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What does boiling temperature measure?

What does boiling temperature measure?. Figure. The boiling temperatures of the n-alkanes. Why do you suppose that curvature is observed as the size of the n-alkane increases?. Modeling boiling temperature

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What does boiling temperature measure?

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  1. What does boiling temperature measure?

  2. Figure. The boiling temperatures of the n-alkanes

  3. Why do you suppose that curvature is observed as the size of the n-alkane increases?

  4. Modeling boiling temperature An exponential function has previously been used to model the behavior observed for the n-alkanes. Woolf, A. A. “Relations between the boiling points of perfluoro-ethers, perfluoroalkanes and normal alkanes”, J. Fluorine Chem. 1993, 63, 19-24. Kreglewski, A.; Zwolinski, B. J. “A new relation for physical properties of n-alkanes and n-alkyl compounds”, J. Phys. Chem.196165, 1050-1052.

  5. Is the boiling temperature of an infinite polymer, finite?

  6. Figure. A plot of the lgHm(TB) measured at T = TB versus the lgSm(TB) also calculated at T = TB of the n-alkanes (C3 to C20): circles, n-alkylcyclo-pentanes (C7 to C21): triangles, and n-alkylcyclohexanes (C8 to C24): squares.

  7. lgHm(TB) = m lgSm(TB) +C lgHm(TB)/ TB = lgSm(TB) Therefore lgHm(TB) = m lgHm(TB)/ TB +C Solving for TB: TB = m lgHm(TB)/( lgHm(TB) - C) This is an equation of a hyperbola As lgHm(TB)  ;TB m

  8. Table 1. The Correlation Equations of Figures 1 and 2 Obtained by Plotting lgHm(TB) Versus lgSm(TB) n-alkanes lgHm(TB) = (3190.722.6) lgSm(TB) – (240583350); r2 = 0.9992 n 1-alkenes lgHm(TB) = (2469.3109.7) lgSm(TB) – (169585951); r2 = 0.9806 n-alkylbenzenes lgHm(TB) = (3370.537.3) lgSm(TB) – (247175296); r2 = 0.9985 n-alkylcyclopentanes lgHm(TB) = (3028.897.4) lgSm(TB) – (220567926); r2 = 0.9877 n-alkylcyclohexanes lgHm(TB) = (3717.887.3) lgSm(TB) – (284890999); r2 = 0.9918 n-alkanethiols lgHm(TB) = (2268.7162.6) lgSm(TB) – (1616931728); r2 = 0.9558 TB() ~ 3000 K

  9. If TB approaches 3000 k in a hyperbolic fashion, then a plot of 1/(1 – TB/TB() versus N, the number of repeat units should result in a straight line Recall that:

  10. Melting temperatures of the even n-alkanes versus the number of methylene groups

  11. A plot of 1/[1- TB/TB()] versus the number of methylene groups using a value of T = 411 K.

  12. squares: phenylalkanes hexagons: alkylcyclopentanes circles: n-alkanes triangles: 1-alkenes Figure. A plot of 1/[1- TB/TB()] versus the number of methylene groups using a value of TB() = 3000 K.

  13. Use of TB() = 3000 K did not result in straight lines as expected. Why wasn’t a straight line obtained as suggested by the plot of lgHm(TB) versus lgSm(TB) ? Consequently TB() was treated as a variable until the best straight line was obtained by using a non-linear least squares program. This resulted in the following:

  14. Figure A plot of 1/[1-TB(N)/TB()] against the number of repeat units, N; , 1-alkenes; , n-alkanes; , n-alkylcyclopentanes; , n-alkylcyclohexanes.

