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# Problem Set 5 - De La Salle University College of...

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De La Salle University College of Engineering Chemical Engineering Department Problem Set 5 Advanced Thermodynamics (CHE618M) Dr. Nathaniel Dugos Dizon, Clarissa S. - 10993770 Term 3, AY-2009-2010 12.1

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The following is a set of VLE data for the system methanol(l)/water(2) at 333.15 K (60°C) (extracted from K. Kurihara et al., J. Chem. Eng. Data, vol. 40, pp. 679-684, 1995): P/kPa x 1 y 1 P/kPa x 1 y 1 19.953 0.0000 0.0000 60.614 0.5282 0.8085 39.223 0.1686 0.5714 63.998 0.6044 0.8383 42.984 0.2167 0.6268 67.924 0.6804 0.8733 48.852 0.3039 0.6943 70.229 0.7255 0.8922 52.784 0.3681 0.7345 72.832 0.7776 0.9141 56.652 0.4461 0.7742 84.562 1.0000 1.0000 a. Basing calculations on Eq. (12. I), find parameter values for the Margules equation that provide the best fit of G E /RT to the data, and prepare a Pxy diagram that compares the experimental points with curves determined from the correlation. b. Repeat (a) for the van Laar equation. c. Repeat (a) for the Wilson equation. d. Using Barker's method, find parameter values for the Margules equation that provide the best fit of the P-x 1 data. Prepare a diagram showing the residuals δP and δy 1 plotted vs. x 1 . e. Repeat (d) for the van Laar equation. f. Repeat (d) for the Wilson equation. Solution: a. Parameter values for the Margules Equation, Pxy diagram To get A 12 and A 21 , G E /(RTx 1 x 2 ) was plotted versus x. Linearizing, A 12 would correspond to the intercept and A 21 would correspond to the sum of the slope and A 12 . Using equation 12.6, G E /RT was obtained. γ is calculated using Equation 12.1.
The table below shows the computed and given values P/kPa x 1 y 1 x 2 y 2 γ 1 γ 2 G E /RT G E / (RTx 1 x 2 ) 39.223 0.1686 0.5714 0.8314 0.4286 1.5720 1.0134 0.0873 0.6229 42.984 0.2167 0.6268 0.7833 0.3732 1.4703 1.0264 0.1039 0.6123 48.852 0.3039 0.6943 0.6961 0.3057 1.3198 1.0752 0.1348 0.6373 52.784 0.3681 0.7345 0.6319 0.2655 1.2455 1.1115 0.1476 0.6346 56.652 0.4461 0.7742 0.5539 0.2258 1.1627 1.1574 0.1482 0.5999 60.614 0.5282 0.8085 0.4718 0.1915 1.0972 1.2330 0.1478 0.5932 63.998 0.6044 0.8383 0.3956 0.1617 1.0497 1.3110 0.1365 0.5707 67.924 0.6804 0.8733 0.3196 0.1267 1.0310 1.3495 0.1166 0.5360 70.229 0.7255 0.8922 0.2745 0.1078 1.0213 1.3822 0.1042 0.5231 72.832 0.7776 0.9141 0.2224 0.0859 1.0125 1.4098 0.0860 0.4975 Plot: The linearized equation of the line is y = -0.2075x + 0.6828. With this, A 12 = Intercept = 0.6828 and A 21 = Slope + A 12 = -0.2075 + 0.6828 = 0.4753 Equations 12.10a and 12.10b computes for the gamma values given the parameter values of Margules Using Modified Raoult’s Law, the new final pressure and final composition of the vapor phase is computed. x 1 γ 1 γ 2 P calc y 1 y 2 0.1686 1.5275 1.0236 38.7575 0.5619 0.4381 0.2167 1.4387 1.0383 42.5919 0.6190 0.3810 0.3039 1.3096 1.0731 48.5603 0.6931 0.3069 0.3681 1.2357 1.1051 52.3976 0.7341 0.2659 0.4461 1.1650 1.1507 56.6630 0.7756 0.2244 0.5282 1.1087 1.2059 60.8733 0.8135 0.1865

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0.6044 1.0699 1.2631 64.6544
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Problem Set 5 - De La Salle University College of...

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