PS 10 - C 2 + k q 1 m O-q 2 m C q 3 m O-q 2 m C (1) Where...

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Chemistry 120A Problem Set 10 (due May 7 th , 2010) 1. Problems 13-14 and 13-20 in McQuarrie and Simon 2. Problems 14-4, 14-5 and 14-37 in McQuarrie and Simon 3. This question concerns the vibrational spectra of water, H 2 O. (a) Which of the three normal modes shown in figure 1 are IR active? Which are Raman active? (b) Experimentally it is seen that water has a very strong absorption in the IR. On the other hand, the Raman spectrum is so weak as to make Raman a very appealing tool for investigating biological systems. Explain these two observations using your results from (a) and your knowledge about IR and Raman spectroscopy. (c) While on the subject of water, explain why H 2 O is blue and D 2 O is colorless. (a) Bend, 1595 cm -1 (b) Sym Stretch, 3657 cm -1 (c) Asym Stretch, 3756 cm -1 Figure 1: Normal modes of vibration for gaseous water. 4. Normal Modes of CO 2 . In order to make this question tractable we will focus only on the stretching modes. For this system the appropriate potential energy is, V ( q 1 ,q 2 ,q 3 ) = 1 2 k ± q 1 m O - q 2 m C ² 2 + 1 2 k ± q 3 m O - q 2 m
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Unformatted text preview: C 2 + k q 1 m O-q 2 m C q 3 m O-q 2 m C (1) Where the q i are the mass weighted coordinates of the atoms. Note that because we are working in only one dimension there is only one coordinate per atom. 1 (a) Find the normal modes (coordinates) of this system and express the associated frequencies in terms of k , m C and m O . (b) If you did part (a) correctly you shouldve found that there are two stretching modes and one translational coordinate (i.e. all the atoms moving in the same direction at the same speed). Knowing that the asymmetric stretching mode has a frequency of 2396 cm-1 and that the symmetric stretching mode has a frequency of 1354 cm-1 estimate the values of the force constants k and k . Make a plot of V using these values. 5. NMR Spectroscopy (a) What is T 1 ? What eect does it have on the spectrum? (b) What is T 2 ? What eect does it have on the spectrum? (c) Can T 1 < T 2 ? Why or why not? 2...
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PS 10 - C 2 + k q 1 m O-q 2 m C q 3 m O-q 2 m C (1) Where...

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