Lecture 6 - Chem 338 Lecture 6 Molecular Partition...

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Chem 338 C h em 3 3 8 L e c t u r e 6 Molecular Partition Functions: Translation & Rotation 1. Total: a. Molar Partition Function: b. q molecular = q trans q rot q vib q elec 2. Translation: a. Quantum b. Classical 3. Rotation: 32 2 2 / B tran Mk T h qV π ⎡⎤ = ⎢⎥ ⎣⎦ [] (,) ! A N A qV T Q N = () 22 2 2 1 4 / B rot IkT h q σ =
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Chem 338 The Translational Partition Function for one atom of a Monatomic Ideal Gas is [2 π mk B T / h 2 ] 3/2 V
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Chem 338 ?
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Chem 338 2 222 2 4 8 xyz n n nnn n g π =++ = 2 2 2 1 8 exp trans n n h qg n ma β = =− 2 1 2 22 2 1 0 44 88 trans n n n n n nn n d n e α ππ = = ⎡⎤ ⎣⎦ to evaluate the integral, we first return to: and now integrate in “spherical coordinates” based on the total energy. Let: Let: = h 2 /8 ma 2
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Chem 338 ] 2 2 2 2 0 00 0 22 0 0 2 4 4 4 8 44 d trans trans n n du n dn v dn n uv n qn d n v d u u v u d v n nn qd n e e e ee π α ππ αα ∞∞ =− == ≈= = −−
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This note was uploaded on 06/28/2010 for the course CHEM 338 taught by Professor Petersson during the Spring '10 term at Wesleyan.

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Lecture 6 - Chem 338 Lecture 6 Molecular Partition...

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