Consider an ideal gas at 25.1°C and 1.10 atm pressure. To get some idea how clos
ID: 2000267 • Letter: C
Question
Consider an ideal gas at 25.1°C and 1.10 atm pressure. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube.
(a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap?
b) How does this distance compare with the diameter of a typical molecule?
(c) How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart?
Explanation / Answer
pV=NkT (1)
V=volume of the container (total volume of molecules)
N=total number of molecules
k=Boltzmann's constant
V=V1*N
V1=volume of 1 molecule
k=1.38*10-23 J/K
T=t+273.15 (K) In this case: T=298.25 K
Replace in (1) and get V1=kT/p ~ 37.42*10-27 m3
For a cube: V=l3
l=side of the cube
I got for l ~ 3.345*10-9 = 0.3345*10-10 mm
(b) The dimension of an atom is about 0.1-0.5 nm, and for a molecule ~0.3*10-10 m.
Realiable result.
(c) You may appreciate by yourself.