5_60_lecture29

5_60_lecture29 - MIT OpenCourseWare http:/ocw.mit.edu 5.60...

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MIT OpenCourseWare http://ocw.mit.edu Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.60 Spring 2008 Lecture #29 page 1 APPLICATIONS: CHEMICAL AND PHASE EQUILIBRIA Apply statistical mechanics to develop microscopic models for problems you’ve treated so far with macroscopic thermodynamics 0 Products Reactants Separated atoms Product & reactant energy levels E ε r = -D 0,r p = -D 0,p Chemical equilibria Gas phase: Calculate Kp from microscopic properties aA + bB F cC + dD Δ G 0 = R T ln K p = c G C 0 + d G D 0 a G A 0 + b G B 0 Need G 0 for each species G = A + V T ln + p V = ln Q + N k Q q N N ( trans ) ln Q N ln q int ) ln ! ln q q ) N ln G kT ln + NkT =− ln ( int ) =− ln ( = N
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5.60 Spring 2008 Lecture #29 page 2 q = qqq int rot vib elec DkT Dissociation energy D 0 from ground electronic level q elec = e 0 Usually no other electronic levels matter = n ε 0 k T = 1 e ε k T 2 0 k ε 0 k T 1 vib + e + e + = ε 0 kT Note we’ve set the zero of vibrational energy as the lowest vibrational level. The zero-point vibrational energy has been included in q elec by using the dissociation energy rather than the bottom of the electronic potential energy. kT (300 K) -1 Most molecular vibrational frequencies > 500 cm -1 q vib 1 - Need to calculate it, but it’s not large We have not treated q rot . Levels are NOT evenly spaced: ε rot = J(J + 1) ε 0, rot where J = 0, 1, 2,…, and ε 0, rot
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

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5_60_lecture29 - MIT OpenCourseWare http:/ocw.mit.edu 5.60...

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