lecture12 (10-27-2006) Ch 6

lecture12 (10-27-2006) Ch 6 - Chemistry 2A-c F2006...

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Chemistry 2A Chemistry 2A -c F2006 c F2006 (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: point-mass approximation. 3. Molecule-wall collisions are elastic (no loss in kinetic energy). 5. The average kinetic energy of gaseous molecules is proportional to the temp. (in K). (To be derived later) 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 F2006 c F2006 (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 [Here, use R= 8.314 J/mol-K] 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 F2006 c F2006 (Ch6 (Ch6 -25)96 25)96 Example: The speed of eight particles were found to be 1.0, 4.0, 6.0, 6.0, 6.0, 8.0, 8.0, and 10 m/s. Calculate their average speed <u>, rms speed (u rms ), and the most probable speed (u mp ). Solution: (a) <u>= (1.0+4.0+6.0+6.0+6.0+8.0+8.0+10)/8 m/s = 5.6 m/s (b) u rms =[(1.0 2 +4.0 2 +6.0 2 +6.0 2 +6.0 2 +8.0 2 +8.0 2 +10 2 )1/2]/8 m/s = 6.2 m/s (c) u mp = 6.0 m/s (occurs three times) Calculate these values
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Chemistry 2A Chemistry 2A -c F2006 c F2006 (Ch6 (Ch6 -14)85 14)85 Fraction of molecules
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Chemistry 2A Chemistry 2A -c F2006 c F2006 (Ch6 (Ch6 -15)86 15)86 Diffusion: Effusion:
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This note was uploaded on 04/23/2008 for the course CHEM 2A taught by Professor Guo during the Fall '08 term at UC Davis.

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lecture12 (10-27-2006) Ch 6 - Chemistry 2A-c F2006...

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