Gas Kinetics

# Gas Kinetics - Real Gases Review Compressibility factor = z...

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GasKinetics 1 Real Gases Review z expanded as a power series on P: ... P ' C P ' B 1 RT V P z 2 + + + = = 2 2 2 T R ) ' C ' B ( C and RT ' B B + = = van der Waals equation of state 2 V a b V RT P = σ , the van der Waals diameter = 3 2 b 3 π 2 b C RT a b B = = RT V P z = = factor ility Compressib ... V C V B 1 RT V P z 2 + + + = = z expanded as a power series on : V 1 intermolecular forces (a) excluded volume (b) bR a T B = Boyle’s temperature

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GasKinetics 2 Dalton’s Law for ideal gases: = = i T i i i T P x P P Critical region and van der Waals parameters: 8 3 z bR 27 a 8 T b 27 a P b 3 V c c 2 c c = = = = T R =2 T R =1.2 T R =1 Law of corresponding states: c R c R P P P T T T = = z P R
GasKinetics 3 TOPICS IN GASES / GAS KINETICS 1. Properties of condensed phases isothermal compressibility , thermal expansion 3. Properties due to the fact that the gas particles are moving. pressure , diffusion , effusion , viscosity , thermal conduction 4. Effects of intermolecular forces. 2. Real gas mixtures

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GasKinetics 4 Real gas mixtures Applying virial equations to a mixture of 2 gases: () 2 2 2 1 2 1 2 2 1 2 2 2 2 1 1 2 1 2 1 2 2 2 2 1 1 2 1 2 2 2 2 1 1 2 1 2 1 2 2 2 2 2 2 1 1 1 1 2 B x B x V 1 1 n n n B n B V 1 1 RT V P ] n n by ator min deno & numerator multiply [ V n n n B n B 1 RT n n PV V n B n B RT RT n n PV P P P Since V n RT B RT n V P : 2 gas For V n RT B RT n V P : 1 gas For V n BRT nRT PV ) terms 2 only ( V 1 BRT RT V P + + = + + + = + + + + = + + + + = = + + = + = + = + = The second virial coefficient is weighed by the square of the mole fraction. The “real” aspect of each gas is represented by B i . The “real” aspect of the mixture will manifest in the total V.
GasKinetics 5 For van der Waals gases : 8 ) b b ( b where x x b 2 b x b x b ) a x a x ( a n n V V 3 3 1 2 3 1 1 12 2 1 12 2 2 2 1 2 1 2 2 1 2 2 2 1 1 1 2 1 + = + + = + = + = Example: 2:1 mixture of H 2 and CO. x 1 and x 2 are the mole fractions na ( L 2 bar/mol 2 )b ( L / m o l ) x H 2 2 0.248 0.027 0.667 CO 1 1.505 0.040 0.333 a= 0.549 L 2 bar/mol 2 b 12 = 0.033 L/mol b= 0.031 L/mol

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GasKinetics 6 The compressibility factor of a 2:1 mixture of H 2 and CO has been measured at 25 o C and 300 bar, z=1.2968. Calculate the volume occupied by 2 moles of H 2 mixed with 1 mole of CO at these conditions using Dalton’s law and van der Waals gases. L 3213 . 0 bar 300 K ) 273 25 ( x mol . K bar . L 08315 . 0 x 2968 . 1 x 3 P znRT V = + = = Experimental volume: Predicted by Dalton’s law and ideal gas law: ) smaller % 22 ( L 2478 . 0 L 2478 . 0 x 3 1 L 2478 . 0 x 3 2 : mean Weighted L 2478 . 0 100 ) 273 25 ( x 08315 . 0 x 1 : alone if V L 2478 . 0 200 ) 273 25 ( x 08315 . 0 x 2 : alone if V bar 100 bar 300 3 1 P bar 200 bar 300 3 2 P CO 2 H CO 2 H = + = + = + = = = = L 2478 . 0 bar 300 K ) 273 25 ( x mol . K . bar . L 08315 . 0 x mol 3 P nRT V or 1 1 T = + = =
GasKinetics 7 Predicted by van der Waals equation, using average a, b and b 12 : 0 0170 . 0 V 549 . 0 V ) 777 . 24 3 . 9 ( V 300 0 ab V a V ) RT bP ( V P V a b V RT P 2 3 2 3 2 = + + = + + = Molar volume = 0.101 L Volume = 3 x 0.101 L = 0.303 L 5% smaller By successive approximations: a= 0.549 L 2 bar/mol 2 b12= 0.033 L/mol b= 0.031 L/mol 300 V^3 - 34.077 V^2 + 0.549 V - 0.0170 = 0 V f(V) 1 266.4550 0.1 -0.0029 0.2 1.1297 0.11 0.0304 0.102 0.0028

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GasKinetics 8 PVT BEHAVIOR IN ANY PHASE V=V(P,T) The (molar) volume of any substance in any phase can be determined given P and T.
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## This note was uploaded on 05/01/2011 for the course CHEM 346 taught by Professor Cardelino during the Spring '11 term at Spelman.

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Gas Kinetics - Real Gases Review Compressibility factor = z...

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