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1 Homework 2 Answer (Due 01/26/2011 Wednesday) 1. (a) Calculate the molar volume, temperature, pressure of N 2 at the critical point using van der Waals parameters a and b (see Table 1.1). (b) Obtain the density of N 2 at the critical point, and compare it with that of liquid N 2 (~0.8 g/mL). Assume that the molar mass of N 2 is 28.0. a) at critical point b 3 V C 2 C 27b a P 27Rb 8a T C 11 C V 3 3 0.0387 0.1161 bL m o l L m o l   2- 2 C 21 2 a 1.370L barmol P3 3 . 8 8 27b 27 (0.0387 ) bar Lmol 2 C 1 8a 8 1.370L barmol T 126.2 27Rb 27 0.0831447 0.0387 K LbarK mol Lmol  b) Density at critical point: -1 -1 28.0gmol D 0.241 / 1000 0.1161Lmol 1 g mL mL L 2. Assume T c ~ 2T m . Answer which of He, Ar, CO 2 , N 2 , H 2 O have the highest and lowest T m based on T c estimated from Table 1.1. Give reasoning with calculations of T m . H 2 O has the highest T m , He has the lowest T m . 8 4 ~ 2 2 27 27 mc aa TT R bR b T c (K) T m (K) He 5.2 2.6 Ar 151 75 CO 2 304 152 N 2 126 64 H 2 O 647 323 3. Calculate the pressures for (a) He and (b) H 2 O from van der Waals equation when the molar volume is 0.6 L and 310 K. a) 3- 1 - 1 2 - 2 He 1 1 2 RT a 0.08314 310 0.0346 P 44.73 0.096 44.6 0.6000 0.0238 (0.6000 ) mm dm barK mol K L barmol bar bar bar V b V Lmol Lmol Lmol 

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2 b) 2 3- 1 - 1 2 - 2 HO 21 1 1 2 0.08314 310 5.537 P 45.25 15.38 29.87 0.6000 0.03049 (0.6000 ) mm RT a dm barK mol K L barmol bar bar bar V b V Lmol Lmol Lmol    4. (From Atkins Ch1) The critical constants of ethane are T c = 309.15 K, V mc = 112.7 cm 3 mol -1 . (a) Calculate the van der Wa a ls parameters of the gas. (b) Calculate the critical pressure p c . (c) Estimate the radius of the molecules. a) b 3 V C 2 C 27b a P 27Rb 8a T C Van der Waals parameters: 1 31 1 112.7cm mol 37.57 0.03757 33 C V b cm mol Lmol  11 1 22 27 27 0.08206 0.03757 309.15 3.217 88 c RbT La tmm o l K Lm o l K aa t m L m o l   b)  2 2 1 3.217 84.41 27 27 0.03757 C t m L m o l P K b Lmol c) Van der Waals volume: 23 3 23 37.57 6.238 10 / 6.022 10 / W A bc m m o l V cm molecule N molecule mol 3 WW 4 V 3 r Molecule radius: 23 3 8 9 W 6 . 2 3 81 0 / 2 .
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