Amagat's law
Amagat's law or the Law of Partial Volumes of 1880 describes the behaviour and properties of mixtures of ideal (as well as some cases of non-ideal) gases. Of use in chemistry and thermodynamics, Amagat's law states that the volume Vm of a gas mixture is equal to the sum of volumes Vi of the K component gases, if the temperature T and the pressure p remain the same:[1]
\[ V_m(T,p)=\sum_{i=1}^K V_i(T,p).\ \]
This is the experimental expression of volume as an extensive quantity. It is named after Emile Amagat.
Both Amagat's and Dalton's Law predict the properties of gas mixtures. Their predictions are the same for ideal gases. However, for real (non-ideal) gases, the results differ.[2] Dalton's Law of Partial Pressures assumes that the gases in the mixture are non-interacting (with each other) and each gas independently applies its own pressure, the sum of which is the total pressure. Amagat's Law assumes that the volumes of each component gas (same temperature and pressure) are additive; the interactions of the different gases are the same as the average interactions of the components.
The interactions can be interpreted in terms of a second virial coefficient, B(T), for the mixture. For two components, the second virial coefficient for the mixture can be expressed as:
\[B(T) = X_1B_1 + X_2B_2 + X_1X_2B_{1,2}\ \]
where the subscripts refer to components 1 and 2, the X's are the mole fractions, and the B's are the second virial coefficients. The cross term, B1,2, of the mixture is given by:
\[ B_{1,2} = 0\ \] (Dalton's Law)
and
\[ B_{1,2} = (B_1 + B_2)/2\ \] (Amagat's Law).
When the volumes of each component gas (same temperature and pressure) are very similar, then Amagat's law becomes mathematically equivalent to Vegard's law for solid mixtures.
References
- ↑ Amagat's law of additive volumes
- ↑ J. H. Noggle, Physical Chemistry, 3rd Ed., Harper Collins, New York, 1996.
de:Gesetz von Amagat he:מודל אמגט it:Legge di Amagat zh:阿马加定律
