Transcript
Data Reporter
Tables / graphs of expected results 1.5/2
[[[COMMENT BY Nicholas (2013-11-14T00:08:00Z)]]]
How do you tell if the solution is ideal/nonideal? How close to 0 for consistency is acceptable?
[[[---]]]
(according to Leader’s theory) 1/1
(+ references) 1/1
Tables / graphs for entry data 2/2
Examples of each type of calculation 2/2
(+ conditions / references) 1/1
(accuracy of calculations) 1/1
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Total 9.5/10
DATA TABLES
*error not known at this time, will be included in post lab
Table 1. Experimental Data
Trial 1
Trial 2
Trial 3
Volume of methanol (%)
Volume of pycnometer (ml)
Mass of pyncometer (g)
Mass of initial solution + pycnometer (g)
Mass of initial solution (g)
Temperature of Initial solution (?C)
Time for decantation (min)
Time for 3 decantations (min)
Mass of distillate + pycnometer (g)
Mass of distillate (g)
Tempearture of distillate (?C)
Mass of residue + pycnometer (g)
Mass of residue (g)
Temperature of reside (?C)
Table 2. Data Table for Initial Solution
Trial 1
Trial 2
Trial 3
Density of initial solution (g/ml)
Methanol (wt %)
Methanol (mol)
Water (mol)
Mole fraction of methanol
Mole fraction of water
Table 3. Data Table for Residue
Trial 1
Trial 2
Trial 3
Density of residue (g/ml)
Methanol (wt %)
Methanol (mol)
Water (mol)
Mole fraction of methanol
Mole fraction of water
Table 4. Data Table for Distillate
Trial 1
Trial 2
Trial 3
Density of distillate (g/ml)
Methanol (wt %)
Methanol (mol)
Water (mol)
Mole fraction of methanol
Mole fraction of water
EXPECTED RESULTS
Table 5. Methanol Weight Percent and Density (Perry & Green, 2007)
%
0 °C
10 °C
15.56 °C
20 °C
15 °C
%
0 °C
10 °C
15.56 °C
20 °C
15 °C
%
0 °C
10 °C
15.56 °C
20 °C
15 °C
0 1 2 3 4
0.9999 0.9981 0.9963 0.9946 0.9930
0.9997 0.9980 0.9962 0.9945 0.9929
0.9990 0.9973 0.9955 0.9938 0.9921
0.9982 0.9965 0.9948 0.9931 0.9914
0.99913 0.99727 0.99543 0.99370 0.99198
35 36 37 38 39
0.9534 0.9520 0.9505 0.9490 0.9475
0.9484 0.9469 0.9453 0.9437 0.9420
0.9456 0.9440 0.9422 0.9405 0.9387
0.9433 0.9416 0.9398 0.9381 0.9363
0.94570 0.94404 0.94237 0.94067 0.93894
70 71 72 73 74
0.8869 0.8847 0.8824 0.8801 0.8778
0.8794 0.8770 0.8747 0.8724 0.8699
0.8748 0.8726 0.8702 0.8678 0.8653
0.8715 0.8690 0.8665 0.8641 0.8616
0.87507 0.87271 0.87033 0.86792 0.86546
5 6 7 8 9
0.9914 0.9899 0.9884 0.9870 0.9856
0.9912 0.9896 0.9881 0.9865 0.9849
0.9904 0.9889 0.9872 0.9857 0.9841
0.9896 0.9880 0.9863 0.9847 0.9831
0.99029 0.98864 0.98701 0.98547 0.98394
40 41 42 43 44
0.9459 0.9443 0.9427 0.9411 0.9395
0.9403 0.9387 0.9370 0.9352 0.9334
0.9369 0.9351 0.9333 0.9315 0.9297
0.9345 0.9327 0.9309 0.9290 0.9272
0.93720 0.93543 0.93365 0.93185 0.93001
75 76 77 78 79
0.8754 0.8729 0.8705 0.8680 0.8657
0.8676 0.8651 0.8626 0.8602 0.8577
0.8629 0.8604 0.8579 0.8554 0.8529
0.8592 0.8567 0.8542 0.8518 0.8494
0.86300 0.86051 0.85801 0.85551 0.85300
10 11 12 13 14
0.9842 0.9829 0.9816 0.9804 0.9792
0.9834 0.9820 0.9805 0.9791 0.9778
