A hydrogen molecule (diameter 1.59 × 10 -8 cm), traveling at the rms speed, esca

Question

A hydrogen molecule (diameter 1.59 × 10-8 cm), traveling at the rms speed, escapes from a 4280 K furnace into a chamber containing cold argon atoms (diameter 3.59 × 10-8 cm) at a density of 4.61 × 1019 atoms/cm3(a) What is the speed of the hydrogen molecule? (b) If it collides with an argon atom, what is the closest their centers can be, considering each as spherical? (c) What is the initial number of collisions per second experienced by the hydrogen molecule? (Hint: Assume that the argon atoms are stationary.)

Explanation / Answer

part a )

Vrms = sqrt(3RT/M)

M = 2.02 x 10^-3 kg/mol

Vrms = 7.27 x 10^3 m/s

part b )

d = r1 + r2 = 0.795 x 10^-8 + 1.795 x 10^-8

d = 2.59 x 10^-8 cm

part c )

number of collision per second = pi*d^2*v*N/V

4.61 x 10^19 atoms/cm^3 = 4.61 x 10^25 atoms/m^3

= 7.059 x 10^10 collisions/s

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