GAS LAWS

CONCEPT

Gases respond more dramatically to temperature and pressure than do the other three basic types of matter (liquids, solids and plasma). For gases, temperature and pressure are closely related to volume, and this allows us to predict their behavior 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

Ordinary air pressure at sea level is equal to 14.7 pounds per square inch, a quantity referred to as an atmosphere (atm). Because a pound is a unit of force and a kilogram a unit of mass, the metric equivalent is more complex in derivation. A newton (N), or 0.2248 pounds, is the metric unit of force, and a pascal (Pa)—1 newton per square meter—the unit of pressure. Hence, an atmosphere, expressed in metric terms, is 1.013 × 10⁵ Pa.

Gases vs. Solids and Liquids: A Strikingly Different Response

Regardless of the units you use, however, gases respond to changes in pressure and temperature in a remarkably different way than do solids or liquids. Using a small water sample, say, 0.2642 gal (1 l), an increase in pressure from 1-2 atm will decrease the volume of the water by less than 0.01%. A temperature increase from 32° to 212°F (0 to 100°C) will increase its volume by only 2% The response of a solid to these changes is even less dramatic; however, the reaction of air (a combination of oxygen, nitrogen, and other gases) to changes in pressure and temperature is radically different.

For air, an equivalent temperature increase would result in a volume increase of 37%, and an equivalent pressure increase will decrease the volume by a whopping 50%. Air and other gases also have a boiling point below room temperature, whereas the boiling point for water is higher than room temperature and that of solids is much higher. The reason for this striking difference in response can be explained by comparing all three forms of matter in terms of their overall structure, and in terms of their molecular behavior. (Plasma, a gas-like state found, for instance, in stars and comets' tails, does not exist on Earth, and therefore it will not be included in the comparisons that follow.)

Molecular Structure Determines Reaction

Solids possess a definite volume and a definite shape, and are relatively noncompressible: for instance, if you apply 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 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, too, are random in arrangement, but tend to be more widely spaced than liquid molecules. Solid particles are slow moving, and have a strong attraction to one another, whereas gas particles are fast-moving, and have little or no attraction. (Liquids are moderate in both regards.)

Given these interesting characteristics of gases, it follows that a unique set of parameters—collectively known as the "gas laws"—are needed to describe and predict their behavior. Most of the gas laws were derived during the eighteenth and nineteenth centuries by scientists whose work is commemorated by the association of their names with the laws they discovered. These men include the English chemists Robert Boyle (1627-1691), John Dalton (1766-1844), and William Henry (1774-1836); the French physicists and chemists J. A. C. Charles (1746-1823) and Joseph Gay-Lussac (1778-1850), and the Italian physicist Amedeo Avogadro (1776-1856).

Boyle's, Charles's, and Gay-Lussac'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.

By now a pattern should be emerging: both of the aforementioned laws 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.

Absolute temperature refers to the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907). Drawing on Charles's discovery that gas at 0°C (32°F) regularly contracted by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (−273.15°C or −459.67°F). Using the Kelvin scale of absolute temperature, Gay-Lussac found that at lower temperatures, the pressure of a gas is lower, while at higher temperatures its pressure is higher. Thus, the ratio of pressure to temperature is a constant.

Avogadro's Law

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 science, this would be 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. 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, it was necessary to establish a large quantity as a basic unit, since molecules themselves are very small. For this purpose, Avogadro established the mole, a unit equal to 6.022137 × 10²³ (more than 600 billion trillion) molecules. 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.

Just as one liter of water, or one liter of mercury, has a certain mass, a mole of any given substance has its own particular mass, expressed in grams. The mass of one mole of iron, for instance, will always be greater than that of one mole of oxygen. The ratio between them is exactly the same as the ratio of the mass of one iron atom to one oxygen atom. Thus the mole makes if possible to compare the mass of one element or one compound to that of another.

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, since they each involve two or more of the four parameters: temperature, pressure, volume, and 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 terms in physics, 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 relations: 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. Thus where p ₁V ₁ is the product of its initial pressure and its initial volume, T ₁ its initial temperature,p ₂V ₂ the product of its final volume and final pressure, and T ₂ its final temperature.

Five Postulates Regarding the Behavior of Gases

Five postulates can be applied to gases. Thesemore or less restate the terms of the earlier discussion, in which gases were compared to solidsand liquids; however, now those comparisonscan be seen in light of the gas laws.

