240_l04 - Copy

# 240_l04 - Copy - Real Gases Sections 1.4-1.6(Atkins 6th Ed...

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Real Gases Sections 1.4-1.6 (Atkins 6th Ed.), 1.3-1.5 (Atkins 7th, 8th Eds.) Molecular Interactions Compression factor Virial coefficients Condensation Critical Constants Van der Waals Equation Corresponding States Real gases have very different behaviour from ideal gases, notably in cases of high pressure or near the condensation point - a number of additional interactions must be considered Last updated: Sept. 18, 2006, Slides 1, 16 slight modifications; Added slide 7

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Molecular Interactions Repulsive forces : assist expansion of gas - significant when molecules are close to one another - operative at high pressures, when intermolecular distances are near a single molecular diameter Attractive forces : assist compression of gas - can have influence over a long distance (close but not touching) -operative at moderate pressures
Z ' pV m RT Compression Factor The compression factor of a gas can be defined as where V m is the molar volume , V / n Ideal gas: Z = 1 Departure from Z = 1 means that a gas is not behaving as an ideal gas Intermediate Pressure: Z < 1 Compression is favoured, due to dominance of attractive forces High Pressure: Z > 1 Expansion is favoured, as repulsive forces come into play

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pV m ' RT (1 % B ) p % C ) p 2 % ...) ' RT (1 % B V m % C V 2 m % ...) Virial Coefficients For a real gas with large molar volumes and higher temperatures, the isotherms are almost identical to those of an ideal gas. However, there are some small differences which suggest that the perfect gas law is only the first term in a power series : These are the virial equations of state , where coefficients B and C have to be evaluated at each temperature ! p = 0 : Close to ideal gas law, but not exact p increases : B contributes, linear relation between Z and P p higher : C and higher order terms contribute, deviation from linearity Virial : comes from that Latin word vis , viris , meaning force - the coefficients in the virial equation depend on the forces of interaction between molecules of the gas
dZ dp ' B ) % 2 pC ) % ... 6 B ) as p 6 0 dZ d (1 / V m ) 6 B as V m 64 ,o r p 6 0

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## This note was uploaded on 10/24/2009 for the course CHEM 260 taught by Professor Staff during the Spring '08 term at University of Michigan.

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240_l04 - Copy - Real Gases Sections 1.4-1.6(Atkins 6th Ed...

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