17_562ln08

17_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62...

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MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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2 5.62 Lecture #17: Chemical Equilibrium. II. Examples Readings: Hill, pp. 182-187 Maczek, pp. 83-92 Metiu, pp. 191-196 Dissociation of a Diatomic Molecule AB A + B p °)( p B p °) K p = (q * A / N)(q * B / N) e + Δ D 0 0 RT [unitless] = ( p A (q * AB / ( p AB p °) K p = ( q trans,B N )( q trans,A N ) g 0,B g 0,A q rot,B q rot,A q * vib,B q * vib,A e + Δ D 0 0 RT ( q trans,AB N ) g 0,AB q rot,AB q * vib,AB K p = (2 π m B ) 3/2 (kT) 5/2 (2 π m A ) 3/2 (kT) h 3 p h 3 p h 3 p (2 π m AB ) 3/2 (kT) g 0,B g 0,A 1 1 σθ rot,AB ( g 0,AB T 1 1 1 e −θ vib,AB T ) e + Δ D 0 0 RT × p is in units of bar because the standard state p° = 1 bar = 10 5 pascal. But all terms in statistical mechanical expression for K p are evaluated in S. I. units. Be careful! (2 π µ ) 3/2 (kT) 5/2 g 0,B g 0,A σθ rot ( 1 e vib T ) e + Δ D 0 0 RT K p = h 3 p g 0,AB T where µ = m A m B = m A m B reduced mass m A + m B m AB kg/molecule for SI 2 I 2 2I K p = p I [ p’s in bar ] p I 2 m I = 0.1269 kg mol –1 µ I 2 = 0.06345 kg mol 1 g 0 , I = 4 g 0 , I 2 = 1 σ I 2 = 2 ω e = 214.5 cm –1 θ vib = 308.6K B e = 0.03737 cm –1 θ rot = 0.05377K
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5.62 Spring 2008 Lecture #17, Page 2 D 0 0 ,I 2 = 12440cm –1 = 17889K ( determined by laser spectroscopy! ) [ Be careful about units here! ] Δ D 0 0 = p ( D 0 0 ) − ∑ r ( D 0 0 ) = 0 (17889K) = 17889K p r σ θ rot K p = ( 2 π 0.0634 6·10 23 ) 3/2 ( kT ) 5/2 4·4 2·0.0537 ( 1 e 308.6 ) e 17889 T h 3 ·10 5 1 T 1 bar = 10 5 pascal. 1 pascal = 1N/m 2 . 1N = 1kg m s –2 ) (16) 0.1074 ( 1 e 308.6/T ) e 17889/T K p = ( 13.115 T 5/2 T K p = 22.537 T 3/2 ( 1 e 308.6/T ) e 17889/T T[K] K p (calc) K p (expt) % error 1274 0.1761 0.170±0.001 3% 1173 4.9999 10 –2 (4.68±0.03) 10 –2 2.6% 1073 1.14 10 –2 1.10 10 –2 3% 973 1.93 10 –3 1.82 10 –3 5.4% 872 2.13 10 –4 (1.84±0.17) 10 –4 –14% probably more accurate M. J. Perlman and G. K.
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17_562ln08 - MIT OpenCourseWare http/ocw.mit.edu 5.62...

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