Adventures in Thermochemistry James S. Chickos * Department of Chemistry and Biochemistry University of Missouri-St. Louis Louis MO Gateway to the West

1. Vaporization enthalpies at the boiling temperature are predicted to approach a limiting value 2.Boiling temperatures appear to converge to a finite limit. 3.Critical temperature and boiling temperatures appear to converge as a function of the number of repeat units. 4.Critical pressures appear to converge to some small finite pressure (~1 atm) as the number of repeat units  . Can any of this be experimentally verified? Previously we concluded the following:

If vaporization enthalpies at the boiling point attain some maximum value, then vaporization enthalpies of homologous series as a function of temperature should show some curvature as the size increases. How do known vaporization enthalpies of the n-alkanes at T = K behave as a function of the number of carbons?

 l g H m (T m ) = (5.01±0.007)N + (1.487±0.1) r 2 = Literature Vaporization Enthalpies of the n Alkanes C 5 to C 20 at T = K Ruzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermodynamic Properties Between the Triple Point and Normal Boiling Temperatures for n-Alkanes C 5 -C 20. J. Phys. Chem. Ref. Data 1994, 23, 1.

The measurement of vaporization enthalpies A. Calorimetric B. Vapor pressure dependency on temperature both properties depend on pure samples, moderate quantities (> mg) Our group has been interested in developing a method that could circumvent the requirement of sample purity and quantity and could be applicable in the sub-pascal region Applications of gas chromatography The measurement of vapor pressure A. Various static method B. Effusion methods C. Transpiration methods

A series of isothermal runs. The compounds are n-alkanes

Basic Considerations in Using Gas Chromatography In gas chromatography, the time a compound spends on the column (t a ) is inversely proportional to the compounds vapor pressure on the column. Therefore, the vapor pressure p of a compound is proportional to 1/t a. The amount of time a compound spends on the column, t a, (the adjusted retention time) is obtained by subtracting the retention time of an non-retained reference (often the solvent) from the retention time of each analyte. If 1/t a is proportional to vapor pressure, then for chromatograms run isothermally, a plot of ln(t o /t a ) versus 1/T (K -1 ) over a 30 K temperature range, where t o is the reference time, 1 min, should result in a straight line with a negative slope equal to the enthalpy of transfer from the stationary phase of the column to the gas phase divided by the gas constant,  sln g H m (T m )/R. Both terms are predicted to have the same dependence on size. Coiling of the n- alkane decreasing intermolecular interactions will lead to an attenuation of both  sln g H m (T m ) and  l g H m (T m ).  sln g H m (T m ) =  l g H m (T m ) +  sln H m (T m )

A plot of ln(t o /t a ) versus 1/T (K -1 ) From top to bottom: docosane tetracosane hexacosane nonacosane dotriacontane tetratriacontane hexatriacontane octatriacontane t o = 1 min ln(t o /t a ) = -  sln g H m (T m )/RT +C

Enthalpies of transfer measured at T m = 520 K vs the number of carbon atoms from C 21 to C 38  sln g H m (520 K) = (3005±13.1)N+(3054±287); r 2 =  sln g H m (T m ) =  l g H m (T m )+  sln H m (T m )

Individual n- alkanes are available commercially for most even n-alkanes up to C 60. In addition, alkanes derived from oligomers of polyethylene are available up to ~C 100

C 60 Even Alkanes from Polywax1000 C 86

SlopeIntercept  sln g H m (653 K) kJ mol -1 N dotetracontane tetratetracontane hexatetracontane octatetracontane pentacontane dopentacontane tetrapentacontane hexapentacontane octapentacontane hexacontane dohexacontane tetrahexacontane hexahexacontane octahexacontane heptacontane doheptacontane tetraheptacontane hexaheptacontane

The equation of the linear fit:  sln g H m (653 K) = (2999  13)N + (3039  286); r 2 = The equation of the line fit by a second order polynomial is given by:  sln g H m (653 K) (-8.775)N N ; r 2 = A plot of  sln g H m (T) against the number of carbon atoms, N for N = 42 to 76.

Enthalpies of transfer kJ/mol as a function of the number of carbon atoms from C 50 to C 92 circles:  sln g H m (676 K) = (2.12±0.016)N + (12.43±0.92); r 2 = circles:  sln g H m (676 K) = -(5.64±0.56)10 -3 N 2 +(2.93±0.08)N –(15.1±2.8); r 2 = triangles:  sln g H m (653 K) = (2.12±0.02)N + (16.18±0.73); r 2 = triangles:  sln g H m (653 K) = -(8.37±0.96)10 -3 N 2 +(3.45±0.14)N –(29.6±5.3); r 2 = squares:  sln gH m (676 K)= (2.12±0.018)N + (11.42±0.78); r 2 = squares:  sln g H m (676 K)= -(7.47±0.42)10 -3 N 2 +(3.24±0.06)N –(29.8±2.3); r 2 = to a third order polynomial

Conclusions: Based on the data available, it appears that enthalpies of transfer at temperatures below the boiling temperature do show some curvature as a function of carbon number. Whether this is due to changes in  l g H m (T m ) or  sln H m (T m ) or both is not known from these results.

Hui Zhao William Hanshaw T Richard Heinze Tom Murphy Hui Zhao William Hanshaw Patamaporn Umnahanant (T)