Four gases have the following van der Waals constants (a in atm L 2 / mol 2 , b in L / mol ): P ( a = 1.4 , b = 0.040 ) ; Q ( a = 4.2 , b = 0.044 ) ; R ( a = 0.24 , b = 0.027 ) ; S ( a = 6.7 , b = 0.0

Question

Four gases have the following van der Waals constants (a in $atm L^{2} / mol^{2}$ , b in $L / mol$ ): P $(a = 1.4, b = 0.040)$ ; Q $(a = 4.2, b = 0.044)$ ; R $(a = 0.24, b = 0.027)$ ; S $(a = 6.7, b = 0.057)$ . Match each gas with the statements in Column II that are true for it $(R = 0.0821 L atm K^{- 1} mol^{- 1})$ (a Column I entry may match more than one Column II entry):

Column I (Gas)	Column II (Statement)
(P) gas P	(1) highest critical temperature of the four
(Q) gas Q	(2) lowest critical pressure of the four
(R) gas R	(3) largest critical volume of the four
(S) gas S	(4) Boyle temperature above 1000 K
	(5) $Z < 1$ at 300 K and moderate pressure

Choose the option with the correct matching:

TestHub · Accepted Answer

Use T c ​ = 8 a / ( 27 R b ) , P c ​ = a / ( 27 b 2 ) , V c ​ = 3 b and T B ​ = a / ( R b ) . a / b : 35.0 (P), 95.5 (Q), 8.9 (R), 117.5 (S) (so T c ​ is highest for S: 126 K for P, 349 K for Q, 33 K for R, 430 K for S). a / b 2 : 875 (P), 2169 (Q), 329 (R), 2062 (S) (so P c ​ is lowest for R, about 12 atm). V c ​ = 3 b : largest for S (0.171 L). T B ​ = ( a / b ) /0.0821 : 426 K (P), 1163 K (Q), 108 K (R), 1431 K (S). T B ​ > 1000 K for Q and S. Z < 1 at 300 K needs 300 K < T B ​ : true for P, Q, S, not for R. Correct matching: P to 5; Q to 4,5; R to 2; S to 1,3,4,5. Answer: (B).

Chemistry - Real Gas Question with Solution | TestHub

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