If the slope " Z (compressibility factor) vs " P " curve is constant ( Slope = π
492.6 atm-1) at a particular temperature (300 K) and very high pressure, then calculate the diameter if the molecules?
481I did it like this...
Given,dZ/dP =Ï€*492.6
Z=PV/RT(assuming 1 mole of gas)
Now dZ/dP=V/RT=Ï€*492.6
Assuming the molecules to be spherical
V=4/3*Ï€*r^3 (r-Radius of the molecules)
Solving r=(9.2)^1/3*(10)^2
thus,d=2*(9.2)^1/3*(10)^2
But i don't think my process is right.....and what is the significance of high pressure?
486(P+an2v)(v-nb)=nRT
P(V-nb)=nRT (an2v neglected due to high pressure)
PV=nRT+nbP
Now,Z=PVnRT=nRT+nbPnRT=1+bPRT
bRT=Ï€*492.6
From here we can calculate 'b' the volume correction,so we can get the diameter of the molecule
Anurag Ghosh thanks