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.
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
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, 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
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.
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
P = constant T
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
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.
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 = PA + PB +…
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 (XA = nA÷ntot = PA÷Ptot).
V = nART
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.
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).
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.
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.