The critical temperature of hydrogen gas is `33.2^(@)C` and its critical pressure is 12.4 atm. Find out the values of `a' and `b' for the gas.

Explanation

We know
`T_(c) = (8a)/(27 Rb) …. (i) , P_(c) = (a)/(27b^(2)) … (ii)`
Dividing (i) by (ii) we get
`(T_(c))/(P_(c)) = (8a)/(27Rb) xx (27 b^(2))/(a) = (8b)/(R) …. (iii)`
Given `T_(c) = 33.2 ^(@) C = 33.2 + 273 = 306.2 K ` and `P_c = 12.4` atm , R = 0.082 atm litre `K^(-1) mol^(-1)` . Substituting the values in equation (iii) , we get `(306.2)/(12.4) = (8 xx b)/(0.082)`
`b = (306.2 xx 0.082)/(12.4 xx 8)`
`= 0.253` litre `mol^(-1)`
Now substituting the value of .b. in equation (i) we have `T_(c) = (8a)/(27 Rb) (or) 306.2 = (8 xx a)/(27 xx 0.082 xx 0.253)`
(or) `a = 21.439 atm "litre"^(2) mol^(-1)`