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# PS_1_Answer_Key_2011 - Massachusetts Institute of...

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Massachusetts Institute of Technology Organic Chemistry 5.12 February 15, 2011 By Hyung Kyoo Kwon, Yu-Pu Wang and Phil Hamzik Solutions to Problem Set #1 (1) For compounds with the molecular formula CH 4 N 2 (a) Calculate the number of valence electrons. (b) Calculate the number of degrees of unsaturation (c) Draw all reasonable Lewis structures, showing lone pair (unshared) electrons and formal charges. (d) Do stereoisomers exist for any of these Lewis structures? For the purposes of this problem, assume that there is no inversion at sp 3 nitrogen atoms. ANSWER: (a) The number of valence electrons can be calculated by summing up the number of valence electrons of each atom (Tools and Techniques #2, Lecture 1): H, 1; C, 4; N, 5; O, 6; halogen, 7. Thus, # valence electrons = 1(4) + 4(1) + 2(5) = 18 valence electrons . (b) The number of degrees of unsaturation (a.k.a. index of hydrogen deficiency; Tools and Techniques #3, Lecture 2) for a molecule containing no hypervalent atoms can be calculated using the following formula: D of U = (2C + N – H + 2) / 2, Where C = number of carbons, N = total number of nitrogens and phosphorus, H = total number of hydrogens and halogens. In this case, D of U = (2(1) + 2 – 4 + 2) / 2 = 1 (c) Since the degree of unsaturation is 1, there must be exactly one double bond or one ring in the molecule (Tools and Techniques #3). In a linear molecule (without rings) there are two possible arrangements of non-hydrogen atoms: C-N-N and N-C-N. Adding hydrogens and a double bond give the following 3 possible reasonable structures (with no formal charges on all atoms): H 3 C N NH H 2 C N NH 2 H 2 N H C NH Next, we can consider cyclic structures. Since D of U = 1, there can only be one ring and no double bonds, so the only reasonable structure is: HN NH H 2 C This material may not be reproduced or posted on an internet website without written permission of Profs Danheiser and Jamison.

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(d) Two of the linear molecules have E / Z stereoisomers (Smith, 10.3), and the cyclic molecule has cis (meso) and trans (2 enantiomeric) isomers: H 3 C N N H H 3 C N N H ( E ) ( Z ) H 2 N C N H H H 2 N C N H H ( E ) ( Z ) N N H H N N H H N N H H cis trans (enantiomers) (2) RDX ("cyclonite") is a powerful high explosive that was used extensively in World War 2. Today it is widely used as the main component of plastic explosives such as C-4 and Semtex. Professor John Sheehan of MIT (who we previously mentioned in connection with his development of the first synthesis of penicillin) was also involved in the development of the method used to prepare RDX during the Second World War while working in the laboratory of Werner Bachmann. Shown to the right is a representation of the structure of RDX. Calculate the number of valence electrons and then complete this Lewis structure by filling in all of the lone pair electrons and formal charges.
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