FNT8 - FNT#8 Particles and the Lennard-Jones potential...

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FNT #8: Particles and the Lennard-Jones potential Damien Martin November 29, 2006 Question 1 How far apart are molecules in the gas phase? You know from chemistry that the molecules of an ideal gas do not interact. Relate this idea to the particle-particle interaction (i.e. Lennard-Jones interaction). Solution You should have found from your activity in class with the liquid nitrogen to gaseous nitrogen that the volume increased by a factor of 1000, so that the separation of particles increased by a factor of 10. No one in my class did it, so let us look at another way of getting the same result. For one mole of ideal gas we have PV = RT . At standard temperature and pressure ( T = 273 K and P = 1 . 01 × 10 5 Pa) we have V = 0 . 0224 m 3 . If you have done chemistry you know that the volume should be 22.4 liters – this is just the same value expressed in terms of m 3 instead. So what is the spacing between atoms? Well, I have N A atoms (remember this is one mole of gas) and they take up 2 . 24 × 10 - 2 m 3 . Therefore average volume that I can take and only find one atom in (on average) is V only one atom = V N A = 2 . 24 × 10 - 2 m 3 6 . 02 × 10 23 atoms = 3 . 72 × 10 - 26 m 3 /atom If the distance between nearest neighbours in a gas is , then the volume where only one atom can be found is roughly 3 . Therefore I have 3 = 3 . 72 × 10 - 26 m 3 = 3 . 34 × 10 - 9 m 3 1
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independent of the size of the gas molecules! That does not make sense – after all, if I pretended my atoms where huge ( 1 m in diameter, for example) then it does not make sense for them to be only 10 - 9 metres away from their nearest neighbour! The resolution is that
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