surface at least, easily perceivable. Clearly water is a liquid, just as ice is a solid and steam a vapor or gas. Yet the ways in which various substances convert between phases are often complex, as are the interrelations between these phases. Ultimately, understanding of the phases depends on an awareness of what takes place at the molecular level.
All molecules are in motion, and the rate of that motion determines the attraction between them. The movement of molecules generates kinetic energy, or the energy of movement, which is manifested as thermal energy. In everyday language, thermal energy is what people mean when they say "heat"; but in scientific terms, heat has a different definition.
The force that attracts atoms to atoms, or molecules to molecules, is not the same as gravitational force, which holds the Moon in orbit around Earth, Earth in orbit around the Sun, and so on. By contrast, the force of interatomic and intermolecular attraction is electromagnetic. Just as the north pole of a magnet is attracted to the south pole of another magnet and repelled by that other magnet's north pole, so positive electric charges are attracted to negative charges, and negatives to positives. (In fact, electricity and magnetism are both manifestations of an electromagnetic interaction.)
The electromagnetic attractions between molecules are much more complex than this explanation makes it seem, and they play a highly significant role in chemical bonding. In simple terms, however, one can say that the greater the rate of motion for the molecules in relation to one another, the less the attraction between molecules. In addition, the kinetic energy, and hence the thermal energy, is greater in a substance whose molecules are relatively free to move.
When the molecules in a material move slowly in relation to one another, they exert a strong attraction, and the material is called a solid. Molecules of liquid, by contrast, move at moderate speeds and exert a moderate attraction. A material substance whose molecules move at high speeds, and therefore exert little or no attraction, is known as a gas.
Comparison of Gases to Other Phases of Matter
WATER AND AIR COMPARED.
Gases respond to changes in pressure and temperature in a manner remarkably different from that of solids or liquids. Consider the behavior of liquid water as compared with air—a combination of oxygen (O2), nitrogen (N2), and other gases—in response to experiments involving changes in pressure and temperature.
In the first experiment, both samples are subjected to an increase in pressure from 1 atm (that is, normal atmospheric pressure at sea level) to 2 atm. In the second, both experience an increase in temperature from 32°F (0°C) to 212°F (100°C). The differences in the responses of water and air are striking.
A sample of water that experiences an increase in pressure from 1 to 2 atm will decrease in volume by less than 0.01%, while a temperature increase from the freezing point to the boiling point will result in only a 2% increase in volume. For air, however, an equivalent pressure increase will decrease the volume by a whopping 50%, and an equivalent temperature increase results in a volume increase of 37%.
Air and other gases, by definition, have a boiling point below room temperature. If they did not boil and thus become gas well below ordinary temperatures, they would not be described as substances that are in the gaseous state in most circumstances. The boiling point of water, of course, is higher than room temperature, and that of solids is much higher.
THE ARRANGEMENT OF PARTICLES.
Solids possess a definite volume and a definite shape, and are relatively noncompressible: for instance, if one applies extreme pressure to a steel plate, it will bend, but not much. Liquids have a definite volume, but no definite shape, and tend to be noncompressible. Gases, on the other hand, possess no definite volume or shape, and are highly compressible.
At the molecular level, particles of solids tend to be definite in their arrangement and close in proximity—indeed, part of what makes a solid "solid," in the everyday meaning of that term, is the fact that its constituent parts are basically immovable. Liquid molecules, too, are close in proximity, though random in arrangement. Gas molecules are random in arrangement, but tend to be more widely spaced than liquid molecules.
There are a number of statements, collectively known as the "gas laws," that describe and predict the behavior of gases in response to changes in temperature, pressure, and volume. Temperature and volume are discussed elsewhere in this book. However, the subject of pressure requires some attention before we can continue with a discussion of the gas laws.
When a force is applied perpendicular to a surface area, it exerts pressure on that surface. Hence the formula for pressure is p = F /A, where p is pressure, F force, and A the area over which the force is applied. The greater the force, and the smaller the area of application, the greater the pressure; conversely, an increase in area—even without a reduction in force—reduces the overall pressure.
Pressure is measured by a number of units in the English and SI systems. Because p = F /A, all units of pressure represent some ratio of force to surface area.
UNITS OF PRESSURE.
The principal SI unit of pressure is called a pascal (Pa), or 1 N/m2. It is named for French mathematician and physicist Blaise Pascal (1623-1662), who is credited with Pascal's principle. The latter holds that the external pressure applied on a fluid—which, in the physical sciences, can mean either a gas or a liquid—is transmitted uniformly throughout the entire body of that fluid.
A newton (N), the SI unit of force, is equal to the force required to accelerate 1 kg of mass at a rate of 1 m/sec2. Thus a Pascal is the pressure of 1 newton over a surface area of 1 m2. In the English or British system, pressure is measured in terms of pounds per square inch, abbreviated as lbs./in2. This is equal to 6.89 · 103 Pa, or 6,890 Pa.
Another important measure of pressure is the atmosphere (atm), which is the average pressure exerted by air at sea level. In English units, this is equal to 14.7 lb/in2, and in SI units, to 1.013 · 105 Pa.
There are two other specialized units of pressure measurement in the SI system: the bar, equal to 105 Pa, and the torr, equal to 133 Pa. Meteorologists, scientists who study weather patterns, use the millibar (mb), which, as its name implies, is equal to 0.001 bars. At sea level, atmospheric pressure is approximately 1,013 mb.
