Ideal Gas Equation
Gases differ greatly from liquids and solids in their compressibility. Almost all ordinary gases have the property that, for a given sample at a given temperature, the volume is inversely proportional to the applied pressure.
at constant temperature
If the volume is decreased by a factor of two, the pressure will have doubled. This was established by Robert Boyle in the 17th century and is known as Boyle’s law.
For the most part this behavior is independent of the composition of the gas. This property depends on the absence of interaction between the gas molecules. In the rare examples where there is interaction in response to pressure changes (such as the formation of dimers), the relationship between volume and pressure is more complex.
Some hundred years later it was established that many common gases expand and contract in the same regular manner with temperature changes. For each increase in temperature of 1° C at constant pressure, a gas sample expands its volume by a factor of 1/273. This is known as the law of Charles and Gay-Lussac. This behavior was extrapolated to zero volume at -273.15° C. This was called absolute zero, the lowest possible temperature. With this the Kelvin absolute temperature scale was established that started at absolute zero and used a degree the same as in the Celcius scale. In the Kelvin scale water freezes at 273.15K.
The law of Charles and Gay-Lussac says that the volume is proportional to the absolute temperature for a given sample at constant temperature.
at constant pressure.
In 1811 Amedeo Avogadro proposed that the a given volume of a dilute gas at a certain temperature and pressure will contain a certain number of molecules of the substance. At 25° C and 1 atmosphere pressure one molecular weight in grams of a gas will occupy 22.4 liters. The 22.4 liters of gas at standard conditions contains 6.02 x 1023 molecules of the gas. Thus combining volumes of a gas reaction parallel the chemical formulas of reactants and products. At standard conditions two volumes of H2 gas will react with one volume of O2 to form two volumes of H2O. 2H2 + O2 = 2H2O. (Avogadro had also posulated that elemental gases were diatomic.)/p>
At a given temperature and volume the pressure could be increased by adding more gas molecules. Likewise, if temperature and pressure are held constant, the volume could be increased by adding more gas molecules. Using n to represent the number of moles (molecular weight in grams), both volume and pressure are proportional to the number of moles of gas at constant temperature.
at constant temperature
at constant temperature
The laws of Boyle, Charles and Gay-Lussac, and Avogadro can be combined into what is called the ideal gas law
where R is a proportionality constant. The value of R depends on the units of pressure and volume. Values are 8.314 J mol-1 K-1 and 0.08206 liter atm K-1 mol-1.
It is common practice in handling gaseous reactants to measure the amount (moles) by enclosing the gas sample in a known volume and measuring the pressure and temperature.
For further refinement of the ideal gas equation see the van der Waals equation.