The Italian scientist Avogadro hypothesized that, in the case of "ideal gases," if the pressure (P), volume (V) and temperature (T) of two samples are the same, then the number of gas particles in each sample is likewise the same. This is true regardless of whether the gas consists of atoms or of molecules. The relationship holds even if the samples compared are of different gases. Alone, Avogadro’s law is of limited value, but if coupled with Boyle’s law, Charles’ law and Gay-Lussac’s law, the important ideal gas equation is derived.
For two different gases, the following mathematical relationships exist: P_{1}V_{1}/T_{1}=k_{1} and P_{2}V_{2}/T_{2}=k_{2}. Avogadro’s hypothesis, better known today as Avogadro’s law, indicates that if the left-hand sides of the above expressions are the same, the number of particles in both instances is identical. So the number of particles equals k times some other value dependent upon the specific gas. This other value incorporates the mass of the particles; that is, it is related to their molecular weight. Avogadro's law enables these characteristics to be put into compact mathematical form.
Manipulation of the above leads to an ideal gas equation with the form PV=nRT. Here "R" is defined as the ideal gas constant, while "n" represents the number of moles, or multiples of the molecular weight (MW) of the gas, in grams. For instance, 1.0 gram of hydrogen gas — formula H_{2}, MW=2.0 — amounts to 0.5 moles. If the value of P is given in atmospheres with V in liters and T in degrees Kelvin, then R is expressed in liter-atmospheres-per-mole-degree Kelvin. Although the expression PV=nRT is useful for many applications, in some instances, deviation is considerable.
The difficulty lies in the definition of ideality; it imposes restrictions that cannot exist in the real world. Gas particles must possess no attractive or repellant polarities — this is another way of saying collisions between particles must be elastic. Another unrealistic assumption is that particles must be points and their volumes, zero. Many of these deviations from ideality can be compensated for by the inclusion of mathematical terms that bear a physical interpretation. Other deviations require virial terms, which, unfortunately, do not satisfyingly correspond to any physical property; this does not cast Avogadro's law into any disrepute.
A simple upgrade of the ideal gas law adds two parameters, "a" and "b." It reads (P+(n^{2}a/V^{2}))(V-nb)=nRT. Although "a" must be determined experimentally, it relates to the physical property of particle interaction. The constant "b" also relates to a physical property and takes into consideration the excluded volume.
While physically interpretable modifications are appealing, there are unique advantages to using virial expansion terms. One of these is that they can be used to closely match reality, allowing explanation in some instances of the behavior of liquids. Avogadro's law, originally applied to the gas phase only, has thus made possible a better understanding of at least one condensed state of matter.