Chem 4A - Fall 2006 - Head-Gordon - Midterm 2

# Chem 4A - Fall 2006 - Head-Gordon - Midterm 2 - WE Midterm...

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Unformatted text preview: WE Midterm Exam 2, October 20, 2006. Prof. Head-Gordon, Prof. Moretto m QMDIW KEY TA: Grade: 1. (8 points) 2. (5 points) 3. (6 points) 4. (6 points) Total: 1L Closed book exam. There are 6 pages. Calculators are OK. Set brains to wavelength for stimulated emission of knowledge and go! Use back side of pages for scribble paper Some possibly useful facts and ﬁgu_res: R = 8.3145 J mot1 K“ h = 6.6261x 10‘34 J s c = 2.9979 x 108 m 9;1 me = 9.1094 x 10'31 kg N0 = 6.0221 x 10” mol‘1 Some possibly relevant equations: Planck relation: kinetic energy diatomic rotational energies moment of inertia reduced mass of a diatomic harmonic oscillator frequency molar volume at STP = 22.4 L h=hl27t k3 = 1.38066 x 10'23 J K'1 latm = 101325 Pa E=hV _1 hz E =—J(J+l) J 87:21 I=,ur2 u: "W2 "11+m2 l k v:-—— — degeneracy gJ=2J+1 1. (8 points) Molecular orbitals for the electrons in thioformaldehyde, H2C=S. (a) (2 points) Predict the geometry of the molecule using the VSEPR method. What kind of hybrid orbitals will you use on the C (Z=6) and S (Z=16) atoms to most conveniently predict the molecular orbitals? (b) (2 points) Sketch the shape (boundary surface) of the 4 molecular orbitals ((5 and 6*) that describe interactions between C and the 2 H atoms. Also draw an energy level diagram showing the A0 and MO energies, and which MO’s are occupied. lsH ——~ I“\ 1P? ~~(SPL) C it o" (H’s OK 41) l m w.--) are at .— @ e o (c) (2 points) Sketch the shape (boundary surface) of the 4 (G and 6*) molecular orbitals that describe 6 interactions between C and S (don’t forget lone pairsl). Also draw an energy level diagram showing the A0 and MO energies, and which MO’s are occupied. l \1 a @o 89 a)“ 6:; C \ aat:-,\-.————.S (d) (2 points) Sketch the shape (boundary surface) of the TC and 712* molecular orbitals that describe 1t interactions between C and S. Also draw an energy level diagram showing the A0 and MO energies, and which MO’s are occupied. ,/ a\\ Q 9 S “VG--’- S KIT TF4: _.\ T" c 4‘ S *H: ‘IT (5 points) It is found that the rotational transition from J=O to J=1 of the NaH molecule occurs at a frequency of 2.94><1011 Hz. (a) (1 point) Predict the frequency of the J=2 to J=3 transition for the NaH molecule. V233: [034181682 :91) =3v 1’3 0—91 to». [2—01 w 28 u: (b) (2 points) From the observed frequency, what is the moment of inertia, I, for the NaH molecule? Be sure to include its units. 7) 0—51— _ / (3—31 = k3 mlst1 = karma» (c) (1 point) Given that the reduced mass of NaH is 1.603><10‘27 kg, what is the bond length of the NaH molecule? I=FR1 an" E = l‘887xlO—‘Om (V88? R) (d) (1 point) Explain why you would expect the rotational spectrum of H2 to be either more intense or less intense than the rotational spectrum of NaH. “2 i104) NaH has 0. Siva? W ramped N1 grmcl-rwW-l-o LLMMQ‘LQA/ 3. (6 points) Suppose absorption of IR radiation of wavelength 3><10‘6 m excites the Vibration of an OH group, such as in alcohols or water, with reduced mass 1.574 x 10'27 kg. (a) (2 points) What is the force constant for this vibration? Give its units. v: (3/, :7 h: M X" ,, \ _ MW ~ 0’ =>k=4205 Nm' (ark?) M// S the OH stretch, explaining your logic fully. The atomic masses of O, H and D are 15.9949 amu, 1.0078 amu and 2.0141 amu respectively, 13.0.13 = HMO“ :23 ﬂ 2: .1... you ﬂop MD \[E La. “(La OD Si—r‘ci’clm mu L2. M 70070 cé "he, %tL/. OH sink/k-.- (c) (2 points) If the OH bond participates in a hydrogen bond With the lone pair of another oxygen atom (ie. OH----O), draw a donor-acceptor type orbital interaction diagram and suggest how the OH vibrational frequency will be affected. 5);; ‘-'."»\’/~.\> CIOWOY mixes OH \ 4. (6 points) Aluminum metal (m=26.9815 amu) reacts with excess aqueous hydrochloric acid (HCl) to produce hydrogen gas and water-soluble aluminum chloride (AlCl3). (a) (1 point) Write a balanced chemical equation for this reaction. QAQCS) + Aug“? _..> ZAQCQBw-D; 3H; (5) (b) (2 points) What mass of aluminum is necessary to produce 5 L of hydrogen gas at a pressure of 1 atm and a temperature of 300°C? n = BY. = 0.20! We Hz _ 1 mm - 3W1: 0434 rude. :> mug: nMMAL ‘- 3'42 3 (c) (1 point) Suppose the SL of gas was forced into a 1L container, which was cooled to 0°C. What would be the pressure inside the container be (in atm)? P\/ =ﬂlZT ,. 2) P.\/\ __ l3va PL: loc’lM) VL: S L) TL: 303 K >Tl T), VIZlL‘) TzQVBK PleT 1“ 5 x ° l 2.. (d) (2 points) Given that the average energy per molecule in the kinetic theory is 3kBT/2, obtain an expression for the root mean square speed, and use this to ﬁnd the root mean square speed of the molecules inside the 0°C container. E 2 3:3? .. 3|;sz ——3 :> V = 3kBT mu _ 2" lg:_§?§"'0 kg m 1 4,0221th @MM = 3:342xlo‘1 Lg ...
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## Chem 4A - Fall 2006 - Head-Gordon - Midterm 2 - WE Midterm...

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