V-b 002 (part 1 of 3) 10.0 point:s In an ultrahigh vacuum system, the pressure i

Question

V-b 002 (part 1 of 3) 10.0 point:s In an ultrahigh vacuum system, the pressure is measured to be 5.5 × 10-11 torr (where 1 torr = 133 Pa). The gas molecules have a molecular diameter of 2.9 × 10-10 m and the temperature is 290 K. Avogadro's number is 6.02214 × 1023 1/mol Find the number of molecules in a volume of 1.31 m3 Answer in units of molecules 2 .3935 Xi012 mous 003 (part 2 of 3) 10.0 points Find the mean free path of the molecules. s of m Answer 4.5859 x1ort rn 004 (part 3 of 3) 10.0 points Find the collision frequency, assuming an av- erage speed of 450 m/s. Answer in units of s1 005 10.0 points The constant h that annears in van der Waals'

Explanation / Answer

a) P V = R T (N / NA)

N = P V NA / R T = (5.5 * 10-11 * 133 * 1.31 * 6.02214 * 1023) / (8.314 * 290)

= 2.39 * 1012 molecules

b) l = v / [nv * pi * d2 * sqrt2] = 1.31 / (2.39 * 1012 * pi * (2.9 * 10-10)2 * sqrt 2)

= 1.47 * 106 m

c) f = v / l = 450 / (1.47 * 106)

= 3.07 * 10-4 s-1

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