Lecture #12&13

Lecture #12&13 - Chemistry 2A-c W2009 (Ch6-12)83 V....

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Chemistry 2A Chemistry 2A -c W2009 c W2009 (Ch6 (Ch6 -12)83 12)83 V. Simple Kinetic Molecular Model of Gases 1. Molecules move randomly (in straight-line) until hitting the wall of the container. 2. Volume of molecules are negligible (occupy no volume): point-mass approximation. 3. Molecule-molecule and molecule-wall collisions are elastic (no loss in kinetic energy). 4. No attractive forces exist between molecules. 5. The average kinetic energy of gaseous molecules is proportional to the temp. (in K). Kinetic energy: KE =(1/2)mu 2 The average kinetic energy (<KE>): <KE> =(1/2)m<u 2 > (per molecule) = (1/2)M<u 2 > (per mol) Here M is the molecular weight, <u 2 > is the average of u 2 , and u is the velocity of the gaseous molecules
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Chemistry 2A Chemistry 2A -c W2009 c W2009 (Ch6 (Ch6 -13)84 13)84 Distribution of molecular speed (Maxwell-Boltzmann Distribution of molecular speed) Fraction of molecules u m = most probable speed = (2RT/M) 1/2 u av =average speed = (u 1 + u 2 + u 3 +…)/N= (8RT/ π M) 1/2 u rms = root-mean-square = <u 2 >= = (3RT/M) 1/2 u m < u av av < u rms For a given T N u u u / ...) ( 2 3 2 2 2 1 + + +
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Chemistry 2A Chemistry 2A -c W2009 c W2009 (Ch6 (Ch6 -14)85 14)85 Fraction of molecules
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Chemistry 2A Chemistry 2A -c W2009 c W2009 (Ch6 (Ch6 -15)86 15)86 Diffusion: Effusion:
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Chemistry 2A Chemistry 2A -c W2009 c W2009 (Ch6 (Ch6 -16)87 16)87 VI. Pressure for an ideal gas Force exerted on the wall by one impact: F x = ma x =m( Δ u x / Δ t)= Δ (mu x )/ Δ t =[mu x –(-mu x )]/(2 l /u x ) = (mu x 2 )/ l Let N A = Avogadro’s # of molecules in the box l mu x -mu x x y Pressure (P) = (Total force)/area = [N A (<mu x 2 )/ l> ]/ l 2 = (N A m<u x 2 >/ l 3 = (N
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Lecture #12&amp;amp;13 - Chemistry 2A-c W2009 (Ch6-12)83 V....

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