Lecture 4 - Why do gases attract? (16.6, 16.7) For gas...

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Lecture 4 1 Why do gases attract? (16.6, 16.7) For gas molecules, repulsion is (relatively) easy to explain: electron cloud (charge density) overlap (for closed shell systems) gives rise to a strong repulsive force (~1/r 12 or hard sphere). But what causes attraction? Assume we have neutral species (not a plasma, but a gas!) Simple answer: electrostatics. Consider 2 interacting dipoles: 1 μ 2 N 12 unit vector ˆ rrr =⋅ G ( )( ) () 12 1 211 22 int 2 3 ˆˆ 3 Interaction energy = 4 o rr u r μμ πε −⋅ = G GG G But, our gas molecules have freedom of movement (translate, rotate), so on average: 2 int 2 6 21 3 4 dd B oB u ur kT r == Average over all orientations Fig. 16.16
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Lecture 4 2 Example: CO at 80K -31 For CO, is small (0.1D or 3.3 10 ) Cm μ × 23 1 21 B At T = 80K, k 1.38 10 80 1.10 10 Thermal Energy TJ K KJ −− = () ( ) 4 31 4 4 22 6 12 10 4 2 2 21 3.3 10 33 4 1.11 10 1.10 10 dd oB ru kT CJ m J μμ πε × −= = ×× 68 2 6 5.8 10 dd Jm × o 10 25 for 3A 3 10 7.96 10 dd rm u J == × →= × This is very small compared to thermal energy!
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Lecture 4 - Why do gases attract? (16.6, 16.7) For gas...

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