A cubic box with sides of 20.0 cm contains 2.00 × 1023 molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10-27 kg. What is the average pressure exerted by the molecules on the walls of the container? (The Boltzmann constant is 1.38 × 10-23 J/K and the ideal gas constant is R = 8.314 J/mol•K .) (12 pts.)

1.133 kPa is the average pressure exerted by the molecules on the walls of the container.

Explanation:

Side of the cubic box = s = 20.0 cm

Volume of the box ,V=

Root mean square speed of the of helium molecule : 200m/s

The formula used for root mean square speed is:

where,

= root mean square speed

k = Boltzmann’s constant =

T = temperature = 370 K

M = mass helium =

= Avogadro’s number =

Moles of helium gas = n

Number of helium molecules = N =

N =

Ideal gas equation:

PV = nRT

Substitution of values of T and n from above :

(1 Pa = 0.001 kPa)

1.133 kPa is the average pressure exerted by the molecules on the walls of the container.