Gas laws

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 It has been suggested that Combined gas law, Boyle's law, Charles's law, Gay-Lussac's law, Avogadro's law, Graham's law, Dalton's law and Amagat's law be merged into this article or section. (Discuss)


This article outlines the historical development of the laws describing ideal gases. For a detailed description of the ideal gas laws and their further development, see Ideal gas, Ideal gas law and Gas

The early gas laws were developed at the end of the eighteenth century, when scientists began to realize that relationships between the pressure, volume and temperature of a sample of gas could be obtained which would hold for all gases. Gases behave in a similar way over a wide variety of conditions because to a good approximation they all have molecules which are widely spaced, and nowadays the equation of state for an ideal gas is derived from kinetic theory. The earlier gas laws are now considered as special cases of the ideal gas equation, with one or more of the variables held constant.

Three earlier gas laws:

{P_1V_1} = {P_2V_2} \,,
  • Charles' law or law of volumes (1787, relating volume and temperature):
\frac {V_1} {T_1} = \frac {V_2} {T_2}
  • Pressure law or Third gas law (Gay-Lussac in 1809, relating temperature and pressure)
\frac {P_1} {T_1} = \frac {P_2} {T_2}


The combined gas law or general gas equation is formed by the combination of the three laws, and shows the relationship between the pressure, volume and temperature for a fixed mass of gas:

\frac {P_1V_1} {T_1} = \frac {P_2V_2} {T_2}


There is also Avogadro's Law, which is particularly useful in chemistry: For any gas, the ratio of Liters of the gas to moles of the gas is:

\frac {V} {n} = k \,, and uses the molar volume of a gas: 22.4 Liters.

With the addition of Avogadro's law, the combined gas law developed into the ideal gas law:

PV = nRT \,,

where

P is the absolute pressure (Unit used: atmospheres, atm)
V is the volume (Unit used: Liter, L)
n is the amount of substance (loosely number of moles of gas)
R is the gas constant, which is the same for all gases (Unit and number used: 0.0821 L·atm·mol-1·K-1
T is the temperature on the absolute temperature scale (Unit used: Kelvin).

(The law works with any consistent set of units, provided that the temperature scale starts at absolute zero, and the gas constant is in the correct units.)

An equivalent formulation of this law is:

PV = kNT \,

where

k is the Boltzmann constant
N is the number of molecules.

These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.

This law has the following important consequences:

  1. If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
  2. If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
  3. If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
  4. If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.

Other gas laws of historical importance include:

  • Graham's law states that the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.
  • Dalton's law of Partial Pressures states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton's Law is as follows:
P_{{{Total of Gas Mixture}}} = P_1 + P_2 + P_3 + ... \,,

OR

P_{{{Total}}} = P_{{{Gas}}} + P_{{{H}_2{O}}} \,,

Where PTotal is the total pressure of the atmosphere, PGas is the Pressure of the gas mixture in the atmosphere, and PH2O is the water pressure at that temperature.

At a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.
p = k_{\rm H}\, c


[edit] References

  • Castka, Joseph F.; Metcalfe, H. Clark; Davis, Raymond E.; Williams, John E. (2002). Modern Chemistry. Holt, Rinehart and Winston. ISBN 0-03-056537-5. 
  • Guch, Ian (2003). The Complete Idiot's Guide to Chemistry. Alpha, Penguin Group Inc.. ISBN 1-59257-101-8. 
  • Zumdahl, Steven S (1998). Chemical Principles. Houghton Millfin Company. ISBN 0-395-83995-5. 
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