The graphic shows the effective collision cross section, or area:
From this we can estimate the diameter of the atoms:
sf(A=pid^2)
:.sf(d=sqrt(A/pi)=0.36/3.142==0.3385color(white)(x)nm)
The mean free path sf(lambda) is the average distance between collisions.
The expression is:
sf(lambda=(1)/(sqrt(2)pid^(2)n_v)
sf(n_v) is the number of molecules per unit volume.
We can eliminate this using the Ideal Gas Expression:
sf(PV=nRT)
sf(n_v=(nN_A)/V)
Where sf(N_A) is the Avogadro Constant.
Since sf(V=(nRT)/P)
We can write:
sf(n_v=(cancel(n)N_A)/((cancel(n)RT)/P)=(N_AP)/(RT))
Substituting this into the expression for sf(lambdarArr)
sf(lambda=(RT)/(sqrt(2)pid^2N_AP))
:.sf(P=(RT)/(lambdasqrt(2)d^2N_A))
We can now set the condition that sf(lambda=d)
:.sf(P=(RT)/(sqrt(2)pid^3N_A))
Putting in the numbers:
sf(P=(8.31xx298)/(1.414xx3.142xx(0.3385xx10^(-9))^3xx6.02xx10^(23))color(white)(x)"N/m"^2)
sf(P=2.837xx10^7color(white)(x)"N/m"^2)