The torr, also known as the millimeter of mercury (mm Hg), is the amount of pressure required to raise a column of mercury (chemical symbol Hg) by 1 mm. It is named for Italian physicist Evangelista Torricelli (1608-1647), who invented the barometer, an instrument for measuring atmospheric pressure.
The barometer constructed by Torricelli in 1643 consisted of a long glass tube filled with mercury. The tube was open at one end, and turned upside down into a dish containing more mercury: the open end was submerged in mercury, while the closed end at the top constituted a vacuum—that is, an area devoid of matter, including air.
The pressure of the surrounding air pushed down on the surface of the mercury in the bowl, while the vacuum at the top of the tube provided an area of virtually no pressure into which the mercury could rise. Thus the height to which the mercury rose in the glass tube represented normal air pressure (that is, 1 atm.) Torricelli discovered that at standard atmospheric pressure, the column of mercury rose to 760 mm (29.92 in).
The value of 1 atm was thus established asequal to the pressure exerted on a column ofmercury 760 mm high at a temperature of 0°C(32°F). In time, Torricelli's invention became afixture both of scientific laboratories and ofhouseholds. Since changes in atmospheric pressure have an effect on weather patterns, manyhome indoor-outdoor thermometers today alsoinclude a barometer.
Introduction to the Gas Laws
English chemist Robert Boyle (1627-1691), who made a number of important contributions to chemistry—including his definition and identification of elements—seems to have been influenced by Torricelli. If so, this is an interesting example of ideas passing from one great thinker to another: Torricelli, a student of Galileo Galilei (1564-1642), was no doubt influenced by Galileo's thermoscope.
Like Torricelli, Boyle conducted tests involving the introduction of mercury to a tube closed at the other end. The tube Boyle used was shaped like the letter J, and it was so long that he had to use the multi-story foyer of his house as a laboratory. At the tip of the curved bottom was an area of trapped gas, and into the top of the tube, Boyle introduced increasing quantities of mercury. He found that the greater the volume of mercury, the greater the pressure on the gas, and the less the volume of gas at the end of the tube. As a result, he formulated the gas law associated with his name.
The gas laws are not a set of government regulations concerning use of heating fuel; rather, they are a series of statements concerning the behavior of gases in response to changes in temperature, pressure, and volume. These were derived, beginning with Boyle's law, during the seventeenth, eighteenth, and nineteenth centuries by scientists whose work is commemorated through the association of their names with the laws they discovered. In addition to Boyle, these men include fellow English chemists John Dalton (1766-1844) and William Henry (1774-1836); French physicists and chemists J. A. C. Charles (1746-1823) and Joseph Gay-Lussac (1778-1850); and Italian physicist Amedeo Avogadro (1776-1856).
There is a close relationship between Boyle's, Charles's, and Gay-Lussac's laws. All of these treat one of three parameters—temperature, pressure, or volume—as fixed quantities in order to explain the relationship between the other two variables. Avogadro's law treats two of the parameters as fixed, thereby establishing a relationship between volume and the number of molecules in a gas. The ideal gas law sums up these four laws, and the kinetic theory of gases constitutes an attempt to predict the behavior of gases based on these laws. Finally, Dalton's and Henry's laws both relate to partial pressure of gases.
Boyle's, Charles's, and Gay-Lussac's Laws
BOYLE'S AND CHARLES'S LAWS.
Boyle's law holds that in isothermal conditions (that is, a situation in which temperature is kept constant), an inverse relationship exists between the volume and pressure of a gas. (An inverse relationship is a situation involving two variables, in which one of the two increases in direct proportion to the decrease in the other.) In this case, the greater the pressure, the less the volume and vice versa. Therefore, the product of the volume multiplied by the pressure remains constant in all circumstances.
Charles's law also yields a constant, but in this case the temperature and volume are allowed to vary under isobarometric conditions—that is, a situation in which the pressure remains the same. As gas heats up, its volume increases, and when it cools down, its volume reduces accordingly. Hence, Charles established that the ratio of temperature to volume is constant.
In about 1787, Charles made an interesting discovery: that at 0°C (32°F), the volume of gas at constant pressure drops by 1/273 for every Celsius degree drop in temperature. This seemed to suggest that the gas would simply disappear if cooled to −273°C (−459.4°F), which, of course, made no sense. In any case, the gas would most likely become first a liquid, and then a solid, long before it reached that temperature.
The man who solved the quandary raised by Charles's discovery was born a year after Charles died. He was William Thomson, Lord Kelvin (1824-1907); in 1848, he put forward the suggestion that it was molecular translational energy—the energy generated by molecules in motion—and not volume, that would become zero at −273°C. He went on to establish what came to be known as the Kelvin scale of absolute temperature.
Sometimes known as the absolute temperature scale, the Kelvin scale is based not on the freezing point of water, but on absolute zero—the temperature at which molecular motion comes to a virtual stop. This is −273.15°C (−459.67°F). In the Kelvin scale, which uses neither the term nor the symbol for "degree," absolute zero is designated as 0K.
Scientists prefer the Kelvin scale to the Celsius, and certainly to the Fahrenheit, scales. If the Kelvin temperature of an object is doubled, its average molecular translational energy has doubled as well. The same cannot be said if the temperature were doubled from, say, 10°C to 20°C, or from 40°F to 80°F, since neither the Celsius nor the Fahrenheit scale is based on absolute zero.
