Amagat's law
Encyclopedia
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:
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 gas
es. However, for real (non-ideal) gases, the results differ. 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:
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:
(Dalton's Law
)
and
(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.
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
(as well as some cases of non-ideal) gases. Of use in chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
and thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, 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:
This is the experimental expression of volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
as an extensive quantity. It is named after Emile Amagat
Emile Amagat
Emile Hilaire Amagat was a French physicist. His doctoral thesis, published in 1872, expanded on the work of Thomas Andrews, and included plots of the isotherms of carbon dioxide at high pressures...
.
Both Amagat's and Dalton's Law
Dalton's law
In chemistry and physics, Dalton's law states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture...
predict the properties of gas mixtures. Their predictions are the same for ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
es. However, for real (non-ideal) gases, the results differ. Dalton's Law
Dalton's law
In chemistry and physics, Dalton's law states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture...
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
Virial coefficient
Virial coefficients B_i appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law...
, B(T), for the mixture. For two components, the second virial coefficient for the mixture can be expressed as:
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:
(Dalton's LawDalton's law
In chemistry and physics, Dalton's law states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture...
)
and
(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
Vegard's law
In metallurgy, Vegard's law is an approximate empirical rule which holds that a linear relation exists, at constant temperature, between the crystal lattice parameter of an alloy and the concentrations of the constituent elements....
for solid mixtures.