PS3 - 10 September 2010 Michael F Brown CHEMISTRY...

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Unformatted text preview: 10 September, 2010 Michael F. Brown CHEMISTRY 480A (Physical Chemistry) Problem Set 03 ——————_____.______—________ To be turned in by: Monday, 20 September Worked examples for this course are dealt with primarily in the Discussion Section; whereas new concepts are introduced in the Lectures. You can get help with the homework problems in the Discussion Sections (14:00—14:50 Tuesday, Chemistry 209; and 15:30—16:20 Tuesday, Chemistry 134). The problem sets will be graded P+, P, or F and will be used to increase or decrease borderline grades. On all computational problems be sure to use Sl units, and indicate your answer to the proper number of significant figures. For maximum credit show clearly how you obtained your answer, i.e. what numbers were combined to yield the final result. Background reading:Atkins & de Paula, Sections 1.3, 1.4, Mathematical background 1 Back of Chapter Exercises related to the homework (optional): 1.13(a), 1.14(a), 1.15(a), 1.16(a), 1.17(a), 1.18(a), 1.19(a), 1.20(a), 1.21(a) Back of Chapter Problems related to the homework (optional): 1.7,1.9,1.11.1.15,1.21,1.29 Problem 1. A scientist at the National Center for Atmospheric Research (NCAR) in Colorado is studying a sample of Cl2 gas at a temperature of 350 K and pressure of 2.30 atm. a) Assuming the perfect gas equation of state calculate the molar volume of Gig. b) Given the van der Waals equation of state find the molar volume of Gig. c) From the answer to part (a) assume the van der Waals equation and calculate to a first approximation the correction term for attraction. Finally use successive approximations to obtain a numerical answer for the molar volume of Clz. Problem 2. A planetary scientist is interested in the atmosphere of a new planet. Assume that the gases in question are non-ideal and obey the van der Waals equation of state. a) Express the van der Waals equation as a virial expansion in powers of UV and calculate formulas for B and C in terms of the parameters a and b. The series expansion needed is: 1 l—x 2 =1+x+x +... b) Experimental measurements on argon yield B = —21.7 cm3 mole‘1 and C = 1200 cm6 mole‘ for the virial coefficients at 273 K. What are the values of a and b in the corresponding van der Waals equation of state? Problem 3. You have become interested in the possibility of extraterrestrial life involving a reducing atmosphere based on carbon dioxide (C02). Let us consider the van der Waals equation of state for carbon dioxide. a) Assuming the virial equation of state is applicable, derive a mathematical expression for the second virial coefficient B in terms of the van der Waals constants a and b: b) Calculate the numerical value of the Boyle temperature for the case of C02: Problem 4. You are a chemical engineer interested in exploring a newly discovered natural gas field in the Gulf of Mexico. Consider an amount comprising n = 2.0 mole of methane gas, CH4, at a temperature of T= 100 00 having a volume of V = 100 L. a) Calculate the pressure exerted by the CH4 assuming it behaves as a perfect gas: b) Calculate the pressure exerted by the CH4 given the van der Waals equation of state: (Consult the data in your textbook.) 09-10—10 chem480A\10\prob\003\mw.doc j; a) Perécf‘fiy 4; 1M)”. 7 _, __ _ ,, 22v _: 226%?" $ Cy) :_1/,,7 =: 6:2,: , , , _~ , , . . Eda—ZWXSSQXLW, 2-¢g? L, 274/_/‘ _ , _ __ : Z _ -_,: ’Z‘ W, ‘____ _ , y < 2- 3110/42/44! fie—(7644473227 71?,” {/gf/UMC. Féf’, {Ag 2252.216: 9/; ,7 625? 242.2,», 2C?» ,,N_42Z.s,_. 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