View source for Physics:Monatomic gas

{{Short description|Gas made of free atoms}}
In [[Physics:Physics|physics]] and [[Chemistry:Chemistry|chemistry]], "monatomic" is a combination of the words "mono" and "atomic", and means "single [[Physics:Atom|atom]]". It is usually applied to [[Physics:Gas|gas]]es: a '''monatomic gas''' is a gas in which atoms are not bound to each other. Examples at [[Standard temperature and pressure|standard conditions of temperature and pressure]] include all the [[Chemistry:Noble gas|noble gas]]es ([[Chemistry:Helium|helium]], [[Chemistry:Neon|neon]], [[Chemistry:Argon|argon]], [[Chemistry:Krypton|krypton]], [[Chemistry:Xenon|xenon]], and [[Chemistry:Radon|radon]]), though all chemical elements will be monatomic in the gas phase at sufficiently high temperature (or very low pressure). The [[Physics:Thermodynamics|thermodynamic]] behavior of a monatomic gas is much simpler when compared to polyatomic gases because it is free of any [[Rotational energy|rotational]] or vibrational energy.<ref>{{cite web|title=monatomic gas|url=http://www.britannica.com/science/monatomic-gas|publisher=Encyclopædia Britannica|access-date=6 June 2016}}</ref>

==Noble gases==
The only chemical elements that are stable single atoms (so they are not molecules) at [[Standard temperature and pressure|standard temperature and pressure]] (STP) are the [[Chemistry:Noble gas|noble gas]]es.  These are [[Chemistry:Helium|helium]], [[Chemistry:Neon|neon]], [[Chemistry:Argon|argon]], [[Chemistry:Krypton|krypton]], [[Chemistry:Xenon|xenon]], and [[Chemistry:Radon|radon]]. Noble gases have a full outer valence shell making them rather non-reactive species.<ref>{{Cite journal|last1=Laszlo|first1=Pierre|last2=Schrobilgen|first2=Gary J.|date=1988-04-01|title=Ein Pionier oder mehrere Pioniere? Die Entdeckung der Edelgas-Verbindungen|journal=Angewandte Chemie|language=en|volume=100|issue=4|pages=495–506|doi=10.1002/ange.19881000406|bibcode=1988AngCh.100..495L |issn=1521-3757}}</ref> While these elements have been described historically as completely inert, chemical compounds have been synthesized with all but neon and helium.<ref>{{Cite journal|last=Christe|first=Karl O.|date=2001-04-17|title=A Renaissance in Noble Gas Chemistry|url=http://onlinelibrary.wiley.com/doi/10.1002/1521-3773(20010417)40:83.0.CO;2-J/abstract|journal=Angewandte Chemie International Edition|language=en|volume=40|issue=8|pages=1419–1421|doi=10.1002/1521-3773(20010417)40:8<1419::aid-anie1419>3.0.co;2-j|pmid=11317290|issn=1521-3773}}</ref>

When grouped together with the homonuclear diatomic gases such as [[Chemistry:Nitrogen|nitrogen]] (N<sub>2</sub>), the noble gases are called "elemental gases" to distinguish them from molecules that are also chemical compounds.

==Thermodynamic properties==
The only possible motion of an atom in a monatomic gas is translation (electronic excitation is not important at room temperature). Thus by the [[Physics:Equipartition theorem|equipartition theorem]], the [[Physics:Kinetic energy|kinetic energy]] of a single atom of a monatomic gas at [[Physics:Thermodynamic temperature|thermodynamic temperature]] ''T'' is given by <math>\frac{3}{2}k_bT</math>, where ''k<sub>b</sub>'' is [[Physics:Boltzmann's constant|Boltzmann's constant]]. One mole of atoms contains an [[Chemistry:Avogadro number|Avogadro number]] (<math>\mathcal{N}_a</math>) of atoms, so that the energy of one mole of atoms of a monatomic gas is <math> \frac{3}{2} k_b T \mathcal{N}_a  = \frac{3}{2} RT </math>, where ''R'' is the [[Physics:Gas constant|gas constant]]. 

In an [[Physics:Adiabatic process|adiabatic process]], monatomic gases have an idealised [[Physics:Heat capacity ratio|''γ''-factor]] (''C<sub>p</sub>''/''C<sub>v</sub>'') of 5/3, as opposed to 7/5 for ideal diatomic gases where rotation (but not vibration at room temperature) also contributes. Also, for ideal monatomic gases:<ref>[http://physics.bu.edu/~redner/211-sp06/class-thermodynamics/heatcap_volume.html Heat Capacity of an Ideal Gas]</ref><ref>[https://ccrma.stanford.edu/~jos/pasp/Heat_Capacity_Ideal_Gases.html Heat Capacity of Ideal Gases]</ref><ref>[http://depts.washington.edu/chemcrs/bulkdisk/chem152A_aut10/notes_Lecture_03_100610_revised.pdf Lecture 3: Thermodynamics of Ideal Gases & Calorimetry]{{dead link|date=February 2018 |bot=InternetArchiveBot |fix-attempted=yes }}, p. 2</ref> 
{{block indent|1=the molar [[Physics:Heat capacity|heat capacity]] at constant pressure (''C<sub>p</sub>'') is 5/2&nbsp;''R''&nbsp;= 20.8&nbsp;J&thinsp;K<sup>−1</sup>&thinsp;mol<sup>−1</sup> (4.97&nbsp;[[Calorie|cal]]&thinsp;K<sup>−1</sup>&thinsp;mol<sup>−1</sup>).}}
{{block indent|1=the molar heat capacity at constant volume (''C<sub>v</sub>'') is 3/2&nbsp;''R''&nbsp;= 12.5&nbsp;J&thinsp;K<sup>−1</sup>&thinsp;mol<sup>−1</sup> (2.98&nbsp;cal&thinsp;K<sup>−1</sup>&thinsp;mol<sup>−1</sup>).}}

== References ==
{{Reflist}}

[[Category:Gases]]

{{Sourceattribution|Monatomic gas}}