Question

Argon is confined to a vessel at 20 degrees C, 0.001 torr. How many collisions will the molecules of argon make with 1cm^2of the wall in 1 second.

Answer 1

Use the ideal gas law to find the number density: PV = nKT K= constante de Boltzman

n/V = P/ KT = (0.001 mmHg) /(1.38x10^-23J/K)(293.15 K) = 2..47 x10¹⁷ = N (molecules per unit of volume)

Now we need to assume that all the molecules in the gas have the same velocity v_x in the same x-direction. A velocity of v_x measures in ms^-1, menas that in one second a molecule will travel a distance of v_x meters in the x-direction. Thus, if the molecule is within a distance v_x of the wall it will hit the wall during the 1s interval; if it is further away, it will not. For a container of area A, all the molecules that are moving toward the wall that are contained within a volume Av_x will hit. Then

number of molecules hitting the wall= 1/2 NAv_x per second

the term !/2 is added, because in average only the half of the molecules will hit the wall.

#mol= (0.5) (2..47 x10¹⁷)(1cm²) / 1 s = 1.24x10¹⁸ moleculas