  15. Table 2. The Results Obtained by Treating TBof a Series of Homologous Compounds as Function of the Number of Repeat Units, N, and Allowing TB()to Vary; aBm, bBm: Values of aB and bB Obtained by Using the Mean Value of TB()= 1217 K Polyethylene Series TB()/K aB bB /K aBm bBm /K data points n-alkanes 1076 0.06231 1.214 0.9 0.04694 1.1984 3.6 18 2-methyl-n-alkanes 1110 0.05675 1.3164 0.2 0.0461 1.2868 0.3 8 1-alkenes 1090 0.06025 1.265 0.4 0.04655 1.242 2.7 17 n-alkylcyclopentanes 1140 0.05601 1.4369 0.6 0.04732 1.4037 1.3 15 n-alkylcyclohexanes 1120 0.05921 1.5054 0.1 0.04723 1.4543 1.2 13 n-alkylbenzenes 1140 0.05534 1.5027 1.1 0.05684 1.5074 1.4 15 1-amino-n-alkanes 1185 0.04893 1.274 3.4 0.04607 1.267 3.4 15 1-chloro-n-alkanes 1125 0.05717 1.2831 0.3 0.04775 1.2628 1.6 13 1-bromo-n-alkanes 1125 0.05740 1.3264 1.0 0.0481 1.2993 1.5 12 1-fluoro-n-alkanes 1075 0.05833 1.2214 0.4 0.04495 1.1987 2.1 9 1-hydroxy-n-alkanes 1820 0.01806 1.220 0.8 0.03953 1.3559 3.6 12 2-hydroxy-n-alkanes 1055 0.05131 1.4923 1.8 0.03732 1.4031 1.8 7 n-alkanals 910 0.08139 1.4561 1.4 0.04277 1.3177 2.5 7 2-alkanones 1440 0.03071 1.2905 1.6 0.0430 1.3613 1.7 8

  16. Polyethylene Series TB()/K aB bB /K aBm bBm /K data points n-alkane-1-thiols 1090 0.06170 1.3322 0.2 0.042 1.3635 2.8 14 n-dialkyl disulfides 1190 0.08720 1.4739 0.4 0.08207 1.4608 0.6 9 n-alkylnitriles 1855 0.01907 1.2294 2.6 0.04295 1.3869 3.4 11 n-alkanoic acids 1185 0.0440 1.4964 1.3 0.04100 1.4790 1.3 16 methyl n-alkanoates 1395 0.03158 1.3069 2.6 0.04200 1.3635 2.8 10 Mean Value of TB()= (1217246) K The results for TB()are remarkably constant considering the use of data with finite values of N to evaluate TB(N) for N (). These results are also in good agreement with the values reported previously for the n-alkanes by Kreglewski and Zwolinski (TB() = 1078 K) and Somayajulu (TB() = 1021 K). Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem.196165, 1050-1052. Somayajulu, G. R. Internat. J. Thermophys. 1990, 11, 555-72.

  17. A value of TB()= (1217246) K is considerably less than TB()= 3000 K, the value obtained by assuming that lgHm(TB)   asTB . Since TB = m lgHm(TB)/( lgHm(TB) - C) from the plot of lgHm(TB) vs lgSm(TB), solving for lgHm(TB)maxin this equationresults in: lgHm(TB)max = C (TB())/(m - TB()) lgHm(TB)max = 154.5  18.5 kJ mol-1 Why do all of the polyethylene series converge to approximately 154.5  18.5 kJ mol-1? A limiting value 154.5 kJ mol-1 for lgHm(TB)max suggests that this property may also be modeled effectively by a hyperbolic function

  18. A plot of1/[1- lgHm(TB)/ lgHm(TB()] against the number of repeat units, N For the 1-alkenes (circles) and n-alkylcyclohexanes (squares) using a value of 154 kJ mol-1 for lgHm(TB)max..

  19. A plot oflgHm(TB) against the number of repeat units, N; points: experimental values; lines: calculated values; circles: n-alkanes; triangles: alkylthiols; squares: alkylcyclopentanes.

