090116_Lecture3

090116_Lecture3 - Physical Chemistry I for Biochemists Chem340 Lecture 3 Yoshitaka Ishii Note Slides in p1-6 are the same as those in lecture 2 So

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1 Physical Chemistry I for Biochemists Chem340 Lecture 3 (1/16/09) Yoshitaka Ishii Note: Slides in p1-6 are the same as those in lecture 2 So print out the rest if you want to save papers Non-Ideal Gas (Ch 1 & Raff p21-41) Kinetic Theory of Gas Problems van der Waals Equation for CO 2 0 100 200 300 400 500 600 700 0 0.1 0.2 0.3 0.4 0.5 0.6 Vm (Lmol-1) P (bar) P (bar) (ideal gas at 300K) P (CO2) at 290K P (CO2) 304.3K P (CO2) 315K P (CO2) 350K a = 3.658 L 2 bar mol -2 b = 0.04286 Lmol -1 b V RT P m = 2 m V a
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2 van der Waals Equation for CO 2 0 20 40 60 80 100 120 140 0 0.1 0.2 0.3 0.4 0.5 0.6 V (Lmol-1) P (bar) P (bar) (ideal gas at 300K) P (CO2) at 290K P (CO2) 304.3K P (CO2) 315K P (CO2) 350K Critical temp obtained from dP/dV m = 0 and d 2 P/dV m 2 =0 Well reproduces the experimental curves above T c ! Maxwell construction reproduces G-L transition Isothermal P-V Plots for Real Gas (CO 2 ) Condensation from gas to liquid below Tc 50 ° C 40 ° C 31.4 ° C (Tc) 20 ° C 0 ° C Liquid CO 2 Raff (p21-41) x Tc: Critical temperature X denotes inflection point in isotherm (dP/dV = 0, d 2 P/dV 2 =0) P & V at this point are named Pc and Vc.
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3 The meaning of a? a defines attractive force between gas molecules Æ If a is high, melting point is also high. Maxwell Reconstruction Correct the oscillatory behavior of vdW eq. to reproduce a transition from gas to liquid
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4 Calculate T c from Van der Waals Eq. 2 m m V a b V RT P = () 0 2 3 2 = + = m m c m V a b V RT V P 0 6 2 4 3 2 2 = = m m c m V a b V RT V P At T c, the following relationships are expected. Æ 3 2 2 mC mC C V a b V RT = 3 4 2 6 b V RT V a mC C mC = Æ V m c = 3 b , T c = 8 a /(27 b R), P c = a /27 b 2 8 3 / c mc c RT V P = b V V mC mC = 4 6 Calculated critical constants Experimental Tc (K) Ar 150.8 K CO 2 304.1 K Ne 44.4 K
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5 Sample question • If you compare the density of gas at critical point, with that of an ideal gas, which one has a lower density? • What is the ratio of the densities of the gas in the two states (ideal gas state and gas at the critical state) at the same temperature and pressure? c c c m P RT V 8 3 / = P RT V ideal m / _ = VdW Eq for Reduced Parameters • When P R P/P c ,V mR V m /V mc , T R =T/T C 2 3 3 1 3 8 mR mR R R V V T P = ) / (
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6 Summary: van der Waals Equation of State 2 2 2 m m V a b V RT V a n nb V nRT P = = V/n >> b, (a) 1/2 Æ The Equation approaches the ideal gas eq.
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This note was uploaded on 10/11/2009 for the course CHEM 340 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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090116_Lecture3 - Physical Chemistry I for Biochemists Chem340 Lecture 3 Yoshitaka Ishii Note Slides in p1-6 are the same as those in lecture 2 So

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