From Boyle's and Charles's law, a pattern should be emerging: both treat one parameter (temperature in Boyle's, pressure in Charles's) as unvarying, while two other factors are treated as variables. Both, in turn, yield relationships between the two variables: in Boyle's law, pressure and volume are inversely related, whereas in Charles's law, temperature and volume are directly related.
In Gay-Lussac's law, a third parameter, volume, is treated as a constant, and the result is a constant ratio between the variables of pressure and temperature. According to Gay-Lussac's law, the pressure of a gas is directly related to its absolute temperature.
Gay-Lussac also discovered that the ratio in which gases combine to form compounds can be expressed in whole numbers: for instance, water is composed of one part oxygen and two parts hydrogen. In the language of modern chemistry, this is expressed as a relationship between molecules and atoms: one molecule of water contains one oxygen atom and two hydrogen atoms.
In the early nineteenth century, however, scientists had yet to recognize a meaningful distinction between atoms and molecules, and Avogadro was the first to achieve an understanding of the difference. Intrigued by the whole-number relationship discovered by Gay-Lussac, Avogadro reasoned that one liter of any gas must contain the same number of particles as a liter of another gas. He further maintained that gas consists of particles—which he called molecules—that in turn consist of one or more smaller particles.
In order to discuss the behavior of molecules, Avogadro suggested the use of a large quantity as a basic unit, since molecules themselves are very small. Avogadro himself did not calculate the number of molecules that should be used for these comparisons, but when that number was later calculated, it received the name "Avogadro's number" in honor of the man who introduced the idea of the molecule. Equal to 6.022137 · 1023, Avogadro's number designates the quantity of atoms or molecules (depending on whether the substance in question is an element or a compound) in a mole.
Today the mole (abbreviated mol), the SI unit for "amount of substance," is defined precisely as the number of carbon atoms in 12.01 g of carbon. The term "mole" can be used in the same way we use the word "dozen." Just as "a dozen" can refer to twelve cakes or twelve chickens, so "mole" always describes the same number of molecules. The ratio of mass between a mole of Element A and Element B, or Compound A and Compound B, is the same as the ratio between the mass of Atom A and Atom B, or Molecule A and Molecule B. Avogadro's law describes the connection between gas volume and number of moles. According to Avogadro's law, if the volume of gas is increased under isothermal and isobarometric conditions, the number of moles also increases. The ratio between volume and number of moles is therefore a constant.
The Ideal Gas Law
Once again, it is easy to see how Avogadro's law can be related to the laws discussed earlier. Like the other three, this one involves the parameters of temperature, pressure, and volume, but it also introduces a fourth—quantity of molecules (that is, number of moles). In fact, all the laws so far described are brought together in what is known as the ideal gas law, sometimes called the combined gas law.
The ideal gas law can be stated as a formula, pV = nRT, where p stands for pressure, V for volume, n for number of moles, and T for temperature. R is known as the universal gas constant, a figure equal to 0.0821 atm · liter/mole · K. (Like most figures in chemistry, this one is best expressed in metric rather than English units.)
Given the equation pV = nRT and the fact that R is a constant, it is possible to find the value of any one variable—pressure, volume, number of moles, or temperature—as long as one knows the value of the other three. The ideal gas law also makes it possible to discern certain relationships: thus, if a gas is in a relatively cool state, the product of its pressure and volume is proportionately low; and if heated, its pressure and volume product increases correspondingly.
The Kinetic Theory of Gases
From the preceding gas laws, a set of propositions known collectively as the kinetic theory of gases has been derived. Collectively, these put forth the proposition that a gas consists of numerous molecules, relatively far apart in space, which interact by colliding. These collisions are responsible for the production of thermal energy, because when the velocity of the molecules increases—as it does after collision—the temperature increases as well.
There are five basic postulates to the kinetic theory of gases:
- 1. Gases consist of tiny molecular or atomic particles.
- 2. The proportion between the size of these particles and the distances between them is so small that the individual particles can be assumed to have negligible volume.
- 3. These particles experience continual random motion. When placed in a container, their collisions with the walls of the container constitute the pressure exerted by the gas.
- 4. The particles neither attract nor repel one another.
- 5. The average kinetic energy of the particles in a gas is directly related to absolute temperature.
These observations may appear to resemble statements made earlier concerning the differences between gases, liquids, and solids in terms of molecular behavior. If so, that is no accident: the kinetic theory constitutes a generally accepted explanation for the reasons why gases behave as they do. Kinetic theories do not work as well for explaining the behaviors of solids and liquids; nonetheless, they do go a long way toward identifying the molecular properties inherent in the various phases of matter.
Laws of Partial Pressure
In addition to all the gas laws so far discussed, two laws address the subject of partial pressure. When two or more gases are present in a container, partial pressure is the pressure that one of them exerts if it alone is in the container.
Dalton's law of partial pressure states that the total pressure of a gas is equal to the sum of its partial pressures. As noted earlier, air is composed mostly of nitrogen and oxygen. Along with these are small components, carbon dioxide, and gases collectively known as the rare or noble gases: argon, helium, krypton, neon, radon, and xenon. Hence, the total pressure of a given quantity of air is equal to the sum of the pressures exerted by each of these gases.
Henry's law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the surface of the solution. This applies only to gases such as oxygen and hydrogen that do not react chemically to liquids. On the other hand, hydrochloric acid will ionize when introduced to water: one or more of its electrons will be removed, and its atoms will convert to ions, which are either positive or negative in charge.
