Avogadro’s law states that in ideal gases with equal pressure, volume, and temperature, the number of particles is the same regardless of the gas. It is used in the ideal gas equation PV=nRT, but this equation has limitations due to the ideal gas assumptions. Modifications like “a” and “b” parameters or virial expansion terms can compensate for these limitations and explain the behavior of liquids.
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 equal, then the number of gas particles in each sample it’s the same. This is true regardless of whether the gas consists of atoms or molecules. The relationship holds even if the compared samples are of different gases. By itself, Avogadro’s law is of limited value, but when 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 relations exist: P1V1/T1=k1 and P2V2/T2=k2. Avogadro’s hypothesis, better known today as Avogadro’s law, states that if the left sides of the above expressions are the same, the number of particles in both cases is identical. So the number of particles is equal to k times another value depending on the specific gas. This other value incorporates the mass of the particles; that is, it is related to their molecular weight. Avogadro’s law allows us to put these characteristics into a compact mathematical form.
Manipulating the above leads to an ideal gas equation of 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 example, 1.0 grams of hydrogen gas — formula H2, 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 litres-atmospheres-per-mole-degree Kelvin. While the expression PV=nRT is useful for many applications, in some cases the bias is considerable.
The difficulty lies in the definition of ideality; it imposes restrictions that cannot exist in the real world. The gas particles must not have attractive or repelling polarities: this is another way of saying that particle collisions must be elastic. Another unrealistic assumption is that the particles must be points and their volume zero. Many of these deviations from ideality can be compensated for by the inclusion of mathematical terms that carry a physical interpretation. Other deviations require virial terms, which, unfortunately, do not correspond satisfactorily to any physical property; this does not discredit Avogadro’s law.
A simple update of the ideal gas law adds two parameters, “a” and “b”. It reads (P+(n2a/V2))(V-nb)=nRT. Although “a” must be determined experimentally, it refers to the physical property of particle interaction. The constant “b” also refers to a physical property and takes into account the excluded volume.
While physically interpretable modifications are attractive, there are unique advantages to using virial expansion terms. One of them is that they can be used to closely match reality, allowing in some cases to explain the behavior of liquids. Avogadro’s law, originally applied only to the gaseous phase, has thus made possible a better understanding of at least one condensed state of matter.
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