First, the size of gas molecules is minusculein comparison to the distance between them, making gas highly compressible. In other words, there is a relatively high proportion of emptyspace between gas molecules.

Second, there is virtually no force attractinggas molecules to one another.

Third, though gas molecules move randomly, frequently colliding with one another, theirnet effect is to create uniform pressure.

Fourth, the elastic nature of the collisionsresults in no net loss of kinetic energy, the energy that an object possesses by virtue of itsmotion. If a stone is dropped from a height, it rapidly builds kinetic energy, but upon hitting anonelastic surface such as pavement, most of thatkinetic energy is transferred to the pavement. In the case of two gas molecules colliding, however, they simply bounce off one another, only to collide with other molecules and so on, with no kinetic energy lost.

Fifth, the kinetic energy of all gas molecules is directly proportional to the absolute temperature of the gas.

Laws of Partial Pressure

Two gas laws describe partial pressure. Dalton's law of partial pressure states that the total pressure of a gas is equal to the sum of its par tial pressures—that is, the pressure exerted by each component of the gas mixture. 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.

REAL-LIFE APPLICATIONS

Pressure Changes

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 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 will eventually go "flat."

FIRE EXTINGUISHERS.

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 near the bottom of the water. 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.

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 latter 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.

When the Temperature Changes

A number of interesting things, some of them unfortunate and some potentially lethal, occur when gases experience a change in temperature. In these instances, it is possible to see the gas laws—particularly Boyle's and Charles's—at work.

There are a number of examples of the disastrous effects that result from an increase in the temperature of a product containing combustible gases, as with 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. By itself, this fact does not depend on any of the gas laws, but rather reflects the concept of buoyancy. However, the way in which the density of the air in the balloon is reduced does indeed reflect the gas laws.

According to Charles's law, heating a gas will increase its volume. Also, as noted in the first and second propositions regarding the behavior of gases, gas molecules are highly nonattractive to one another, and therefore, there is a great deal of space between them. The increase in volume makes that space even greater, leading to a significant difference in density between the air in the balloon and the air outside. As a result, the balloon floats, or becomes buoyant.

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 in which 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 earlier 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 an extremely hot summer day could cause a defective tank to burst. Certainly the laws of physics are there: 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 of the 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 would be dramatically reduced by the time it reached its destination.

Gas Reactions That Move and Stop a Car

In operating a car, we experience two examples of gas laws in operation. One of these, common to everyone, is that which makes the car run: the combustion of gases in the engine. The other is, fortunately, a less frequent phenomenon—but it can and does save lives. This is the operation of an air bag, which, though it is partly related to laws of motion, depends also on the behaviors explained in Charles's law.

With regard to the engine, when the driver pushes down on the accelerator, this activates a throttle valve that sprays droplets of gasoline mixed with air into the engine. (Older vehicles used a carburetor to mix the gasoline and air, but most modern cars use fuel-injection, which sprays the air-gas combination without requiring an intermediate step.) The mixture goes into the cylinder, where the piston moves up, compressing the gas and air.

While the mixture is still compressed (high pressure, high density), an electric spark plug produces a flash that ignites it. 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 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..

But an airbag is much more complicated than it seems. In order for it to save lives, it must deploy within 40 milliseconds (0.04 seconds). Not only that, but it has to begin deflating before the body hits it. An airbag does not inflate if a car simply goes over a bump; it only operates in situations when the vehicle experiences extremedeceleration. When this occurs, there is a rapidtransfer of kinetic energy to rest energy, as with the earlier illustration of a stone hitting concrete. And indeed, if you were to smash against a fullyinflated airbag, it would feel like hitting concrete—with all the expected results.

The airbag's sensor contains a steel ballattached to a permanent magnet or a stiff spring. The spring holds it in place through minormishaps in which an airbag would not be 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 springreleases the ball, sending it down a smooth bore. It flips a switch, turning on an electrical circuit.This in turn ignites a pellet of sodium azide, which fills the bag with nitrogen gas.

The events described in the above illustration take place within 40 milliseconds—less time than it takes for your body to come flying forward; and then the airbag has to begin deflating before the body reaches it. At this point, the highly pressurized nitrogen gas molecules begin escaping through vents. Thus as your body hits the bag, the deflation of the latter is moving it in the same direction that your body is going—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.