  20. Table. Values of the Parameters of aH and bH Generated in Fitting lgHm(TB) of Several Homologous Series Usinga Value of lgHm(TB)max = 154.5  18.5 kJ mol-1.  aH bH /kJ.mol-1 data points n-alkanes 0.02960 1.1235 0.4 18 n-alkylbenzenes 0.02741 1.284 0.5 15 n-alkylcyclohexanes 0.02697 1.2754 0.2 15 n-alkylcyclopentanes 0.02821 1.2475 0.2 15 n-alk-1-enes 0.02796 1.1554 0.4 17 n-alkane-1-thiols 0.03172 1.1854 0.5 13

  21. Why does lgHm(TB)max reach a limit of 154 kJ mol-1?

  22. TC = TB+ TB/[c + d(N+2)] Ambroses’ Equation where c and d are constants and N refers to the number of methylene groups. Since this equation is an equation of a hyperbola, a plot of Ambrose, D. "NPL Report Chemistry 92" (National Physical Laboratory, Teddington, Middlesex UK, 1978).

  23. Figure. A plot of experimental critical temperatures versus N, the number of methylene groups for (top to bottom) the alkanoic acids (hexagons), 2-alkanones (diamonds), 1-hydroxalkanes (solid circles) 1-alkenes (triangles), and the n-alkanes (circles)

  24. Since Ambrose equation is an equation of a hyperbola, a plot of 1/[1-TB/TB()] versus the number of methylene groupsshould result in a straight line.

  25. Table. Results Obtained for the Constants aC and bC by Treating TCas a Function of the Number of Repeat Units, N, and Allowing TC()to Vary; aCm, bCm: Values of aC and bC Obtained by Using the Mean Value of TC = 1217 K Polyethylene data Series TC()/K aC bC /K TC()/K aCm bCm /K points n-alkanes 1050 0.1292 1.4225 1.7 1217 0.07445 1.4029 9.8 16 n-alkanals 1070 0.1171 1.7753 1.0 1217 0.07756 1.6355 1.8 8 alkanoic acids 1105 0.0961 2.1137 3.4 1217 0.06456 1.9329 3.9 31 1-alkanols 1045 0.1157 1.8362 3.6 1217 0.06773 1.6639 4.7 11 2-alkanones 1105 0.10063 1.8371 1.3 1217 0.07193 1.718 1.9 11 3-alkanones 1185 0.07827 1.8168 1.3 1217 0.07158 1.7811 1.3 10 1-alkenes 1035 0.1327 1.5496 0.3 1217 0.08278 1.4518 3.1 8 2-methylalkanes 950 0.16282 1.7767 0.6 1217 0.07862 1.5329 1.7 5

  26. What are the consequences if TB = TC ?

  27. At TC, lgHm(TB) = 0 This explains why lgHm(TB) fails to continue to increase but infact decreases as the size of the molecule get larger. Any inconsistancies here? What does lgHm(TB) measure?

  28. An equation reported by Somayajulu provides a means of describing the possible behavior of lgHm(TB) as a function of TB and TC. lgHm(TB)= e1X + e2X2 + e3X3 +e4X4 where X = (TC-TB)/TC Somayajulu, G. R. “The critical constants of long chain normal paraffins”,Internat. J. Thermophys. 1991, 12, 1039-62.

  29. lgHm(TB)against the number of repeat units, N.

  30. If we know how lgHm(TB)varies as a function of the number of repeat units, and we know how TB also varies, we can determine how a plot oflgHm(TB)versus lgSm(TB)should vary.

  31. Figure. Experimental values of lgHm(TB)as a function of lgSm(TB); n-alkanes: circles, experimental values; solid line, calculated values.

  32. Are their any other consequences if TB = TC ?

  33. If TB = TC , what about PC? PC= the pressurenecessary to keep the material as a liquid at T = TC PB= 1 atm (101.325 kPa) If TCTB , then shouldn’t PB1 atm (101.325 kPa) Furthermore, if PCis finite at TC and approaches 101.325 kPa as the size of the molecule increases, then shouldn’t it also be modeled by a hyperbolic function? Remember for a descending hyperbolic function: X= Xmin/ [1- 1/(mN + b)] as X  Xmin

  34. X= Xmin/ [1- 1/(mN + b)] as X  Xmin In this case: PC= PCmin/ [1- 1/(mN + b)] as P  101.325 kPa (0.101 MPa)

  35. Figure. A plot of the critical pressure versus the number of repeat units for the 1-alkanols (triangles), the n-alkanes (circles), and the 2-methylalkanes (squares).

