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'''Amagat's law ''' or the '''Law of Partial Volumes''' of 1880 describes the behaviour and properties of mixtures of [[ideal gas|ideal]] (as well as some cases of non-ideal) gases. Of use in [[chemistry]] and [[thermodynamics]], Amagat's law states that the extensive volume ''V = N·v'' of a gas mixture is equal to the sum of volumes ''V<sub>i</sub>'' of the ''K'' component gases, if the temperature ''T'' and the pressure ''p'' remain the same:<ref>[http://www.taftan.com/thermodynamics/AMAGAT.HTM Amagat's law of additive volumes<!-- Bot generated title -->]</ref><ref>{{cite book |first=A. |last=Bejan |title=Advanced Engineering Thermodynamics |edition=3rd |publisher=John Wiley & Sons |year=2006 |isbn=0471677639 }}</ref>


:<math> N\cdot v(T,p)=\sum_{i=1}^K N_i\cdot v_i(T,p).\ </math>


This is the experimental expression of [[volume]] as an [[extensive quantity]].  It is named after [[Emile Amagat]].
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According to Amagat’s law of partial volume, the total volume of a non-reacting mixture of gases at constant temperature and pressure should be equal to the sum of the individual partial volumes of the constituent gases. So if <math>V_1, V_2, \dots, V_n</math> are considered to be the partial volumes of components in the gaseous mixture, then the total volume <math>V</math> would be represented as:
 
:<math>V = V_1 + V_2 + V_3 + \dots + V_n = \sum_{i} V_i</math>
 
Both Amagat's and [[Dalton's Law]]s predict the properties of gas mixtures. Their predictions are the same for [[ideal gas]]es. However, for real (non-ideal) gases, the results differ.<ref>{{cite book |first=J. H. |last=Noggle |title=Physical Chemistry |edition=3rd |publisher=Harper Collins |location=New York |year=1996 |isbn=0673523411 }}</ref> [[Dalton's Law]] of Partial Pressures assumes that the gases in the mixture are non-[[Interaction#Physics|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 the component gases (again at the 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:
 
:<math>B(T) = X_1B_1 + X_2B_2 + X_1X_2B_{1,2}\ </math>
 
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, B<sub>1,2</sub>, of the mixture is given by:
 
:<math>B_{1,2} = 0\ </math>  ([[Dalton's Law]])
 
and
 
:<math>B_{1,2} = (B_1 + B_2)/2\ </math> (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==
{{Reflist}}
 
[[Category:Gas laws]]
[[Category:Gases]]

Revision as of 16:52, 1 March 2014


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