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Amagat's Law of Additive Volumes

09th May 2019 @ 4 min read

Physical Chemistry

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.

Statement

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.

Expression

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

Amagat's law of additive volumes

where Vmix is the volume of the ideal mixture, k is the last component of the mixture, Vi is the volume of the ith component.

Explanation

Consider an ideal mixture of 2 components: A and B. The Vmix is the volume of the mixture, and VA and VB 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.

Three balloons, the addition of the first two results in the volume of the third.
Figure 1: The volume of an ideal gas mixture is the sum of individual volumes.

The generalised form of the above equation is discussed below.

Consider an ideal gas mixture of k components. Let n1, n1, n1nk be the moles of individual components.

The volume of the ideal gas mixture at temperature T and pressure P be Vmix(T, P, n1, n2, n3nk).

And the volumes of individual components at the same temperature T and pressure P be V1(T, P, n1), V2(T, P, n2), V3(T, P, n3) … Vk(T, P, nk).

The above equation can be expressed in the mole fractions (x1, x2, x3xk).

In the above equation, volumes are in extensive form.

Let vi be the molar volume such that

The above equation in terms of the molar volume vi is

Dividing nmix both the sides:

Relationship between total volume and individual volume

Vmix is the volume of the ideal gas mixture. So, from the ideal gas law, we get,

Similarly, for Vi

Diving both equations,

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

Limitations of Amagat's Law

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.

Example

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 O2 and N2.

The volume of the mixture is the addition of O2 and N2 volumes.

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Amagat Gas Law

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