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

1. The sum of the vaporization enthalpy and the enthalpy of interaction with the column at ~660 K show curvature suggesting an approach to a limiting value. 2.Boiling temperatures obtained from vapor pressure extrapolations obtained by correlation also appear to show curvature and are modeled by a hyperbolic function reasonably well. What about vaporization enthalpies? Previously we concluded the following:

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. 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. Evaluation of Vaporization Enthalpies

 sln g H m (T m ) =  l g H m (T m ) +  sln H m (T m ) Provided suitable standards are available, enthalpies of transfer values measured at T m are also found empirically to correlate linearly with the vaporization enthalpies of standards evaluated at any temperature, including T = K. The vaporization enthalpies calculated by interpolation are reliable since the standards provide reasonable temperature adjustments due to heat capacity differences. Vaporization enthalpies evaluated by extrapolation are not likely to be as well compensated for temperature.

Evaluation of Vaporization Enthalpies: Previous Work Peacock and Fuchs measured the enthalpies of transfer from the stationary phase of the column to the gas phase on a packed silicone oil column and the measured the enthalpy of solution in silcone oil (DC200). They found that:  sln g H m (T) GC ≈  l g H m (T m ) OM +  sln H m (T m ) sol where OM = other means Several reasons are possible for the small differences between the two values observed that include; i. the approximate nature of their heat capacity adjustments ii interaction of the analyte with the column not truly a solution property but more a surface property iii gas chromatographic results are not a true equilibrium property due to flow Peacock, L. A.; Fuchs, R. Enthalpy of Vaporization Measurements by Gas Chromatography. J. Am. Chem. Soc. 1977, 99,  l g H m (298.15) GC = 1.03  l g H m (298.15) OM r 2 =

A study of the effect of flow rate on the vaporization enthalpy and enthalpy of transfer

RTX mm ID column; 30 m DB-5 MS 0.25 mm ID column 30 m The enthalpy of transfer appears to decrease slightly with decreasing flow. From the results of Peacock and L. A.; Fuchs:  l g H m (298.15) GC = 1.03  l g H m (298.15) om  l g H m (298.15) GC >  l g H m (298.15) om when  l g H m (298.15) om > 27.5 kJ·mol -1 The vaporization enthalpies of the compounds examined ranged from 41 to 80.3 kJ·mol -1 At zero flow rate the slope of 1.03 would probably been smaller since  sln g H m (T) GC would have been slightly smaller.

Adjustments of Phase Change Enthalpies to T = K 1.Vapor pressure equations known to extrapolate well with temperature, require no temperature adjustments.. 2.Vaporization enthalpy measured at elevated temperatures do require adjustments for heat capacity differences between the liquid and gas phases.  l g H m ( K)/(kJ·mol -1 ) =  l g H m (T m )/kJ·mol -1 + [( ·Cp(l)/(J·mol -1 ·K -1 ))( T m /K K)]/ Sublimation enthalpy adjustments  cr g H m ( K)/(kJ·mol-1) =  cr g H m (T m )/kJ·mol -1 + [( ·Cp(cr)/(J·mol -1 ·K -1 ))( T m /K K)]/ Fusion enthalpy adjustments  cr l H m ( K)/(kJ·mol -1 ) =  cr l H m (T fus )/kJ·mol -1 + [(0.15 Cp(cr)-0.26 Cp(l))/(J·mol -1 ·K -1 ) -9.83)] [T fus /K ]/  l g H m ( K) = ∆ cr g H m ( K) - ∆ cr l H m ( K)

Heat Capacity Estimations Cp(cr) and Cp(l) values were estimated by group additivity. Carbon groups are identified by the the hybridization at carbon and the number of H atoms attached: primary, 3; secondary, 2; tertiary 1; quaternary, 0. Distinctions are made between aliphatic, and cyclic carbons and between aromatic and cyclic unsaturated carbon atoms. Groups values are available for a variety of functional groups. A distinction is made for cyclic and acyclic functional groups

Acyclic Groups

Retention Times (min) as a Function of Temperature T/K Retention Times (t) methane octane nonene decane naphthalene dodecane tridecane Solvent: CH 2 Cl 2 t a = t i –t CH4

A plot of natural logarithm of the reciprocal adjusted retention times ln(t o /t a ) for (top to bottom): ,n- octane; , 1-nonene; , n-decane; , naphthalene; , n-dodecane; , n-tridecane as a function of 1/T; t o = 1 min.