WHERE TO LEARN MORE

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

"Chemistry Units: Gas Laws." (Web site). <http://bio.bio.rpi.edu/MS99/ausemaW/chem/gases.hmtl> (February 21, 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.

"Tutorials—6." <http://www.chemistrycoach.com/tutorials-6.html> (February 21, 2001).

KEY TERMS

ABSOLUTE TEMPERATURE:

Temperature in relation to absolute zero (−273.15°C or −459.67°F). Its unit is the Kelvin (K), named after William Thomson, Lord Kelvin (1824-1907), who created the scale. The Kelvin and Celsius scales are directly related; hence, Celsius temperatures can be converted to Kelvins (for which neither the word or symbol for "degree" are used) by adding 273.15.

AVOGADRO'S LAW:

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.

BOYLE'S LAW:

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.

CHARLES'S LAW:

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 PRESSURE:

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.

GAY-LUSSAC'S LAW:

A statement, derived by the 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.

HENRY'S LAW:

A statement, derived by the English chemist William Henry (1774-836), 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 forgases, such as hydrogen and oxygen, that are capable of dissolving in water without undergoing ionization.

IDEAL GAS LAW:

A proposition, also known as the combined gas law, that draws on all the gas laws. The ideal gas law can 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.

INVERSE RELATIONSHIP:

A situation involving two variables, in which one of the two increases in direct proportion to the decrease in the other.

IONIZATION:

A reaction in which anatom or group of atoms loses one or more electrons. The atoms are then converted toions, which are either wholly positive or negative in charge.

ISOTHERMAL:

Referring to a situation in which temperature is kept constant.

ISOBAROMETRIC:

Referring to a situation in which pressure is kept constant.

MOLE:

A unit equal to 6.022137 × 10²³ molecules.

Gas laws

Definition

The gas laws are mathematical formulations of the interrelationships among the four variables that describe the behavior of a gas sample: its volume (V), pressure (P), temperature (T), and the amount (n) of gas present (see Gases, properties of).

The properties of gases were already being studied and described as early as the seventeenth century. Unlike solids, which have a fixed shape and volume, and liquids, which have a fixed volume but can change shape according to the container, gases assume both the shape and the volume of their container. The volume of space occupied by a sample of gas depends on the number of gas mole-cules present and the sample's pressure and temperature.

Simple gas laws

Boyle's law: volume is inversely proportional to pressure

Boyle's law, formulated by English scientist Robert Boyle in 1662, states that the pressure of a fixed amount of gas at a constant temperature is inversely proportional to its volume. In other words, when a sample of gas is allowed to expand to occupy a larger volume, its pressure decreases; and when it is compressed into a smaller volume, its pressure increases. Mathematically, this inverse relationship may be formulated:

P₁V₁ = P₂V₂

or

V = constant ÷ P

In continental Europe, this gas law is known as the law of Mariotte, after Edme Mariotte, who published the results of his studies of the properties of gases a few years later than Boyle.

The working of a syringe can be used to illustrate Boyle's law. When the plunger of a syringe is drawn back, the volume of the air inside the syringe barrel is increased and the pressure decreased relative to the exterior of the syringe, and fluid is pulled into the syringe. When the plunger is depressed, the volume is decreased, the pressure increased, and fluid is forced out.

Charles's law: volume is directly proportional to temperature

Charles's law, which was formulated by French physicist Jacques Charles in 1787, states that the volume of a sample of gas kept at constant pressure is directly proportional to the temperature; or, more simply stated, a gas sample will expand upon heating and contract when cooled. This may be formulated mathematically as:

V₁ ÷ T₁ = V₂ ÷ T₂

or

V = constant× T

A hot air balloon demonstrates the principle of Charles's law. When the balloon is fired, the air is heated and expands to fill the balloon.

Gay-Lussac's law: pressure is directly proportional to temperature

This gas law, published in 1802 by Frenchman Joseph Louis Gay-Lussac, describes the relationship between the gas's pressure and temperature. At constant volume, the pressure of a gas sample is directly proportional to its temperature. In other words, a sample of gas exerts more pressure on its surrounding container when hot than when cold. The mathematical formulation of this law is

P₁ ÷ T₁ = P₂ ÷ T₂

or

P = constant T

Avogadro's law: volume is directly proportional to amount

In the early nineteenth century, the Italian Count Amadeo Avogadro hypothesized that different gases of equal volume at a given temperature and pressure contain equal numbers of gas molecules. Alternatively, samples of two different gases containing the same number of molecules will occupy equal volumes. Avogadro's law mathematically formulated is:

V₁ ÷ n₁ = V₂ ÷ T₂

or

V = constant ×n.

