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×09th May 2019 @ 4 min read

Amagat's law of additive volumes is the law of partial volumes. The law relates the total volume of a mixture with the volumes of individual components. Amagat's law is very similar to Dalton's law of partial pressure. The law is only valid for ideal gases. The law is named after Emile Amagat who was a French Physicist. He published his law of partial volumes in 1880.

For a mixture of non-reacting ideal gases, the total volume of the mixture equals the sum of the partial volumes of individual components at constant pressure and temperature.

As per Amagat's law, the volume of an ideal mixture is

where *V*_{mix} is the volume of the ideal mixture, *k* is the last component of the mixture, *V _{i}* is the volume of the ith component.

Consider an ideal mixture of 2 components: A and B. The Vmix is the volume of the mixture, and *V*_{A} and *V*_{B} are the individual volumes of component A and B respectively. From Amagat's law, the total volume is the addition of individual volumes which is expressed in the below equation.

The generalised form of the above equation is discussed below.

Consider an ideal gas mixture of *k* components. Let *n*_{1}, *n*_{1}, *n*_{1} … *n _{k}* be the moles of individual components.

The volume of the ideal gas mixture at temperature *T* and pressure *P* be *V*_{mix}(*T*, *P*, *n*_{1}, *n*_{2}, *n*_{3} … *n _{k}*).

And the volumes of individual components at the same temperature *T* and pressure *P* be *V*_{1}(*T*, *P*, *n*_{1}), *V*_{2}(*T*, *P*, *n*_{2}), *V*_{3}(*T*, *P*, *n*_{3}) … *V _{k}*(

The above equation can be expressed in the mole fractions (*x*_{1}, *x*_{2}, *x*_{3} … *x _{k}*).

In the above equation, volumes are in extensive form.

Let *v _{i}* be the molar volume such that

The above equation in terms of the molar volume *v _{i}* is

Dividing *n*_{mix} both the sides:

*V*_{mix} is the volume of the ideal gas mixture. So, from the ideal gas law, we get,

Similarly, for *V _{i}*

Diving both equations,

Therefore, the volume of an individual component is mole fraction times the volume of the mixture.

The law is strictly valid for non-reacting ideal gases. It is also assumed the individual components are very similar and interaction among the molecules of the mixture is the same as among the molecules of the individual components. Amagat's law can be used for a very rough approximation of real gases.

50 mol of oxygen is mixed with 190 mol of nitrogen at SATP (*T* = 298.15 K, *P* = 105 Pa). Calculate the total volume of the mixture as per Amagat's law.

From the ideal gas equation, we can calculate the volume of O_{2} and N_{2}.

The volume of the mixture is the addition of O_{2} and N_{2} volumes.

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