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Midterm 1 solutions

# Midterm 1 solutions - Instructor Bowers Course Chem 113C 1...

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Unformatted text preview: Instructor: Bowers Course: Chem. 113C 1 Initial of Midterm Exam 1 Friday, April 25, 2008 last name Name E: \1 Closed Book Closed Notes 8 Total Pages Good Luck ‘ 1. These questions are concerned with velocity distributions (a) The 1-D velocity distribution, f(vx) fOr T1 is drawn below”. On the same graph draw f(vx) for T2 > T1. (4 pts.) ' (b) Determine the average value of vx, v; Show work. (Hint: remember the properties of even and odd functions.) (4 pts.) ‘ T=cp e"; m, (d) We can now determine the spread in velocities in 1‘=D, Avx. Do so. ‘(4 pts.) m {62- ﬁzj‘h . ,_ _ m ,/ (e) In 3-D we are interested in speeds, not velocities. This, same concept is, of course also important in l-D. Hence, deterrnine the l-D speed average, z (speed). (5 pts.) _ ,r‘zl WOOL W‘U‘Kzo—eﬁoo vx(speed)= ( aﬁvm\ {7 W 00 we orch—agﬂc 96mm ‘ILCA. (31%: V'._ ’M‘ (M Zﬁbm (1) I’ve redrawn the 1—D velocity distribution below in units of (kT/m)1/2. Place your values of v: , H X (4 pts.) (Wail E ) l a 4’» —— 1/2 __ (v2) , and Vx (speed) on the graph. I have only drawn the graph for the +VX values for simplicity. o 0.5 1.0 1.5 vx, (kT/m)“2 2. When we have collections of atoms or molecules in ﬂasks at T > 0 they collide with each other. (a) Write the expression for the average collision frequency of an atom in a ﬂask with 11 total atoms. (It is intuitive.) Deﬁne all terms. (5 pts.), ‘ u. (b) On average the atom will travel the “mean free pat” 9t before colliding. Write an expression ‘ for 9» and deﬁne all terms. (5 pts.) 4. Consider the Classical Equipartition Theorem. (a) Give a working deﬁnition of it. (5 pts.) \ F/njum W~ ‘, ‘ ﬂaw, . , at; w. ch‘ - (“I (a e MWMWM) W (AF/2.59 Mﬂé/WW Wm%a,gwﬁzm¢ - (b) Electronic energy is usually ignored in this theorem. Why? When should it not be ignored? ‘ (W h W4 g) ‘ {w a we! C%Mw ' W2 56 (c) What is Wéegﬁtgﬁﬁer molecule according to the Equipartition Theorem in the high-temperature limit? (5 pts.) Ema = [a 5/9)” +%/2(LT+-23lﬂ— (d) What are the rotational symmetry numbers for the following molecules? (C3H3 is a planar equilateral triangle) (6 pts.) ' 2%? FL o(O-H)= [‘ " “ QH— L I: o 1 v 4—» Waltz Ma 1 WA” _ w 5. Consider an atom with two low-lying electronic energy levels. Q El>g1:3 60, g0 =1 with A6 261—60 = 100 cm—1. (a) Write an expression for the electronic partition function for this system (don’t substitute numbers). (5 pts.) mm 60: 0‘ (ski/“ﬂea”? (b) Write an expression for the probability the system is in el (don’tsubstitute numbers)? (5 pts.) (0) Evaluate P1 at temperature T = 0 K and T = 300 K. (5 pts.) -/ i : DJG‘A’OW" (d) Plot P1 vs. T below. The dotted line is P1(max). Evaluate P1(max). (6 pts.) 0 ~ 300 .g _ [600 T(K) P1(max)= 73/” ‘ -:. 3 x! 7‘- ‘7 ‘ a3?" ( ‘ P! M (e) At what temperature will P0 = P1? (6 pts.) w (3MP, poiuawr Loo ' a, 0.59rr V. I #0 pp) OJ“: 3 6 ’Q) (DJ‘TMW-e) ‘3 3’6 ~lw __...- ( +5e aw“ J”%rmr I. 00 L W n , = 013’ '72 ‘“ I '1 [m .460 ' 7‘: ~ ‘ 4 . A ~— 130. v 0.693M43) 74’ K (t) Obtain an expression for ~the average energy E in termsof El and T (do not put in numbers). (p (yam) ...
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Midterm 1 solutions - Instructor Bowers Course Chem 113C 1...

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