Chapter12_A

# Chapter12_A - Chapter 12 Section A Mathcad Solutions 12.1...

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GERT x 1 ln γ 1 () x 2 ln γ 2 + ⎯⎯⎯⎯⎯⎯⎯⎯⎯ := γ 2 y 2 P x 2 Psat 2 ⎯⎯⎯ := γ 1 y 1 P x 1 Psat 1 ⎯⎯⎯ := Calculate EXPERIMENTAL values of activity coefficients and excess Gibbs energy. Psat 2 19.953 kPa := Psat 1 84.562 kPa := Vapor Pressures from equilibrium data: y 2 1y 1 ⎯⎯⎯ := x 2 1x 1 ⎯⎯⎯ := Calculate x2 and y2: i1 n .. := n1 0 = n rows P := Number of data points: y 1 0.5714 0.6268 0.6943 0.7345 0.7742 0.8085 0.8383 0.8733 0.8922 0.9141 := x 1 0.1686 0.2167 0.3039 0.3681 0.4461 0.5282 0.6044 0.6804 0.7255 0.7776 := P 39.223 42.984 48.852 52.784 56.652 60.614 63.998 67.924 70.229 72.832 kPa := T 333.15 K := Methanol(1)/Water(2)-- VLE data: 12.1 Chapter 12 - Section A - Mathcad Solutions 374

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Ans. A 21 0.475 = A 12 0.683 = A 21 Slope A 12 + := A 12 Intercept := Intercept 0.683 = Slope 0.208 = Intercept intercept VX VY , () := Slope slope VX VY , := VY i GERT i x 1 i x 2 i := VX i x 1 i := Fit GE/RT data to Margules eqn. by linear least squares: (a) 0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4 0.5 ln γ 1 i ln γ 2 i GERT i x 1 i GERT i 0.087 0.104 0.135 0.148 0.148 0.148 0.136 0.117 0.104 0.086 = i 1 2 3 4 5 6 7 8 9 10 = ln γ 2 i ( ) 0.013 0.026 0.073 0.106 0.146 0.209 0.271 0.3 0.324 0.343 = ln γ 1 i ( ) 0.452 0.385 0.278 0.22 0.151 0.093 0.049 0.031 0.021 0.012 = γ 2 i 1.013 1.026 1.075 1.112 1.157 1.233 1.311 1.35 1.382 1.41 = γ 1 i 1.572 1.47 1.32 1.246 1.163 1.097 1.05 1.031 1.021 1.012 = 375
The following equations give CALCULATED values: γ 1x1x2 , ( ) exp x2 2 A 12 2A 21 A 12 () x1 + := γ 2x1x2 , ( ) exp x1 2 A 21 12 A 21 x2 + := j 1 101 .. := X 1 j .01 j .01 := X 2 j 1X 1 j := p calc j X 1 j γ 1 j X 2 j , Psat 1 X 2 j γ 2X 1 j X 2 j , Psat 2 + := Y 1calc j X 1 j γ 1 j X 2 j , Psat 1 p calc j := P-x,y Diagram: Margules eqn. fit to GE/RT data. 0 0.2 0.4 0.6 0.8 10 20 30 40 50 60 70 80 90 P-x data P-y data P-x calculated P-y calculated P i kPa P i kPa p calc j kPa p calc j kPa x 1 i y 1 i , X 1 j , Y 1calc j , 376

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X 2 j 1X 1 j := (To avoid singularities) X 1 j .01 j .00999 := j 1 101 .. := γ 2x1x2 , ( ) exp a 21 1 a 21 x2 a 12 x1 + 2 := γ 1x1x2 , ( ) exp a 12 1 a 12 x1 a 21 x2 + 2 := Ans. a 21 0.485 = a 12 0.705 = a 21 1 Slope Intercept + () := a 12 1 Intercept := Intercept 1.418 = Slope 0.641 = Intercept intercept VX VY , := Slope slope VX VY , := VY i x 1 i x 2 i GERT i := VX i x 1 i := Fit GE/RT data to van Laar eqn. by linear least squares: (b) RMS 0.399kPa = RMS i P i P calc i 2 n := RMS deviation in P: y 1calc i x 1 i γ 1x 1 i x 2 i , Psat 1 P calc i := P calc i x 1 i γ 1 i x 2 i , Psat 1 x 2 i γ 2x 1 i x 2 i , Psat 2 + := 377
p calc j X 1 j γ 1X 1 j X 2 j , () Psat 1 X 2 j γ 2X 1 j X 2 j , Psat 2 + := P calc i x 1 i γ 1x 1 i x 2 i , Psat 1 x 2 i γ 2x 1 i x 2 i , Psat 2 + := Y 1calc j X 1 j γ 1 j X 2 j , Psat 1 p calc j := y 1calc i x 1 i γ 1 i x 2 i , Psat 1 P calc i := P-x,y Diagram: van Laar eqn. fit to GE/RT data. 0

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Chapter12_A - Chapter 12 Section A Mathcad Solutions 12.1...

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