Question

A hydrogen molecule (diameter 1.57 × 10^-8 cm), traveling at the rms speed, escapes from a 3820 K furnace into a chamber containing cold argon atoms (diameter 3.22 × 10^-8 cm) at a density of 4.96 × 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.)

Answer 1

(a) v = sqrt ( 3RT / m)

where m is molar mass and for hydrogen, m = 2.02e-3 kg/mol

v = sqrt ( 3 * 8.314 * 3820 / 2.02e-3)

v = 6867.86 m/s

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(b) when both hydrogen and argon atom touch, distance between them

is

d = radius of hydrogen + radius of argon

d = 7.85e-9 + 1.61e-8

d = 2.395e-8 cm

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(c) The density (n) is given as 4.96e19 atoms / cm³ or 4.96e25 atoms / m³

therefore number of collisions per sec

N = Anv

where A is area and v is velocity

N = pi * 2.395e-10² * 4.96e25 * 6867.86

N = 6.138e10 collisions / sec