At standard temperature and pressure (STP), one mole of any gas occupies 22.4 L.

As an example of the law of Avogadro, consider that, during respiration, the amount of air in the lungs is alternately increased and decreased by the movement of the diaphragm that causes the volume of the lungs to be alternately increased and decreased.

It should be noted that all gaseous substances behave alike according to these laws. Also, in each of the formulations above, the proportionality constant has a different meaning and is expressed in different units. Moreover, in calculations, temperature must be expressed in terms of the Kelvin, or absolute, temperature scale.

Ideal gas law

The ideal gas law, first derived in 1834 by Emil Clapeyron, compiles the simple gas laws into a single expression with a single constant, called the ideal gas law:

PV = nRT

The single constant R is called the universal gas constant. The value of the constant depends on the units used to express pressure and volume. The standard units for measuring volume, pressure, amount, and temperature are, respectively, the liter (L), the atmosphere (atm), the mole (mol), and Kelvin (K), giving rise to the value R =0.082 liter atm mol^-1 K^-1;.

All of the relationships established by the simple gas laws are preserved in the expression of the ideal gas law:

• The volume of a gas is inversely proportional to its pressure.
• The volume of a gas is directly proportional to its temperature.
• The pressure of a gas is directly proportional to its temperature.
• The volume of a gas is directly proportional to the amount of gas present

An ideal, or perfect, gas is a hypothetical gas that obeys the gas laws in terms of its pressure, volume, and temperature behavior. Such a gas would have to be composed of molecules that do not interact with one another. Real gases are not always accurately described by the ideal gas equation. Under ordinary conditions, however, the observed behavior of a real gas is only negligibly different from that predicted for an ideal gas.

Dalton's law of partial pressures

The simple and ideal gas laws describe the behavior of pure gaseous substances. Mixtures of gases also behave like ideal gases, provided the different components do not undergo a reaction, or interact in some other way. This concept—that each individual gas in a mixture expands to exert its partial pressure as if the other gas components were not present—was developed by John Dalton in 1801 and is known as Dalton's law of partial pressures.

Given that the pressure of a gas is directly related to the number of moles of gas present, and that all gases behave alike, it follows that the total pressure exerted by a mixture of gases is equal to the sum of the pressures of each of the components of the gas mixture. The pressure exerted by a component gas in a mixture is referred to as the partial pressure of that gas. Thus, for a mixture of gases, A, B,…,

tot = P_A + P_B +…

Each component gas experiences the same temperature and volume conditions as all other components. Application of the ideal gas equation to each pressure term allows formulation of a useful term known as the mole fraction (X) of a gas. The mole fraction is defined as the ratio of the number of moles of one component to the total number of moles of gas in the mixture, which is equal to the ratio of the partial pressure to the total pressure (X_A = n_A÷n_tot = P_A÷P_tot).

V = n_ART

Gay-Lussac's law of combining volumes

In 1808, Gay-Lussac, in collaboration with Alexander von Humbolt, studied the reactions of gases. They determined that, at a given temperature and pressure for the reactions involving gaseous substances, the volumes of the reactant and product gases are in ratios of small whole numbers. For example, two volumes of hydrogen gas react with one volume of oxygen gas to form two volumes of water vapor.

KEY TERMS

Celsius (centigrade) and Kelvin temperature scales —On the Celsius scale, the temperature at which water freezes is defined as zero degrees and the temperature at which water boils is defined as 100°. The Kelvin scale is the official temperature scale of the International System of Units (SI), the units preferred by most international scientific agencies. The Kelvin scale is based on the Celsius scale, with zero defined as the temperature at which molecular motion ceases, equal to –273.15°C.

Gas —One of the three physical states in which matter can exist; gaseous matter conforms to the shape and volume of its container.

Mole —An amount of substance containing a number of atoms or molecules equal to Avogadro's constant, 6.022 10²³.

Pressure —The force or weight per unit area exerted by matter on its surroundings. For calculations involving gas properties, pressure is usually measured in atmospheres (atm); other units of pressure include lb/in.², bar, torr, and mm mercury.

Standard conditions of temperature and pressure (STP) —For gases, standard conditions are 0°C and 1 atm.