Applications of Dalton's and Henry's Laws
PARTIAL PRESSURE: A MATTER OF LIFE AND POSSIBLE DEATH FOR SCUBA DIVERS.
The gas laws are not just a series of abstract statements. Certainly, they do concern the behavior of ideal as opposed to real gases. Like all scientific models, they remove from the equation all outside factors, and treat specific properties in isolation. Yet, the behaviors of the ideal gases described in the gas laws provide a key to understanding the activities of real gases in the real world. For instance, the concept of partial pressure helps scuba divers avoid a possibly fatal sickness.
Imagine what would happen if a substance were to bubble out of one's blood like carbon dioxide bubbling out of a soda can, as described below. This is exactly what can happen to an undersea diver who returns to the surface too quickly: nitrogen rises up within the body, producing decompression sickness—known colloquially as "the bends." This condition may manifest as itching and other skin problems, joint pain, choking, blindness, seizures, unconsciousness, permanent neurological defects such as paraplegia, and possibly even death.
If a scuba diver descending to a depth of 150 ft (45.72 m) or more were to use ordinary air in his or her tanks, the results would be disastrous. The high pressure exerted by the water at such depths creates a high pressure on the air in the tank, meaning a high partial pressure on the nitrogen component in the air. The result would be a high concentration of nitrogen in the blood, and hence the bends.
Instead, divers use a mixture of helium and oxygen. Helium gas does not dissolve well in blood, and thus it is safer for a diver to inhale this oxygen-helium mixture. At the same time, the oxygen exerts the same pressure that it would normally—in other words, it operates in accordance with Dalton's observations concerning partial pressure.
OPENING A SODA CAN.
Inside a can or bottle of carbonated soda is carbon dioxide gas (CO2), most of which is dissolved in the drink itself. But some of it is in the space (sometimes referred to as "head space") that makes up the difference between the volume of the soft drink and the volume of the container.
At the bottling plant, the soda manufacturer adds high-pressure carbon dioxide (CO2) to the head space in order to ensure that more CO2 will be absorbed into the soda itself. This is in accordance with Henry's law: the amount of gas (in this case CO2) dissolved in the liquid (soda) is directly proportional to the partial pressure of the gas above the surface of the solution—that is, the CO2 in the head space. The higher the pressure of the CO2 in the head space, the greater the amount of CO2 in the drink itself; and the greater the CO2 in the drink, the greater the "fizz" of the soda.
Once the container is opened, the pressure in the head space drops dramatically. Once again, Henry's law indicates that this drop in pressure will be reflected by a corresponding drop in the amount of CO2 dissolved in the soda. Over a period of time, the soda will release that gas, and eventually, it will go "flat."
A fire extinguisher consists of a long cylinder with an operating lever at the top. Inside the cylinder is a tube of carbon dioxide surrounded by a quantity of water, which creates pressure around the CO2 tube. A siphon tube runs vertically along the length of the extinguisher, with one opening in the water near the bottom. The other end opens in a chamber containing a spring mechanism attached to a release valve in the CO2 tube.
The water and the CO2 do not fill the entire cylinder: as with the soda can, there is "head space," an area filled with air. When the operating lever is depressed, it activates the spring mechanism, which pierces the release valve at the top of the CO2 tube. When the valve opens, the CO2 spills out in the "head space," exerting pressure on the water. This high-pressure mixture of water and carbon dioxide goes rushing out of the siphon tube, which was opened when the release valve was depressed. All of this happens, of course, in a fraction of a second—plenty of time to put out the fire.
Aerosol cans are similar in structure to fire extinguishers, though with one important difference. As with the fire extinguisher, an aerosol can includes a nozzle that depresses a spring mechanism, which in turn allows fluid to escape through a tube. But instead of a gas cartridge surrounded by water, most of the can's interior is made up of the product (for instance, deodorant), mixed with a liquid propellant.
The "head space" of the aerosol can is filled with highly pressurized propellant in gas form, and, in accordance with Henry's law, a corresponding proportion of this propellant is dissolved in the product itself. When the nozzle is depressed, the pressure of the propellant forces the product out through the nozzle.
A propellant, as its name implies, propels the product itself through the spray nozzle when the nozzle is depressed. In the past, chlorofluorocarbons (CFCs)—manufactured compounds containing carbon, chlorine, and fluorine atoms—were the most widely used form of propellant. Concerns over the harmful effects of CFCs on the environment, however, has led to the development of alternative propellants, most notably hydrochlorofluorocarbons (HCFCs), CFC-like compounds that also contain hydrogen atoms.
Applications of Boyle's, Charles's, and Gay-Lussac's Laws
WHEN THE TEMPERATURE CHANGES.
A number of interesting results occur when gases experience a change in temperature, some of them unfortunate and some potentially lethal. In these instances, it is possible to see the gas laws—particularly Boyle's and Charles's—at work.
There are numerous examples of the disastrous effects that result from an increase in the temperature of combustible gases, including natural gas and petroleum-based products. In addition, the pressure on the gases in aerosol cans makes the cans highly explosive—so much so that discarded cans at a city dump may explode on a hot summer day. Yet, there are other instances when heating a gas can produce positive effects.
