First Hour Exam Key - Michigan State University Fall 2007...

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Unformatted text preview: Michigan State University Fall 2007 CEM 383 First Hour Exam 19 September This exam consists of five problems on the next six pages. Please examine the booklet to make sure you have a complete examination. Equations are provided on a separate sheet. Chemical data are provided in the problems along with constants that you may need. Answer each question in the space provided, continuing on the reverse side of the same page if more space is needed. If a question is not clear, insufficient information is given, or there is an apparent error, please notify a member of the instructional staff immediately. Pay attention to units and to significant figures of your numerical answers. Show your reasoning for all problems on the exam! 1. (30 points) Name: 2. (15 points) Student #2 3. (15 points) Recitation Section: 4. (20 points) 5. (20 points) Total (100 pts) fl \0 ,Z 1. (30 points) 1.00 L of He gas at 0.75 bar is mixed with 2.00 L of Ne gas at 1.5 bar to make a total voMggLiLQQL of gas. Assuming that the temperature remains constant at 298K during this mixing and that the gases are ideal, determine the following: a) What is the total pressure of the final mixture? (MHe = 4.00 g/mole, MNe = 20.2 g/mole, R = 0.083 L-bar/(mole-K) = 8.31 J/(mole-K)) n11”: ~Pfi '_,\/Hr. .— r; ‘55~‘\ L3 .__________,. ‘. 5.;‘30W Ht RT 1.3273 (MM b) What are the partial pressures of He and Ne? a; w I (assexc‘oasfaggam _ V a 1+ 2. (15 points) As part of problem set #1, you derived a hybrid equation of state for real gases by substituting the series approximation for 1/(1-x) into the Van der Waals equation expressed in terms of compressibility. The result was — 2 3 Z=fl=1+(b—iji+[i) +9) +... RT RT V V v Comparing this result to the virial equation of state, — 2 3 z=fl=1+3(;)+c[;] mg] + RT V V V and remembering that the 33er temperature, TB, is the temperature where a plot of Z vs. 1H7 approaches 1/ V = O with zero slope, calculate the Boyle temperature for N2 gas. (for N2, a = 1.39 bar-Lz’lmol2 and b = 0.039 L/mol) 6 ,2 :32 . i . -- ma; [3 42%): +¢b<lf>tt "i- alt/u "‘ ~, A: cabal/w .——-§ 5‘”)ij B’fu/WWLWJW%% E’L_o rat-.3 A 3. (15 points) Pressure Volume a) The above graph is a phase diagram for a substance that was constructed from P vs. V isotherms in the vicinity of the critical temperature. What state(s) of the substance is present in the regions marked by, 1. .15“; met 4_ b) Mark the critical point on the drawing with an X. 5. (20 pointsz n ideal gas at 300K is being held in a cylinder of volume = 3.0L that is fitted with insulating, or adiabatic walls and a frictionless piston. At mechanical Pext=Pintema| = 2/"; . a) Calculate the work, if the external pressure is suddenly decreased W}? bar and the system volume expands to 15.0L. rr-Oi- A ’5‘ a): ’- San (9V '- -— PW gall/ ‘- vpflé ((KOL“3,,QL> , «s. b) What is the final temperature of the gas? ‘- Eh R.) (2 ~. ) \0 TL I L], A“: ‘- Emlt ,2 %+U / ’l 6» ‘- ‘2.Lf Um = i(4:;§(l.oah3L-ém§(7;—3u (a) MM i\~ {2&1 Qiigooslwflams j - 13-11% ‘T (.033 3236000 ’— /1 k ~lbDlE: TL-gobk 7 (ML 1 T1 4. (20 points) a) Calculate the root mean square speed of 02 molecules having a kinetic energy of , 10 kJ/mole. (M02 = 32 g/mole, R=8.31 J/(Komol) = 0.083 L-bar/(moI-K), \ow'k NA = 6.02 x 1023) : q ’10 “Cu-T V \L IL! 2 {313: an kit, 5* m = 7% VS 5 b) At what temperature would the answer to part (a) be the root mean square I!) ? speed? J1 Cums ,_ J 3 (2"? (77/201- ...
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First Hour Exam Key - Michigan State University Fall 2007...

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