Chemistry 21b Final Examination

Transcription

1 Chemistry 21b Final Examination Out: 11 March 2011 Due: 16 March 2011, 5 pm This is an open book examination, and so you may use McQuarrie or Harris and Bertolucci along with the posted Lecture Notes and Problem Sets (with Solutions). Use of a calculator or packages such as Mathematica is also permitted, but the final is closed-web (use of the class web site is fine, to access Lecture notes, Solution Sets, etc.). 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 allocated; 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=15 2=20 (10 for a,b) 3=30 (spread over a-g) 4=15 5=20 (10 for a, 5 each for b,c) 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 if you use loose note paper. Good luck!

2 1. Use group theoretical arguments to answer the following. You can be brief! a). Imagine a perfect surface of a transparent dielectric solid in the (x,y) plane, with the space-fixed z-axis being normal to the surface. Suppose we trap water molecules on this surface so that they are not free to rotate, and further that they are oriented perpendicular to it. If you try to take the vibrational spectrum of these adsorbed molecules, what polarizations of the applied E&M field are needed to detect the three fundamental vibrations and their overtones and combination bands? Figure 14.3 will be helpful here! b). 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? 2. The following spectroscopic constants were determined for the 63 Cu 2 B 1 Σ + X 1 Σ + transition: T e = 21, cm 1... ω e = cm 1 ω e = cm 1 = cm 1 B e = cm 1 B e = cm 1 α e = cm 1 α e = cm 1 ω e x e = cm 1 ω e x e a). Is the 1-0 band degraded to longer or shorter wavelengths? At what J and wavenumber will the 1-0 bandhead occur? b). It can be shown for a Morse potential that the quantitative value of the Franck-Condon factor for the v = 0 v = 0 transition when the upper and lower state have the same force constant is S(0, 0) 2 = e α2 ( R) 2 /2, where R is the change in bond length between the two states and α 2 = kµ/ h 2 (and where k is the force constant of the potential energy curve and µ is the reduced mass). For the 63 Cu 2 B 1 Σ + X 1 Σ + transition, what is S(0, 0) 2 if we assume the force constant is given by that for the X 1 Σ + state? Given your calculated value, do you expect the Franck-Condon progression to be long or short?

3 3. This is a suite of combined IR/NMR spectroscopy problems. 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 4. The following table gives the fundamentals and combination bands in the infrared spectrum of acetylene. The fundamental vibrations are very strong (vs), while combination bands involving only two fundamentals are of medium intensity (m). All other bands are weak (w). In this slightly idealized version of the spectrum, anharmonicity effects can be neglected and the frequency ordering is given by ν 4 <ν 5 <ν 2 <ν 3 <ν 1. Determine the frequencies of the fundamentals and assign the combination bands. Why do only some of the fundamental bands appear in the IR spectrum, and how could you measure those that are electric dipole forbidden? Band Frequency (cm 1 ) Intensity vs m w m vs w m m m m 5. Purely hydrogen-containing compounds have been central to many developments in chemistry and chemical bonding. The polyatomic ion H + 3 was discovered by J.J. Thompson in 1912, and the species H 3 is an important intermediate in the reaction H 2 + H H 3 H + H 2 What we are interested here is whether H 3 is linear, or cyclic. a). Use the Hückel approach, but with 1s instead of 2p orbitals, to calculate the molecular orbitals for linear and cyclic H 3. Set up the appropriate determinants, and solve them if you like or use the appropriate equations in Harris and Bertolucci (cite them in your work) to derive the MO energies. The values of α and β will be quite different from the π-calculations considered in the Lectures, but the mathematics are the same. Is H 3 linear or cyclic? b). For the two forms, how do the energies of H 3 compare to H 2 +H? c). What does Hückel theory say about linear versus cyclic forms of H + 3 and H 3?