Question

A 390-mL spherical flask contains 0.065 mol of an ideal gas at a temperature of 318 K.

What is the average force exerted on the walls of the flask by a single molecule?

Express your answer using two significant figures. In newtons.

Answer 1

Given

ideal gas volume of the spherical flask is v = 4/3 pi *r^3 = 0.39 l

number of moles of the gas n = 0.065
number of molecules present in the volume is N = 0.065*6.023*10^23 = 3.91495*10^22
temperature T = 318 k

ideal gas equation PV = n*R*T

       P = n*R*T/V  
       = N*k*T/V
       = 3.91495*10^22*1.38064852*10^-23*318/(0.00039)

       = 440729.24 N/m2

   we know that P = F/A ==> F = P*A

for radius of the flask 0.00039 = 4/3 pi*r^3, r = 0.045324 m

       surface area of flastk is A = 4 pi r^2 = 4 pi*(0.045324)^2 m2 = 0.025814655 m2

now force is F = P*A = 0.025814655*440729.24 N = 11377.27 N