chem 09 - Problem#1 Chemical Kinetics(20 points total(a[10...

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Unformatted text preview: Problem #1 Chemical Kinetics (20 points total) (a) [10 points] Suppose that two, continuously—operating molecular beams, one of reactant molecule, A, and the other of reactant molecule, B, cross at 90° in a high vacuum chamber to yield product molecules, C and D. How many total product molecules are produced per second? You will find the following information useful in solving this problem. Each reactant beam is traveling at a velocity of 100 m/sec. The intensity of each beam is 1017 molecules/cruised The interaction volume where the two beams overlap can be approximated as a cube, 0.1 cm on each side. The reactive cross section for the reaction, A + B 9 C + D is 100 A2. Recall that intensity is equal to number density times velocity. Show all of your work in detail. If square roots appear in this problem, you do not need to evaluate them. Just leave them as ( )1’ 2 or as W. I suggest that you do everything in units of cm and sec., but it’s up to you. ' (1/3 = 10’8 cm) ' W 3 mA-mg'mwtfi' A 5" W"; 0095-00? 3 Vida}: I/Z'Xm .3; I? 13 10 / -I- mum/fl flaws/V132} ~ g a a. “33 4942‘ J9) my: “thaw/0.. MXMZXMEXZDamxy/o (um cam") ‘13: f g . Problem 1 (continued) 4g fwt g4 +752 m # [ 10 points] (b) Write down the Lindemann mechanism'for “unimolecular” decomposition. Use the steady—state approximation and this mechanism to determine its differential rate law. Show that it appears to be first order at high pressure and second order at low pressure. M24" A715“ . Problem #2 Nuclear Chemistry (15 pts.) K b / Radioactivity is often used in medicine as an diagnostic tool. Several of the methods used to observe metabolic changes in real time involve injecting a radioisotope of the chemically relevant isotope (so it goes to the intended organ) into the patient and scanning the patient’s body with an appropriate high resolution radiation detector. There is a particular method in which the radioisotopes to be injected are prepared just before the procedure by proton bombardment in a cyclotron. This produces a rather short-lived radioisotope, having the advantage that the patient is exposed to radiation for only a short period of time. Now, my question to you is: Using the above method, what type of radiation does the radiologist actually detect during the scan? Explain why. (The primary nuclear decay process, when the radioisotope is first made in the cyclotron, is not electron capture.) Indicate your reasoning in detail. 1 Ni/ Problem #3 Hydrogen atom and the photoelectric effect (15 points) The n = 1 level of the hydrogen atom sits 13.6 eV bel 'ts ionization ons (a n = infinity). That is the ionization energy of the hydrogen atom. W M “’1‘- Imagine shining 15. eV photons on a collection f highly e cited (but not ionized) hydrogen atoms and measuring the resulting electron kine c ener spectrum. What will this spectrum look like? That is, sketch the first three lowest electron kinetic energy peaks of this spectrum quantitatively, labeling the electron kinetic energy value of each peak. When numbers are fractions, you can leave them as such while labeling the spectrum. You don’t have to actually do the arithmetic, but you do have to set—up numerical expressions for the electron kinetic energy of each peak, and you do have to make a reasonable to—scale sketch of the spectrum. 4&5] W W Problem #4 W Field Theory & Periodic Properties of Transition Metals (15 points) 72.5 Consider the coordination complex, [Mn(CN)6]3‘. Use Wield theory to draw out the d orbital splittings. What symmetry does this complex adopt? Label each d orbital correctly, eg., dxy. Label the crystal field splitting parameter, A0 and the fractional Ao’s for the eg and t2g sets of orbitals. Draw in the electron occupancies for the low spin case. Is this complex paramagnetic? .. 3 1“ M» = [M MW 9 ‘96 [fit/173W); W W MNM/samfle fgmrmmwfié W A Mdé’f 911,3, fl/w Problem #5 Energetics (15 points) Typically, ionization potentials ([P), electron affinities (EA), and bond dissociation energies (Do) for atoms and small molecules, as appropriate, are tabulated in the chemical literature. Write an equation for the energy, E, needed to make the process written below occur. Suggestion on symbols; to indicate the [P of Br, for example, write IP(Br). E K + BrC1-—9 K+ + Cl" + Br +IPCK) KW”? W imo( We€+ By M Mi} Problem #6 Molecular Orbital Theory and VSEPR Theory (20 points) (a) [10 points] Draw and label the molecular orbital correlation diagram for the dianion, B24. Is this ion diamagnetic? What is its bond order? (b) [10 points] Using VSEPR theory, predict the structure of Krlz. Indicate you‘i" reasoning in detail. End of exam. ...
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