Volume —The three dimensional space occupied by a substance, measured in liters (l).

Resources

BOOKS

Amend, J.R., B.P. Mundy, and M.T. Armold. General, Organic and Biological Chemistry. Fort Worth, Philadelphia, San Diego, New York, Orlando, Austin, San Antonio, Toronto, Montreal, London, Sydney, and Tokyo: Saunders College Publishing, 1993.

Brown, T.G., H.E. LeMay Jr., and B.E. Bursten. Chemistry: The Central Science. Eaglewood Cliffs: Prentice Hall, 1994.

OTHER

Green, J.M., and A. Peterson. Woodrow Wilson Leadership Program in Chemistry website. 1998. <http://www.woodrow.org/teachers/chemistry>.

Logan, R.H. Gas Laws website. 1996. <http://edie.cprost.sfu.ca/~rhlogan/gas_laws.html>.

Park, J.L. Chem Team website. 1996. <http://dbhs.wvusd.k12.ca.us>.

Patricia L. Bounds, Ph.D.

Gas Laws

Definition

The gas laws are mathematical formulations of the interrelationships among the four variables that describe the behavior of a gas sample: its volume (V), pressure (P), temperature (T), and the amount (n) of gas present (see Gases, properties of).

The properties of gases were already being studied and described as early as the seventeenth century. Unlike solids, which have a fixed shape and volume, and liquids, which have a fixed volume but can change shape according to the container, gases assume both the shape and the volume of their container. The volume of space occupied by a sample of gas depends on the number of gas molecules present and the sample's pressure and temperature.

Simple gas laws

Boyle's law: volume is inversely proportional to pressure

Boyle's law, formulated by English scientist Robert Boyle in 1662, states that the pressure of a fixed amount of gas at a constant temperature is inversely proportional to its volume. In other words, when a sample of gas is allowed to expand to occupy a larger volume, its pressure decreases; and when it is compressed into a smaller volume, its pressure increases. Mathematically, this inverse relationship may be formulated:

P₁V₁ = P₂V₂

or

V = constant ÷ P

In continental Europe, this gas law is known as the law of Mariotte, after Edme Mariotte, who published the results of his studies of the properties of gases a few years later than Boyle.

The working of a syringe can be used to illustrate Boyle's law. When the plunger of a syringe is drawn back, the volume of the air inside the syringe barrel is increased and the pressure decreased relative to the exterior of the syringe, and fluid is pulled into the syringe. When the plunger is depressed, the volume is decreased, the pressure increased, and fluid is forced out.

Charles's law: volume is directly proportional to temperature

Charles's law, which was formulated by French physicist Jacques Charles in 1787, states that the volume of a sample of gas kept at constant pressure is directly proportional to the temperature; or, more simply stated, a gas sample will expand upon heating and contract when cooled. This may be formulated mathematically as:

V₁ ÷ T₁ = V₂ ÷ T₂

or V = constant × T

A hot air balloon demonstrates the principle of Charles's law. When the balloon is fired, the air is heated and expands to fill the balloon.

Gay-Lussac's law: pressure is directly proportional to temperature

This gas law, published in 1802 by Frenchman Joseph Louis Gay-Lussac, describes the relationship between the gas's pressure and temperature. At constant volume, the pressure of a gas sample is directly proportional to its temperature. In other words, a sample of gas exerts more pressure on its surrounding container when hot than when cold. The mathematical formulation of this law is

P₁ ÷ T₁ = P₂ ÷ T₂

or

P = constant × T

Avogadro's law: volume is directly proportional to amount

In the early nineteenth century, the Italian Count Amadeo Avogadro hypothesized that different gases of equal volume at a given temperature and pressure contain equal numbers of gas molecules. Alternatively, samples of two different gases containing the same number of molecules will occupy equal volumes. Avogadro's law mathematically formulated is:

V₁ ÷ n₁ = V₂ ÷ T₂

or V = constant × n.

At standard temperature and pressure (STP), one mole of any gas occupies 22.4 L.

As an example of the law of Avogadro, consider that, during respiration, the amount of air in the lungs is alternately increased and decreased by the movement of the diaphragm that causes the volume of the lungs to be alternately increased and decreased.

It should be noted that all gaseous substances behave alike according to these laws. Also, in each of the formulations above, the proportionality constant has a different meaning and is expressed in different units. Moreover, in calculations, temperature must be expressed in terms of the Kelvin, or absolute, temperature scale.

