A spherical balloon containing nitrogen gas has a radius of 38 cm. If the balloo
ID: 1524419 • Letter: A
Question
A spherical balloon containing nitrogen gas has a radius of 38 cm. If the balloon is at atmospheric pressure and room temperature (293 K), find the average spacing between molecules in the balloon. (Assume each molecule takes up the volume of a cube of side length L.)
The answer is 3.3906e-09
I've asked this question twice already. One person got the answer right but how they got it was not working in my calculator. I'm thinking that there could be a computer error for my homework but I want to know how to properly do this problem.
Thanks
Explanation / Answer
from the given data
r = 38 cm = 0.38 m
T = 293 k
P = 1 atm = 1.013*10^5 pa
volume of the balloon, V = (4/3)*pi*r^3
= (4/3)*pi*0.38^3
= 0.229847296 m^3
let n is the no of moles of the gas.
use Ideal gas equation
P*V = n*R*T
n = P*V/(R*T)
= 1.013*10^5*0.229847296/(8.314*293)
= 9.5580919 moles
no of atoms present, N = n*Na
= 9.5580919*6.023*10^23
= 5.75683875*10^24
volume of each atom = V/N
= 0.229846/(5.75683875*10^24)
= 3.992573*10^-26 m^3
now use, volume of each atom = L^3
3.99*10^-26 = L^3
L = (3.992573*10^-26)^(1/3)
= 3.4178*10^-9 m
so, distance between two atoms(center to center) = L
= 3.4178*10^-9 m
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