A hot-air balloon, for instance, floats because the air inside it is not as dense than the air outside. According to Charles's law, heating a gas will increase its volume, and since gas molecules exert little attraction toward one another, they tend to "spread out" even further with an increase of volume. This, in turn, creates a significant difference in density between the air in the balloon and the air outside, and as a result, the balloon floats.
Although heating a gas can be beneficial, cooling a gas is not always a wise idea. If someone were to put a bag of potato chips into a freezer, thinking this would preserve their flavor, he would be in for a disappointment. Much of what maintains the flavor of the chips is the pressurization of the bag, which ensures a consistent internal environment so that preservative chemicals, added during the manufacture of the chips, can keep them fresh. Placing the bag in the freezer causes a reduction in pressure, as per Gay-Lussac's law, and the bag ends up a limp version of its former self.
Propane tanks and tires offer an example of the pitfalls that may occur by either allowing a gas to heat up or cool down by too much. Because most propane tanks are made according to strict regulations, they are generally safe, but it is not entirely inconceivable that the extreme heat of a summer day could cause a defective tank to burst. An increase in temperature leads to an increase in pressure, in accordance with Gay-Lussac's law, and could lead to an explosion.
Because of the connection between heat and pressure, propane trucks on the highways during the summer are subjected to weight tests to ensure that they are not carrying too much gas. On the other hand, a drastic reduction in temperature could result in a loss in gas pressure. If a propane tank from Florida were transported by truck during the winter to northern Canada, the pressure is dramatically reduced by the time it reaches its destination.
THE INTERNAL-COMBUSTION ENGINE.
In operating a car, we experience two applications of the gas laws. One of these is what makes the car run: the combustion of gases in the engine, which illustrates the interrelation of volume, pressure, and temperature expressed in the laws attributed to Boyle, Charles, and Gay-Lussac. The other is, fortunately, a less frequent phenomenon—but it can and does save lives. This is the operation of an airbag, which depends, in part, on the behaviors explained in Charles's law.
When the driver of a modern, fuel-injection automobile pushes down on the accelerator, this activates a throttle valve that sprays droplets of gasoline mixed with air into the engine. The mixture goes into the cylinder, where the piston moves up, compressing the gas and air. While the mixture is still at a high pressure, the electric spark plug produces a flash that ignites the gasoline-air mixture. The heat from this controlled explosion increases the volume of air, which forces the piston down into the cylinder. This opens an outlet valve, causing the piston to rise and release exhaust gases.
As the piston moves back down again, an inlet valve opens, bringing another burst of gasoline-air mixture into the chamber. The piston, whose downward stroke closed the inlet valve, now shoots back up, compressing the gas and air to repeat the cycle. The reactions of the gasoline and air to changes in pressure, temperature, and volume are what move the piston, which turns a crankshaft that causes the wheels to rotate.
So much for moving—what about stopping? Most modern cars are equipped with an airbag, which reacts to sudden impact by inflating. This protects the driver and front-seat passenger, who, even if they are wearing seatbelts, may otherwise be thrown against the steering wheel or dashboard.
In order to perform its function properly, the airbag must deploy within 40 milliseconds (0.04 seconds) of impact. Not only that, but it has to begin deflating before the body hits it. If a person's body, moving forward at speeds typical in an automobile accident, were to smash against a fully inflated airbag, it would feel like hitting concrete—with all the expected results.
The airbag's sensor contains a steel ball attached to a permanent magnet or a stiff spring. The spring or magnet holds the ball in place through minor mishaps when an airbag is not warranted—for instance, if a car were simply to be "tapped" by another in a parking lot. But in a case of sudden deceleration, the magnet or spring releases the ball, sending it down a smooth bore. The ball flips a switch, turning on an electrical circuit. This in turn ignites a pellet of sodium azide, which fills the bag with nitrogen gas.
At this point, the highly pressurized nitrogen gas molecules begin escaping through vents. Thus, as the driver's or rider's body hits the airbag, the deflation of the bag is moving it in the same direction that the body is moving—only much, much more slowly. Two seconds after impact, which is an eternity in terms of the processes involved, the pressure inside the bag has returned to 1 atm.
The chemistry of the airbag is particularly interesting. The bag releases inert, or non-reactive, nitrogen gas, which poses no hazard to human life; yet one of the chemical ingredients in the airbag is so lethal that some environmentalist groups have begun to raise concerns over its presence in airbags. This is sodium azide (NaN3), one of three compounds—along with potassium nitrate (KNO3) and silicon dioxide (SiO2)—present in an airbag prior to inflation.
The sodium azide and potassium nitrate react to one another, producing a burst of hot nitrogen gas in two back-to-back reactions. In the fractions of a second during which this occurs, the airbag becomes like a solid-rocket booster, experiencing a relatively slow detonation known as "deflagration."
The first reaction releases nitrogen gas, which fills the bag, while the second reaction leaves behind the by-products potassium oxide (K2O) and sodium oxide (Na2O). These combine with the silicon dioxide to produce a safe, stable compound known as alkaline silicate. The latter, similar to the sand used for making glass, is all that remains in the airbag after the nitrogen gas has escaped.
WHERE TO LEARN MORE
"Atmospheric Pressure: The Force Exerted by the Weight of Air" (Web site). <http://kids.earth.nasa.gov/archive/air_pressure/> (April 7, 2001).
"Chemical Sciences Structure: Structure of Matter: Nature of Gases" University of Alberta Chemistry Department (Web site). <http://www.chem.ualberta.ca/~plambeck/che/struct/s0307.htm> (May 12, 2001).
