The critical temperature and critical pressure of a gas are 190 K and 46 atm. Taking it as a van der Waals gas, the radius of its molecule is ( R = 0.0821 L atm K − 1 mol − 1 , N A = 6.022 × 1 0 23

Question

The critical temperature and critical pressure of a gas are 190 K and 46 atm. Taking it as a van der Waals gas, the radius of its molecule is ( R = 0.0821 L atm K − 1 mol − 1 , N A ​ = 6.022 × 1 0 23 )

TestHub · Accepted Answer

b = R T c ​ / ( 8 P c ​ ) = 0.0821 × 190/ ( 8 × 46 ) = 0.0424 L / mol = 42.4 cm 3 / mol . b is four times the actual volume of the molecules: b = 4 N A ​ × ( 4/3 ) π r 3 . r 3 = 42.4/ ( 16.76 × 6.022 × 1 0 23 ) = 4.20 × 1 0 − 24 cm 3 , so r = 1.61 × 1 0 − 8 cm = 1.61 A ˚ . Traps: leaving out the factor 4 gives r = 2.56 A ˚ ; 3.23 A ˚ is the diameter; 0.81 Å is half the radius. Answer: (C).

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