Equations resulting from a linear regression of ln(t o /t a ) versus (1/T)K -1 Compound ln(t o /t a )= -  sln g H m /RT + ln(A i ) n-octane ln(t o /t a )= (-32336/RT) + ( ± 0.008) r 2 = nonene ln(t o /t a )= (-35108/RT) + ( ± 0.010) r 2 = n-decane ln(t o /t a )= (-38973/RT) + ( ± 0.010) r 2 = naphthalene ln(t o /t a )= (-41281/RT) + ( ± 0.008) r 2 = n-dodecane ln(t o /t a )= (-46274/RT) + ( ± 0.010) r 2 = n-tridecane ln(t o /t a )= (-50036/RT) + ( ± 0.010) r 2 =  sln g H m (T m ) =  l g H m (T m ) +  sln H m (T m ) t o = 1 min T m = 368 K

Vaporization enthalpies (J. mol -1 )  sln g H m (368 K)  l g H m ( K) lit  l g H m ( K) Calcd octane ± 1000 nonene ± 1000 decane ± 1100 naphthalene ± 1100 dodecane ± 1200 tridecane ± 1220  l g H m ( K) = (1.416  )  sln g H m (368 K) – (4061  791); r 2 =  l g H m ( K) = (1.416  )  sln g H m (368 K) – (4061  791); r 2 = naphthalene  l g H m ( K) 54.4±1.1 +  cr l H m ( K) 16.9±0.7 =  cr g H m ( K) 71.3±1.3 kJ. mol -1 (recommended value 72.6±0.3)

Applications of the The Correlation-Gas Chromatographic Method Objectives: To go where no one else has gone 1)Evaluation of the vaporization enthalpies of large molecules

Experimental retention times for n-C 14 to C 20 : A: Determination of Vaporization Enthalpy

Enthalpy of Transfer Determination for Hexadecane ln(t o /t a ) = -  g sln H m (T m )/R*1/T + intercept  sln g (T m ) * J mol -1 = kJ mol -1

Equations for the temperature dependence of ln(t o /t a ) for C 14 to C 20 where t o = 1 min: ln(t o /t a ) = -  g sln H m (T m )/R*1/T + intercept

Vaporization enthalpies (in kJ mol -1 ) of the n- alkanes (C 14 to C 20 ):  l g H m ( K) = (1.424  0.019)  sln g H m (T m ) – (3.98  0.35); r 2 =  1.1 ? 81.4unknown

Correlations between vaporization enthalpy at T = K against the enthalpy of transfer

Some Details Concerning the Advantages and Limitations of Correlation-Gas Chromatography 1. The method works well on hydrocarbons and hydrocarbon derivatives regardless of the hydrocarbon structure 2. With hydrocarbon derivatives, standards need to be chosen with the same number and type of functional group as the compound(s) to be evaluated unless demonstrated otherwise 3. Measurements can be made on small sample sizes and purity is not generally an issue 4. Correlation of the standards needs to be documented experimentally 5. The results are only as good as the quality of the standard data 6. Vaporization enthalpies and liquid vapor pressures are obtained for materials that are solid at room temperature 7. Correlations of enthalpies of transfer with vaporization enthalpies at T = K is arbitrary. The correlation can be with vaporization enthalpies at any temperature.

Applications of correlation gas chromatography for the evaluation of the vaporization enthalpies of large n-alkanes. Reliable vaporization enthalpies are available up to eicosane Using the available data from heptadecane to eicosane, vaporization enthalpies were evaluated for C 21,C 22, C 23. These values in turn were used to evaluate the larger n-alkanes in a stepwise process up to C 38, most of which are commercially available. Additionally, a few other larger n-alkanes, C 40, C 42, C 48, C 50, and C 60 are likewise commercially available. These were used in conjunction with polywax as identification standards Comparisons of a few of the results with literature values was possible, most comparisons were with estimations by PERT2 a and estimated Antoine Constants b a PERT2 is a FORTRAN program written by D.L. Morgan in 1996 which includes parameters for n-alkanes from C 1 to C 100 and heat of vaporization and vapor pressure correlations. Morgan, D. L.; Kobayashi, R. “Extension of Pitzer CSP models for vapor pressures and heats of vaporization to long chain hydrocarbons,” Fluid Phase Equilibrium 1994, 94, b Kudchadker, A. P.; Zwolinski, B. J. “Vapor Pressures and Boiling Points of Normal Alkanes, C 21 to C 100,” J. Chem. Eng. Data 1966, 11,

A partial isothermal GC trace of a mixture of Polywax 1000 spiked with n-alkanes C 42, C 50 and C 60 run at T = 648 K C 60 An Partial Isothermal Chromatogram of Polywax 1000

The vaporization enthalpies at T = for C 5 to C 92. N represents the number of carbon atoms. The solid line was derived using the recommended vaporization enthalpies of C 5 to C 20 The empty circles are values calculated values using the program PERT2 The solid circles are values evaluated from correlations of  sln g H m (T m ) with  l g H m (298.15K). Vapor pressures and Vaporization Enthalpies of the n Alkanes from C78 to C92 at T = K by Correlation–Gas Chromatography, Chickos, J. S.; Lipkind, D. J. Chem.Eng. Data 2008, 53, 2432–2440. curvature Since these vaporization enthalpies were obtained by extrapolation, it is likely that the actual curvature is greater as evaluated by PERT2

Vaporization Enthalpies at T/K = Enthalpies of transfer at T/K = 676 A comparison of the curvature observed in vaporization enthalpy vs the enthalpy of transfer More curvature is observed with vaporization enthalpy than with enthalpy of transfer

N  l g H m ( K) kJ mol -1 N  l g H m ( K) kJ mol -1 N  l g H m ( K) kJ mol -1 N  l g H m ( K) kJ mol ± ± ± ± ± ± ± ±5.7 b ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±1.4 b ± ± ± ± ± ± ± ± ± ± ± ±5.4 b ± ±4.5 The Vaporization Enthalpies of the n-Alkanes at T = K As A Function of the Number of Carbon Atoms, N How is it possible to measure a vaporization enthalpy greater that a C-C bond strength (~335 kJmol -1 )?