"Chemistry Units: Gas Laws." <http://bio.bio.rpi.edu/MS99/ausemaW/chem/gases.html> (February 21, 2001).
"Homework: Science: Chemistry: Gases" Channelone.com (Web site). <http://www.channelone.com/fasttrack/science/chemistry/gases.html> (May 12, 2001).
"Kinetic Theory of Gases: A Brief Review" University of Virginia Department of Physics (Web site). <http://www.phys.virginia.edu/classes/252/kinetic_theory.html> (April 15, 2001).
Laws of Gases. New York: Arno Press, 1981.
Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.
Mebane, Robert C. and Thomas R. Rybolt. Air and Other Gases. Illustrations by Anni Matsick. New York: Twenty-First Century Books, 1995.
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
Temperature in relation to absolute zero (−273.15°C or −459.67°F), as measured on the Kelvin scale. The Kelvin and Celsiusscales are directly related; hence, Celsius temperatures can be converted to Kelvins (for which neither the word nor the symbol for "degree" are used) by adding273.15.
A measure of pressure, abbreviated "atm" and equal to the average pressure exerted by air at sea level. In English units, this is equal to 14.7 lb/in2, and in SI units, to 101,300 pascals.
A statement, derived by the Italian physicist Amedeo Avogadro (1776-1856), which holds that as the volume of gas increases under isothermal and isobarometric conditions, the number of molecules (expressed in terms of mole number), increases as well. Thus, the ratio of volume to mole number is aconstant.
An instrument form easuring atmospheric pressure.
A statement, derived by English chemist Robert Boyle (1627-1691), which holds that for gases in isothermal conditions, an inverse relationship exists between the volume and pressure of a gas. This means that the greater the pressure, the less the volume and viceversa, and therefore the product of pressure multiplied by volume yields a constantfigure.
A statement, derived by French physicist and chemist J. A. C. Charles (1746-1823), which holds that for gases in isobarometric conditions, the ratio between the volume and temperature of a gas is constant. This means that the greater the temperature, the greater the volume, and vice versa.
DALTON'S LAW OF PARTIAL PRES SURE:
A statement, derived by the English chemist John Dalton (1766-1844), which holds that the total pressure of a gas is equal to the sum of its partial pressures—that is, the pressure exerted by each component of the gas mixture.
A phase of matter in which molecules move at high speeds, and therefore exert little or no attraction toward one another.
A series of statements concerning the behavior of gases in response to changes in temperature, pressure, and volume. The gas laws, developed by scientists during the seventeenth, eighteenth, and nineteenth centuries, include Avogadro's law, Boyle's law, Charles's law, Dalton's law of partial pressures, Gay-Lussac's law, and Henry's law. These are summed up in the ideal gas law. The kinetic theory of gases is based on observations garnered from these laws.
A statement, derived by French physicist and chemist Joseph Gay-Lussac (1778-1850), which holds that the pressure of a gas is directly related to its absolute temperature. Hence, the ratio of pressure to absolute temperature is a constant.
A statement, derived by English chemist William Henry (1774-1836), which holds that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the solution. This holds true only for gases, such as hydrogen and oxygen, which don ot react chemically to liquids.
IDEAL GAS LAW:
A proposition, also known as the combined gas law, which draws on all the gas laws. The ideal gas lawcan be expressed as the formula pV = nRT, where p stands for pressure, V for volume, n for number of moles, and T for temperature. R is known as the universal gas constant, a figure equal to 0.0821 atm · liter/mole · K.
Referring to a situation in which temperature is kept constant.
Referring to a situation in which pressure is kept constant.
The energy that an object possesses by virtue of its motion.
KINETIC THEORY OF GASES:
A set of propositions describing a gas as consisting of numerous molecules, relatively far apart in space, which interact by colliding. These collisions are responsible for the production of thermal energy, because when the velocity of the molecules increases—as it does after collision—the temperature increases as well.
MILLIMETER OF MERCURY:
Another name for the torr, abbreviated mm Hg.
The SI fundamental unit for "amount of substance." The quantity of molecules or atoms in a mole is, generallyspeaking, the same as Avogadro's number: 6.022137 · 1023. However, in the more precise SI definition, a mole is equal to the number of carbon atoms in 12.01 g of carbon.
When two or more gases are present in a container, partial pressure is the pressure that one of them exerts if it alone is in the container. Dalton's law of partial pressure and Henry's law relate to the partial pressure of gases.
The principle SI or metricunit of pressure, abbreviated "Pa" and equal to 1 N/m2.
The ratio of force to surface area, when force is applied in a direction perpendicular to that surface.
A form of kinetic energy—commonly called "heat"—that is produced by the movement of atomic or molecular particles. The greater the motion of these particles relative to one another, the greater the thermal energy.
An SI unit, also known as the millimeter of mercury, that represents the pressure required to raise a column of mercury 1 mm. The torr, equal to 133 Pascals, is named for the Italian physicist Evangelista Torricelli (1608-1647), who invented the barometer.
A gas is a state of matter in which a substance does not have a specific shape or volume of its own, but adopts the form and size of its container. It was the early-seventeenth-century Flemish chemist-physician Jan Baptista van Helmont who coined the word "gas" (from the Greek chaos ) in order to convey the idea that a gas had an indefinite shape and size. This is an apt name because, as was later hypothesized and confirmed, gas molecules are distributed uniformly throughout a container without any apparent spatial organization, and they undergo incessant, seemingly chaotic, random motion.
