Chemistry 21b Final Examination

Transcription

1 Chemistry 21b Final Examination Out: 12 March 2018 Due: 16 March 2018, 2 pm This is an open book examination, and so you may use the PDF d versions of Atkins and Friedman, Harris and Bertolucci, and/or Maczek along with the posted Lecture Notes and Problem Sets (with Solutions). Use of a calculator or packages such as Mathematica is also permitted. The exam must be done in one continuous sitting of three hours. I believe you should be able to complete the exam in the time allotted; but if not, please draw a line across where the time limit is reached and continue if you wish to. The TAs will record the grades for points awarded within the time allocated and that after. The problems are worth: 1=20 (10 for a, 10 for b) 2=30 (spread over a-g) 3=50 (10 each for a,b, 15 for c, d) To facilitate the grading of the exam, please begin the solution of each problem on a new sheet, and remember to sign your name on every page of your solutions. Good luck!

2 1. Use group theoretical arguments to answer the following. You can be brief! a). Assess the polarization of the 1 A 2 1 A 1 transition in H 2 CO and the 1 B 2u 1 A g transition in ethylene (CH 2 =CH 2 ), including vibrational coupling if necessary. Is the latter transition electric dipole allowed? b). Below the normal modes of vibration of the diborane molecule are shown. What is the point group for this molecule? From the symmetries listed, which modes are IR active, which are Raman active, and why is there no overlap between these two lists?

3 2. This is a suite of combined IR/NMR spectroscopy problems, with UV/Vis results added for some. From the spectra and information below, derive the molecular structure. Explain your reasoning. a). The compound whose IR and NMR spectra are shown below has a parent ion peak at 102 amu and a strong fragment at 57 amu. There is no UV absorption above 205 nm.

4 b). The mass spectrum of this compound shows an intense molecular ion peak at 172 amu and an M +2 peak of approximately the same size. The largest fragment ion appears at 65 amu. The IR spectrum of this solid compound was obtained by casting a film on salt plates from a CCl 4 solution. What is the structure of this compound?

5 c). The local anesthetic benzocaine has the formula C 9 H 11 NO 2. From the spectra below, determine the structure.

6 d). The mass of this compound, a neat liquid, is 86 amu, and it has a near UV absorption band at 280 nm in 95% ethanol. From the spectra below, determine the structure.

7 e). The UV spectrum of this molecule shows no maximum longward of 205 nm, and the IR spectrum was obtained on a neat liquid. What is the structure of this compound? (Hint: The single NMR peak with integral = 3 actually arises from two functional groups that participate in hydrogen bonds hence the peaks are averaged on the timescale of the NMR measurement and no spin-spin splitting occurs.)

8 f). The chemical formula of this molecule is C 6 H 12 O 2, and in the NMR spectrum below the peaks near δ=3.9 and 0.8 are triplets, that near 1.9 is a singlet. The relative integrated areas from high to low chemical shift are 2, 3, 2, 2, 3.

9 g). Last, but not least, the two NMR peaks below are the only ones seen in this molecule with chemical formula C 5 H 8 O. The integrated areas of the two NMR features are equal.

10 3. A selection of statistical thermodynamics questions: a). From group theoretical arguments, what is the symmetry number σ that must be used in the canonical rotational partition function for: 1 = trans-dibromoethylene (HBrC=CBrH), 2 = Deuterated methane (CH 3 D), 3 = Sulfur hexafluoride (SF 6, all bond lengths equal), 4 = Allene (C 3 H 4, carbon atoms linear), 5 = Phosphorous pentafluoride (PF 5, trigonal bipyramidal structure), 6=silane (SiH 4 ), and 7=Pt(CN) 4 (planar)? b). For a crystal with a sublimation energy U 0 and considered to consist of a 3D suite of coupled harmonic oscillators, it can be shown that the approximate partition function (that is, the Q that ignores anharmonicity) can be expressed as Q = ( e hν/2kt 1 e hν/kt ) 3N e U 0/kT, where hν/k Θ E is a constant characteristic of the crystal (the Einstein temperature, specifically). Calculate the heat capacity from this simple partition function and show that at high temperatures one obtains the law of Dulong and Petit, namely, that C V 3Nk. c). An approximate canonical partition function for a dense gas is of the form Q(N,V,T) = 1 N! ( ) 3N/2 2πmkT (V Nb) N e an2 /VkT, h 2 where a and b are constants that are given in terms of molecular parameters. Derive the equation of state from this partition function along with the thermodynamic energy and heat capacity. How do these equations compare to what we learned about ideal gases in class (think about the dilute limit, or N/V 0)? And, hopefully the equation of state looks familiar to you. What, qualitatively, is the physical origin of the constants a and b? d). Finally, consider a paramagnetic crystal of spin-1/2 spins, where the interactions between the spins can be neglected. If a magnetic field B is applied, the spin energies therefore become ±µb, where µ is the magnetic dipole moment of the spins. What is the partition function for a mole of such spins, in the presence of a magnetic field? From this, determine the molar entropy of the crystal (the hint here is that the derivative of ln[cosh(ax)] is a[tanh(ax)], where 2cosh(ax) = (e ax + e ax ) is the hyperbolic cosine). What are the low temperature (that is, T 0) limits of S in the presence and absence of a magnetic field, and how can these limits be explained given the statistical thermodynamic interpretation of the Third Law? If such a crystal is cooled to a temperature T i in the presence of a magnetic field B i, thermally isolated, and the field changed to B f in a reversible fashion, the entropy remains constant. In this event, there is a very simple prediction for the final spin temperature in terms of T i, B i and B f. What isit? Thisapproach isused experimentally tocool paramagnetic solids to very low temperatures.