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hw_5 - process C H 2> CH 2 h ν Use the quantum RRK...

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C/P/A 740 Winter Quarter 2008 Dr. Herbst HOMEWORK ASSIGNMENT # 5 Due: Tuesday, 26 February 1. Use the steady-state method to derive the rate law for three-body association. Label the reactants A + and B, with the bath gas C. Label the rate coefficients k 1 , k -1 , and k 2 . Find the limiting laws at both high C density and low C density. 2. Now consider a system in which both three-body and radiative association occur. Obtain the effective two-body rate coefficient, defined by the relation d [ AB + ] dt = k eff [ A + ][ B ] and sketch its logarithm as a function of the logarithm of the bath gas density [C] from both the high density limit to the low density limit. Identify three regimes. You may assume that k -1 >> k r . 3. Estimate the radiative association rate coefficient at low temperature for the following
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Unformatted text preview: process: C + + H 2--> CH 2 + + h ν Use the quantum RRK approach. For this reaction, the radiative stabilization step is rather fast: k r = 10 6 s-1 . The bond energy is about 4.3 eV (1 eV of energy corresponds to 8065 cm-1 after division by hc) , and the average frequency of the complex is 2000 cm-1 (s=3). 4. Assuming that H atoms do not react on grain surfaces, calculate the average number of H atoms per grain at steady state in a dense cloud at 10 K and at 20 K by considering accretion and thermal desorption processes. You may assume that the gas-phase H atom concentration is 1 cm-3 . What does your answer say about the possible efficiency of H 2 formation at the two temperatures? Use the silicate binding energy E D /k = 373 K....
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