A liquid, like a gas, has no shape of its own, but it does have a definite volume. Both states of matter are referred to as fluids because of their mobility, or tendency to flow. A gas is actually a low density fluid because the molecules are much farther apart than in a liquid where molecules are in close contact with each other. For example, at room temperature and at atmospheric pressure the density of air is about 0.0012 grams (0.000042 ounces) per cubic centimeter (g/cm3), whereas the density of liquid air is approximately 0.810 g/cm3 (at its normal boiling point of −209°C, or −344°F). This corresponds to an average separation between molecules in the gas phase that is about nine times larger than that for the liquid. A liquid is thus called a condensed phase—or a high density fluid—and is roughly 1,000 times more dense than a gas.
A compound exists in the gaseous state because the attractive forces between the molecules are weak and/or the average distance between them is large. Liquifaction, or condensation of the gas, may occur if the kinetic energy of the molecules is reduced (by cooling) and/or the intermolecular distance is made smaller (by compression).
There are four intrinsic, measurable properties of a gas (or, for that matter, any substance): its pressure P, temperature T, volume (in the case of a gas, the container volume) V, and mass m, or mole number n. The gas density d is a derived quantity, which is m/V. Before the relationships between these properties for a gas are discussed, the units in which they are usually reported will be outlined.
Pressure is defined as force per unit area. In the International System of Units (SI, or mks), unit pressure corresponds to one newton per square meter, which is denoted as one pascal or Pa (named after Blaise Pascal, the seventeenth-century French scientist). There are several other, more commonly used pressure units, however. One is the atmosphere or atm; it is based on the magnitude of the pressure actually exerted by Earth's atmosphere at sea level. Because atmospheric pressure varies, one atmosphere is simply defined as the pressure that is exerted by a 760-mm-high column of mercury, a dense liquid sometimes used to measure pressures. Note that 760 mm is equivalent to 29.91 inches, which is close to the value sometimes cited in weather reports of atmospheric pressure. Another pressure unit is the torr (named after the seventeenth-century Italian scientist Evangelista Torricelli). One torr is equivalent to one mm Hg.
One pascal corresponds to a very small pressure as compared with one atm, that is, 1 Pa = 9.86923 × 10−6 atm. The bar is another commonly used pressure unit. One bar is defined as 105 Pa and is equal to 750 torr.
Temperature is often reported in degrees Celsius. One Celsius degree is defined as 1/100 of the temperature difference between boiling water and freezing water (both at 1 atm pressure). In this scale, the temperature of pure water at its freezing point is 0°C (32°F) at 1 atm pressure. Another important temperature scale is the absolute temperature. The absolute temperature of pure liquid water in coexistence with ice and water vapor (the triple point) is defined as exactly 273.16 kelvins (K). This condition corresponds to 0.01°C, and thus the relationship between the Celsius (t) and Kelvin scales (T) is
t = T − 273.15°
The significance of the Kelvin scale is that 0 K represents the lowest temperature that can, in theory, be attained and corresponds to the condition in which molecular translational and rotational motion ceases.
The SI unit of volume is the cubic meter (m3), but in most scientific applications, volumes are usually measured in cubic centimeters (cm3) or liters (L). One liter contains 1,000 milliliters (mL), or equivalently, 1,000 cm3.
The SI unit of quantity is called the mole (symbol n and abbreviation mol). It is derived from the Latin moles (meaning "a mass"). One mole of a substance contains Avogadro's number of elementary units of the substance. Because atoms and molecules are extremely small entities, Avogadro's number (N A) is incomprehensibly large, 6.022 × 1023 particles/mol. Thus, one mole of hydrogen atoms contains 6.022 × 1023 H atoms, one mole of sucrose molecules consists of 6.022 × 1023 sucrose molecules, and so forth.
Relationships among Gas Properties
From the earliest days of quantitative inquiry, scientists have sought to uncover the mathematical relationships that describe natural phenomena, including the properties of gases. Because there are four fundamental properties of a gas, namely, P, T, V, and n, discovering the relationship between any two requires that the other two properties be kept constant. Some of the earliest quantitative studies of gases were reported in the mid-1600s by British chemist Robert Boyle, who found that for a fixed amount of a gas at a specific temperature (i.e., constant n and T ), the volume was inversely proportional to the applied pressure. This V-P relationship, known as Boyle's law, is represented as
V = c/P
PV = c
where c is an experimental constant that depends on the amount of gas and its temperature.
Figure 1 illustrates Boyle's law with a plot of the volume occupied by one mole of a gas at 300 K as a function of pressure.
In the later part of the eighteenth century, French chemist Jacques Charles studied the relationship between the volume of a fixed amount of gas and its temperature, while keeping the gas at constant pressure. He found that V was a linear function of the temperature. Figure 2 graphically represents this relationship, known as Charles's law, with a plot of the gas volume versus the temperature in Celsius, t.
Mathematically, Charles's law is expressed as
V = a + bt
where a and b are constants. The same data are plotted with expanded scales in Figure 3 to illustrate the fact that the x -intercept a has a value of −273.15°C, and it is evident that this value, called absolute zero, corresponds to the temperature at which the volume of a gas extrapolates to zero, its logically limiting value. This condition is the basis of the absolute temperature, or Kelvin scale, and was proposed in the mid-1800s by Lord Kelvin (British physicist William Thomson). Charles's law can be expressed in terms of the absolute temperature as
V = c′T
where c′ is a constant; thus, the volume of a gas is directly proportional to its absolute temperature.