Ideal gas law

The ideal gas law, first derived in 1834 by Emil Clapeyron, compiles the simple gas laws into a single expression with a single constant, called the ideal gas law:

PV = nRT

The single constant R is called the universal gas constant. The value of the constant depends on the units used to express pressure and volume. The standard units for measuring volume, pressure, amount, and temperature are, respectively, the liter (L), the atmosphere (atm), the mole (mol), and Kelvin (K), giving rise to the value R = 0.082 liter atm mol⁻¹ K^−1;.

All of the relationships established by the simple gas laws are preserved in the expression of the ideal gas law:

• The volume of a gas is inversely proportional to its pressure.
• The volume of a gas is directly proportional to its temperature.
• The pressure of a gas is directly proportional to its temperature.
• The volume of a gas is directly proportional to the amount of gas present.

An ideal, or perfect, gas is a hypothetical gas that obeys the gas laws in terms of its pressure, volume, and temperature behavior. Such a gas would have to be composed of molecules that do not interact with one another. Real gases are not always accurately described by the ideal gas equation. Under ordinary conditions, however, the observed behavior of a real gas is only negligibly different from that predicted for an ideal gas.

Dalton's law of partial pressures

The simple and ideal gas laws describe the behavior of pure gaseous substances. Mixtures of gases also behave like ideal gases, provided the different components do not undergo a reaction, or interact in some other way. This concept—that each individual gas in a mixture expands to exert its partial pressure as if the other gas components were not present—was developed by John Dalton in 1801 and is known as Dalton's law of partial pressures.

Given that the pressure of a gas is directly related to the number of moles of gas present, and that all gases behave alike, it follows that the total pressure exerted by a mixture of gases is equal to the sum of the pressures of each of the components of the gas mixture. The pressure exerted by a component gas in a mixture is referred to as the partial pressure of that gas. Thus, for a mixture of gases, A, B,…,

_tot = P_A + P_B +…

Each component gas experiences the same temperature and volume conditions as all other components. Application of the ideal gas equation to each pressure term allows formulation of a useful term known as the mole fraction (X) of a gas. The mole fraction is defined as the ratio of the number of moles of one component to the total number of moles of gas in the mixture, which is equal to the ratio of the partial pressure to the total pressure (X_A = n_A ÷ n_tot = P_A ÷ P_tot.

V = n_ART

KEY TERMS

Celsius (centigrade) and Kelvin temperature scales— On the Celsius scale, the temperature at which water freezes is defined as zero degrees and the temperature at which water boils is defined as 100°. The Kelvin scale is the official temperature scale of the International System of Units (SI), the units preferred by most international scientific agencies. The Kelvin scale is based on the Celsius scale, with zero defined as the temperature at which molecular motion ceases, equal to −273.15°C.

Gas— One of the three physical states in which matter can exist; gaseous matter conforms to the shape and volume of its container.

Mole— An amount of substance containing a number of atoms or molecules equal to Avogadro's constant, 6.022 × 10²³.

Pressure— The force or weight per unit area exerted by matter on its surroundings. For calculations involving gas properties, pressure is usually measured in atmospheres (atm); other units of pressure include lb/in.², bar, torr, and mm mercury.

Standard conditions of temperature and pressure (STP)— For gases, standard conditions are 0°C and 1 atm.

Volume— The three dimensional space occupied by a substance, measured in liters (l).

Gay-Lussac's law of combining volumes

In 1808, Joseph Louis Gay-Lussac, in collaboration with Alexander von Humbolt, studied the reactions of gases. They determined that, at a given temperature and pressure for the reactions involving gaseous substances, the volumes of the reactant and product gases are in ratios of small whole numbers. For example, two volumes of hydrogen gas react with one volume of oxygen gas to form two volumes of water vapor.

Resources

BOOKS

Amend, J.R., B.P. Mundy, and M.T. Armold. General, Organic and Biological Chemistry. Fort Worth, TX: Saunders College Publishing, 1993.

Brown, T.G., H.E. LeMay Jr., and B.E. Bursten. Chemistry: The Central Science. Englewood Cliffs, NJ: Prentice Hall, 1994.

OTHER

Green, J.M., and A. Peterson. Woodrow Wilson Leadership Program in Chemistry website. 1998. (March 24, 2006). 〈http://www.woodrow.org/teachers/chemistry〉.