Values of at Δ sln g H m (449 K) and Δ l g H m (449 K) on an SPB-5 Column T m = 449 K -slope/T intercept Δ sln g H m (449 K) Δ l g H m (449 K) kJ  mol -1 kJ  mol -1 lit 1 calcd (eq 1) tetradecane ± ± ± ±0.8 pentadecane ± ± ± ±0.8 hexadecane ± ± ± ±0.9 heptadecane ± ± ± ±0.9 octadecane ± ± ± ±1.0 nonadecane ± ± ± ±1.0 eicosane ± ± ± ±1.1  g l H m (449 K)/kJ  mol -1 = (1.098  )  sln g H m (449 K) - (1.39  0.25) r 2 = (1) 1 Ruzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermal data Between the Triple Point and Normal Boiling Temperatures for n-Alkanes C 5 -C 20. J. Phys. Chem. Ref. Data 1994, 23, Vapor pressures and vaporization enthalpies for C 14 to C 20 are known over a large temperature range.  g l H m (T m ) and Δ sln g H m (T m ) correlate at any temperature  sln g H m (T m ) =  l g H m (T m ) +  sln H m (T m )  sln H m (T m ) must be of opposite sign to  l g H m (T m )

 l g H m (509 K)/kJ  mol -1 = (1.062  0.004)  sln g H m (509 K) + (  0.07) r 2 = Values of at Δ sln g H m (509K) and Δ l g H m (509 K) on an SPB-5 Column -slope T intercept Δ sln g H m (509 K) Δ l g H m (509 K) kJ ⋅ mol -1 kJ ⋅ mol -1 lit 1,2 calcd heptadecane ± ± ± ±0.3 octadecane6489.9± ± ± ±0.3 nonadecane6901.0± ± ± ±0.3 eicosane ± ± ± ±0.3 heneicosane7670.9± ± ± ±0.3 docosane ± ± ± ±0.4 tricosane8451.1± ± ± ±0.4 1 Ruzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermal data Between the Triple Point and Normal Boiling Temperatures for n-Alkanes C 5 -C 20. J. Phys. Chem. Ref. Data 1994, 23, Chickos, J. S.; Hanshaw, W. Vapor pressures and vaporization enthalpies of the n-alkanes from C 21 -C 30 at T = K by correlation–gas chromatography, J. Chem. Eng Data 2004, 49,

-Δ sln g H m (449 K) -Δ l g H m (449 K) (lit) Δ sln H m (449 K) kJ ⋅ mol -1 tetradecane -53.2± ±0.8 pentadecane -56.4± ±0.6 hexadecane -60.3± ±0.5 heptadecane -63.3± ±0.5 octadecane -66.6± ±0.6 nonadecane -70.3± ±0.6 eicosane -74.2± ±0.7 -Δ sln g H m (509 K) -Δ l g H m (509 K) (lit) Δ sln H m (509 K) kJ ⋅ mol-1 heptadecane -50.8± ±0.7 octadecane -54.0± ±0.5 nonadecane -57.4± ±0.5 eicosane -60.4± ±0.5 heneicosane -63.8± ±0.5 docosane -67.1± ±0.6 tricosane -70.3± ±0.7  g sln H m (T m ) =  l g H m (T m ) +  sln H m (T m ) Enthalpies of Condensation: -  sln g H m (T), -  l g H m (T) and  sln H m (T) as a Function of Temperature

Figure. The effect of temperature, 450, 509, 539 K, on the magnitude of  sln H m (T/ K). ■, eicosane; ●, nonadecane.

Conclusions: 1.The enthalpy of interaction of analyte with the column is endothermic and a function of temperature; this allows access to the measurement of large vaporization enthalpies 2.The overall enthalpy of condensation on the column is still highly exothermic, just less so then might have been imagined

Graduate Students William Hanshaw Patamaporn Umnahanant Hui Zhao Dmitry Lipkind Visiting Graduate Students Manuel Temprado, Instituto de Química Física “Rocasolano”, Madrid 28006, Spain Visiting Faculty and Collaborators Maria Victoria Roux, On leave from the Instituto de Química Física “Rocasolano”, Madrid 28006, Spain Sergey Verevkin, University of Rostock, Rostock Germany

Brad Hart Jack Uang Don Hesse Sid Kamath Sarah Hosseini