A real gas is supposed to obey the gas equation `P(V-b) =nRT` at `STP` if one mole of gas occupies `25dm^(3)` volume at `STP` calculate
(a) diameter of each gas molecule
(b) Compressibility factor for gas .

Explanation

Given `P(V-b) = nRT`
`1 xx (25 -b) = 1 xx 0.0821 xx 273` ltbr gt` ( :' V =25 dm^(3) = 25 litre)`
`b = 2.586 litre`
Also diameter of molecule `d =2r` ltbr gtWe have ` b = 4 xx N xx` Volume of molecule
`=4 xx 6.023 xx 10^(23) xx (4)/(3) pi r^(3)`
`:. 2.586 = 4 xx 6.023 xx 10^(23) xx (4)/(3) xx (22)/(7) ((d)/(2))^(3)`
`:. d = 1.270 xx 10^(-8) cm`
(b) Given `P (V-b) =nRT, PV -Pb = nRT`
`(PV)/(nRT) - (Pb)/(nRT) = 1`
or `Z -(Pb)/(nRT) =1`
`( :' (PV)/(nRT) =Z` compressibility factor) ltbr gt or `Z =1 + (Pb)/(nRT) =1 + (1 xx2.586)/(1 xx 0.0821 xx 273) = 1.115` .