0.9826 0.9811 0.9796 0.9781 0.9766
0.9815 0.9799 0.9784 0.9768 0.9754
0.98241 0.98093 0.97945 0.97802 0.97660
45 46 47 48 49
0.9377 0.9360 0.9342 0.9324 0.9306
0.9316 0.9298 0.9279 0.9260 0.9240
0.9279 0.9261 0.9242 0.9223 0.9204
0.9252 0.9234 0.9214 0.9196 0.9176
0.92815 0.92627 0.92436 0.92242 0.92048
80 81 82 83 84
0.8634 0.8610 0.8585 0.8560 0.8535
0.8551 0.8527 0.8501 0.8475 0.8449
0.8503 0.8478 0.8452 0.8426 0.8400
0.8469 0.8446 0.8420 0.8394 0.8366
0.85048 0.84794 0.84536 0.84274 0.84009
15 16 17 18 19
0.9780 0.9769 0.9758 0.9747 0.9736
0.9764 0.9751 0.9739 0.9726 0.9713
0.9752 0.9738 0.9723 0.9709 0.9695
0.9740 0.9725 0.9710 0.9696 0.9681
0.97518 0.97377 0.97237 0.97096 0.96955
50 51 52 53 54
0.9287 0.9269 0.9250 0.9230 0.9211
0.9221 0.9202 0.9182 0.9162 0.9142
0.9185 0.9166 0.9146 0.9126 0.9106
0.9156 0.9135 0.9114 0.9094 0.9073
0.91852 0.91653 0.91451 0.91248 0.91044
85 86 87 88 89
0.8510 0.8483 0.8456 0.8428 0.8400
0.8422 0.8394 0.8367 0.8340 0.8314
0.8374 0.8347 0.8320 0.8294 0.8267
0.8340 0.8314 0.8286 0.8258 0.8230
0.83742 0.83475 0.83207 0.82937 0.82667
20 21 22 23 24
0.9725 0.9714 0.9702 0.9690 0.9678
0.9700 0.9687 0.9673 0.9660 0.9646
0.9680 0.9666 0.9652 0.9638 0.9624
0.9666 0.9651 0.9636 0.9622 0.9607
0.96814 0.96673 0.96533 0.96392 0.96251
55 56 57 58 59
0.9191 0.9172 0.9151 0.9131 0.9111
0.9122 0.9101 0.9080 0.9060 0.9039
0.9086 0.9065 0.9045 0.9024 0.9002
0.9052 0.9032 0.9010 0.8988 0.8968
0.90839 0.90631 0.90421 0.90210 0.89996
90 91 92 93 94
0.8374 0.8347 0.8320 0.8293 0.8266
0.8287 0.8261 0.8234 0.8208 0.8180
0.8239 0.8212 0.8185 0.8157 0.8129
0.8202 0.8174 0.8146 0.8118 0.8090
0.82396 0.82124 0.81849 0.81568 0.81285
25 26 27 28 29
0.9666 0.9654 0.9642 0.9629 0.9616
0.9632 0.9618 0.9604 0.9590 0.9575
0.9609 0.9595 0.9580 0.9565 0.9550
0.9592 0.9576 0.9562 0.9546 0.9531
0.96108 0.95963 0.95817 0.95668 0.95518
60 61 62 63 64
0.9090 0.9068 0.9046 0.9024 0.9002
0.9018 0.8998 0.8977 0.8955 0.8933
0.8980 0.8958 0.8936 0.8913 0.8890
0.8946 0.8924 0.8902 0.8879 0.8856
0.89781 0.89563 0.89341 0.89117 0.88890
95 96 97 98 99
0.8240 0.8212 0.8186 0.8158 0.8130
0.8152 0.8124 0.8096 0.8068 0.8040
0.8101 0.8073 0.8045 0.8016 0.7987
0.8062 0.8034 0.8005 0.7976 0.7948
0.80999 0.80713 0.80428 0.80143 0.79859
30 31 32 33 34
0.9604 0.9590 0.9576 0.9563 0.9549
0.9560 0.9546 0.9531 0.9516 0.9500
0.9535 0.9521 0.9505 0.9489 0.9473
0.9515 0.9499 0.9483 0.9466 0.9450
0.95366 0.95213 0.95056 0.94896 0.94734
65 66 67 68 69
0.8980 0.8958 0.8935 0.8913 0.8891
0.8911 0.8888 0.8865 0.8842 0.8818
0.8867 0.8844 0.8820 0.8797 0.8771
0.8834 0.8811 0.8787 0.8763 0.8738
0.88662 0.88433 0.88203 0.87971 0.87739
100
0.8102
0.8009
0.7959
0.7917
0.79577
*It should be noted that the values for 100 percent do not agree with some data available elsewhere, e.g., American Institute of Physics Handbook, McGraw-Hill, New York, 1957. Also, see Atack, Handbook of Chemical Data, Reinhold, New York, 1957. Also, see Tables 2-234 and 2-305 for pure component densities.
