Ideal gas equation is represented as `PV=nRT`. Gases present in the universe were found ideal n the Boyle's temperature range only. The compressibility factor for an ideal gas, `Z= (PV)/(nRT) `. The main cause to show deviations were due to wrong assumptions made bout forces of attractions (which becomes significant at high pressure). olume occupied by molecules V, in PV = nRT, is supposed to be volume of as or, the volume of container in which gas is placed by assuming that aseous molecules do not have appreciable volume. Actual volume of the as is that volume in which each molecule of a gas can move freely. If olume occupied by gaseous molecule is not negligible, then the term V hould be replaced by the ideal volume which is available for free motion of ach molecule of gas.
Similarly for n moles of gas `V_("actual") = V-nb `
The excluded volume can be calculated by considering bimolecular collisions. The excluded volume is the volume occupied by the sphere of 2r for each pair of molecule.
Thus, excluded volume for one pair of molecules = `4/3 pi (2r)^3 = (4 xx 8 pi r^3)/3`
The excluded volume for 1 molecule `= 2/3 xx 8 pi r^3 = 4 xx (4/3 pi r^3) = 4V`
The excluded volume for N molecules `= 4NV = b `(where N is Avogadro's No.) The compressibility factor for `N_2` at `-50^@C` and 800 atm pressure is 1.95. Number of moles of `N_2` required to fill a balloon of 100 L capacity is :

Options

A. `2.244 xx 10^3`
B. `2.244 xx10^2`
C. `2.244`
D. `22.44`

Explanation

`Z = 1.95 = (PV)/(nRT) , 1.95 = (800 xx 100)/(n xx 0.0821 xx 223)`
`n = 2.24 xx 10^(3)`.