Question

A cubical box with each side of length 0.255 m contains 1.095 moles of neon gas at room temperature (293 K). What is the average rate (in atoms/s) at which neon atoms collide with one side of the container? The mass of a single neon atom is 3.35 10-26 kg.

_______ atoms/s

Answer 1

given T = 293 K ,

a = 0.255 m

K = 1.38 X 10^-23 J

n = 1.095 moles

m = 3.35 X 10^-26 kg

and N_A = 6.023 X 10²³

using equation

dN/ dt = ( 1 /3 ) a² ( n_N ) v_rms

we have n_N = n N_A / a³

dN /dt = ( n N_A / 3 a ) v_rms

but v_rms = ( 3 KT / m )^1/2

first v_rms = ( 3 KT / m )^1/2

v_rms = ( 3 X 1.38 X 10^-23 X 293 / 3.35 X 10^-26 )^1/2

v_rms = 601.74 m/sec

now finding dN /dt = ( n N_A / 3 a ) v_rms

dN /dt = ( 1.095 X 6.023 X 10²³ / 3 X 0.255 ) X 601.74

dN /dt = 7.78 X 10²⁶ atoms/sec