SAMPLE CALCULATIONS
Density of initial solution:
?=mass of initial solution+pycnometer-mass of empty pycnometervolume of pycnometer
=41.00-19.0025.00
=0.8800 g/ml
Weight percent of methanol via table 5 and interpolation:
y=x-x1(y2-y1)(x2-x1)+y1
=0.8800-.8787(66-67)(.8811-.8787)+67
=66.46
Number of moles of methanol:
mass of methanol=mass of initial solution(weight percent of methanol)
=22.00(.6646)
=14.62
moles of methanol=mass of methanolmolecular weight of methanol
=14.6232.04
=.4563
Mole fraction of methanol:
mole fraction of methanol=moles of methanolmoles of methanol+moles of water
=.4563.4563+.6000
=.4320
Vapour pressure via Antoine equation (constants from Seader et al, 2006):
log10PM=A-BT+C
log10PM=7.87863-1473.1180.00+230
PM=1338 mmHg
Mole fraction in vapour phase via Raoult’s Law:
In liquid phase:
xm=Ptotal-PWPM-PW
=760.0-355.31338-355.3
=.4118
In vapour phase:
yM=(PM)(xM)Ptotal
=1338(.4118)760.0
=.7250
Non-ideal calculations via van Laar equation (constants from Seader et al, 2006):
ln?M=A121+xMA12xWA212
ln?M=.80411+(.4118)(.8041)(.5882)(.5619)2
?M=1.222
[[[COMMENT BY Nicholas (2013-11-14T00:07:00Z)]]]
Can you determine these with your experimental data?
[[[---]]]
ln?W=A211+x2A21x1A122
ln?W=.56191+(.4118)(.5619)(.5882)(.8041)2
?W=1.288
yM=(?M)(PM)(xM)Ptotal
=(1.222)1338(.4118)760.0
=.8859
[[[COMMENT BY Nicholas (2013-11-14T00:07:00Z)]]]
How do you tell if this is ideal/nonideal
[[[---]]]
Thermodynamic consistency verification
x1dln(?1)+x2dln(?2)=0
x=0x=1ln?(?1/?2)dx=0
abfxdx?h3[fa+4fa+b2+f(b)]
Plotting ln(?M/?W) vs. xM a straight line is formed. The equation from this line is used to calculate the area under the graph via simpson’s one third rule. If this value is approximately equal to 0 the data is thermodynamically
[[[COMMENT BY Nicholas (2013-11-14T00:07:00Z)]]]
How close is acceptable?
[[[---]]]
consistent.
Calculating percent error for ideal solution methanol mole fraction in vapour phase:
Percentage Error=?yM, theo-yM,exp?yM,theo*100
Percentage Error=?.625-..7250?.625*100
Percentage Error=16%
REFERENCES
Turcotte, G., CHE415 Laboratory Manual 2013: Liquid-Vapor Equilibrium Othmer Equilibrium Still, Ryerson University, Blackboard Site.
Seader, J.D., Henley, D.J. (2006). Separation Process Principles. 2nd ed. New York: J. Wiley.
Winnick, J. (1997). Chemical Engineering Thermodynamics. New York: John Wiley & Sons, Inc.
Perry, R. H., & Green, D. W. (2007). Perry's chemical engineers' handbook. New York, NY: McGraw-Hill.