  36. Figure. A plot of the critical pressure versus the number of repeat units for the n-alkanoic acids (circles), and 1-alkenes (squares). The data for the alkanoic acids includes a few multiple determinations to give a sense of the scatter in the experimental data.

  37. Summary: All of the homologues series examined related to polyethylene 1. approach a limiting boiling temperature, 1217 K; 2. approach a limiting critical temperature, 1217 K; 3. have vaporization enthalpies that increase initially, and then decrease to 0 kJ mol-1; 4. have critical pressures that can be modeled as approaching a limiting pressure of 101.325 kPa .

  38. All of the homologous series examined so far, in the limit, become polyethylene. Hypothesis: If a homologous series is related related to a different polymer, that series in the limit should also approach the boiling temperature of that polymer. For example, how do the boiling temperatures of the perfluorinated compounds compare to each other?

  39. Boiling temperatures of the perfluoro-n-alkanes and perfluoro-n-alkanoic acids

  40. 1/[1-TB/TB()] was plotted against the number of CF2 groups using TB() as a variable

  41. Table. Values of the Parameters of aB and bB Generated in Fitting TB of Several Homologous Perfluorinated Series and Allowing TB() to Vary in 5 K Increments; aBm, bBm: Values of aB and bB Using an Average Value of TB() = 915 K TB()/K aB bB /K TB()/K aBm bBm /K N  n-perfluoroalkanes 880 0.07679 1.2905 2.1 915 0.06965 1.2816 2.2 13 n-perfluoroalkanoic acids 950 0.06313 1.5765 1.2 915 0.07053 1.6085 1.3 8 methyl n-perfluoroalkanoates 915 0.06637 1.5000 1.6 4 1-iodo-n-perfluoroalkanes 915 0.07409 1.3751 1.8 5

  42. Figure. A plot of 1/[1-TB/TB()] vs the number of CF2 groups using TB() = 915 K; squares: perfluorocarboxylic acids; circles: perfluoro-n-alkanes.

  43. What about TC of the perfluorinated compounds?

  44. Figure. A plot of experimental critical temperatures versus N, the number of methylene groups for (top to bottom) the alkanoic acids (hexagons), 2-alkanones (diamonds), 1-hydroxalkanes (solid circles) 1-alkenes (triangles), the n-alkanes (circles), and n-perfluoroalkanes (solid squares). The lines were calculated using of TC() = 1217 K for the hydrocarbons and derivatives and TC() = 915 K for the fluorocarbons.

  45. Polyperfluoroethylene Series TC()/K aCbC/K TC()/K aCm bCm /K N n-perfluoroalkanes 920 0.1166 1.4813 1.1 915 0.1203 1.487 1.6 8 Despite the limited amount of available data, TCof the perfluorinated compounds behave analogously to the corresponding hydrocarbons.

  46. Recall the equation reported by Somayajulu as a means of describing the possible behavior of lgHm(TB) as a function of TB and TC. lgHm(TB)= e1X + e2X2 + e3X3 +e4X4 where X = (TC-TB)/TC Somayajulu, G. R. “The critical constants of long chain normal paraffins”,Internat. J. Thermophys. 1991, 12, 1039-62.

  47. Figure. Values of lgHm(TB)as a function of the number of repeat units; n-alkanes: solid line, calculated values; circles, experimental values; n-perfluoro-alkanes: dashed line, calculated values, triangles, experimental values.

  48. Figure. Experimental values of lgHm(TB)as a function of lgSm(TB); n-alkanes: circles, experimental values; solid line, calculated values; n-perfluoroalkanes: triangles, experimental values; dashed line, calculated values.

  49. What about PC for the perfluorinated compounds? Remember for a descending hyperbolic function: P= Pmin/ [1- 1/(mN + b)] as P  Pmin or 0.1 MPa

  50. Figure. A plot of the critical pressure versus the number of repeat units for the n-alkanoic acids (circles), 1-alkenes (squares), and perfluoroalkanes (solid diamonds). The data for the alkanoic acids includes a few multiple determinations to give the reader a sense of the scatter in the experimental data.

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