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.

The critical temperature of hydrogen gas is 33.2^(@)C and its critical

1.	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.
Answer» Solution :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)`