The relationship between the volume of a gas and the quantity of the gaseous material, as represented by the number of moles, was established by Amedeo Avogadro in the early 1800s. He deduced from experiments performed by Joseph-Louis Gay-Lussac that equal volumes of different gases at the same temperature and pressure contained the same number of moles. This idea leads to Avogadro's law, which states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas, or
V = c″n
where c″ is a constant.
The three relations, Boyle's, Charles's, and Avogadro's laws, connecting the volume of a gas with its pressure, (absolute) temperature, and mole number, respectively, can be combined into one expression, called the ideal-gas equation of state, or V = nRT/P, in which R is a universal constant, valid for all gases. The value of R is 0.08206 L-atm/mol-K or, in SI units, 8.314 J/mol-K. The ideal-gas equation is usually expressed as
PV = nRT
A gas that obeys this equation is called an ideal or perfect gas. Notice that the identity of the gas is not represented in this equation; in this sense, an ideal gas is hypothetical. The ideal-gas equation works well in the limit of low pressures (where intermolecular interactions are negligible) and/or high temperatures.
There are many other equations of state, such as the van der Waals equation, that are designed to account for gas properties at higher pressures and/or lower temperatures. These equations contain one or more parameters whose values are specific for the gas in question.
Beginning with the empirical development of the gas laws, which explained how gases behave, scientists began to seek an understanding of the mechanism of this behavior. By the mid-1800s the work of several scientists, including James Joule, Rudolf Clausius, James Clerk Maxwell, and Ludwig Boltzmann, led to the development of the kinetic-molecular theory (KMT) of gases. This theory employed several assumptions: (1) Gas particles (i.e., atoms or molecules) are point masses—meaning they have negligible volume, (2) they undergo constant random motion involving frequent collisions, (3) attractive and repulsive forces between molecules are negligible, and (4) the average kinetic energy of molecules is proportional to the absolute temperature.
According to this model, pressure is caused by the collisions that molecules make with the walls of its container. An analysis of this molecular motion using Newton's laws leads to an expression identical to the ideal-gas law. An important result of the theory is that the average kinetic energy of one mole of gas can be expressed in terms of the absolute temperature
|COMPOSITION OF GASES IN EARTH'S ATMOSPHERE AT SEA LEVEL IN VOLUME (OR MOLE) PERCENT|
|Composition||Component (% by Volume)a|
|aNote that percent by volume is equivalent to percent by moles (Avogadro's law)|
|CO2, carbon dioxide||0.0345|
where M is the molar mass, u its average molecular speed, R the gas constant. The average kinetic energy of a gas depends only on T and is independent of its mass. The root-mean-square speed, u rms , of a gas is equal to
and the KMT predicts that for methane, CH4 (M = 0.0160 kg/mol), near room temperature (300 K) u rms = 394 m/s (or 882 miles/hr!). Although this result seems very large, experimental measurements are consistent with this value. Another property obtained from the KMT is the mean free path λ, which is the average distance a molecule travels between collisions. Analysis shows that λ varies inversely with pressure, as well as the size of the molecule, a property not accounted for in simple KMT. For a pure gas,
where d is the molecular diameter. For the oxygen molecule O2, d ≈ 2.4 × 10−10m, and λ ≈ 1.6 × 10−7m at 300 K and 1 atm. Under these conditions, the molecule travels a distance that is about 670 times its diameter before it collides with another molecule.
Perhaps the most important and ubiquitous gas is Earth's atmosphere, which is a complex mixture of compounds. The composition of gases in the atmosphere at sea level, excluding water vapor, aerosols, and particulate suspensions, which vary regionally and climatically, is listed in Table 1.
Although carbon dioxide (CO2) is present in trace amounts, it is an exceedingly important constituent. Until about 1800 CO2 composition was constant at about 0.028 percent. After that time it began to increase, presumably because of the combustion of fossil fuels. In 1900 the CO2 level was ca. 0.0295 percent; currently it is 0.0345 percent. CO2 and several other gases, such as methane (CH4) and nitrogen oxides, which are, in part, anthropogenic, are called greenhouse gases because they absorb infrared radiation from Earth that would otherwise be transmitted into space. Thus, these gases, while transmitting visible light from the Sun, essentially retain heat in a way similar to the glass panels of a greenhouse. The apparent trend in global warming has been attributed to the rapid and continuing increase in the atmospheric composition of greenhouse gases observed in the past 50 to 100 years.
see also Avogadro, Amedeo; Air Pollution; Boltzmann, Ludwig; Boyle, Robert; Charles, Jacques; Gay-Lussac, Joseph-Louis; Maxwell, James Clerk; Noble Gases.
Arthur M. Halpern
Jacob, Daniel J. (1999). Introduction to Atmospheric Chemistry. Princeton, NJ: Princeton University Press.
Lide, David R., ed. (2002). CRC Handbook of Chemistry and Physics, 83rd edition. Boca Raton, FL: CRC Press.
Zumdahl, Steven S., and Zumdahl, Susan A. (2000). Chemistry, 5th edition. Boston: Houghton Mifflin, pp. 187–230, 270–271.