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

Applications of the Correlation-Gas Chromatographic Method Objectives: To go where no one else has gone 1. Evaluation of the vaporization enthalpies of large molecules 2.Application of Correlation-Gas Chromatography to a Tautomeric Mixture –Acetylacetone 3. Evaluation of the Vaporization Enthalpy of Complex Hydrocarbon Mixtures

VAPORIZATION ENTHALPIES OF COMPLEX MIXTURES The use of gas-chromatography to measure the vaporization enthalpy of complex hydrocarbon mixtures Vaporization Enthalpies of High Energy Density Fuels for Aerospace Propulsion RP-1, JP-7, JP-8

Why is it important to know the ∆ l g H m ( K) of complex mixtures as found in aviation fuels? The most obvious role for aviation fuel in advanced aircraft is for propulsion. A second and increasingly important role is as an airframe coolant in supersonic aircraft. Recently there has been an interest in finding endothermic fuels which initially undergoes an endothermic reaction to form secondary products that are subsequently used for propulsion.

RP-1 (Rocket Propellant 1) Refined petroleum, a mixture of complex hydrocarbons

A GC plot of RP-1 without standards Compound number distribution for RP-1 without standards

Physical properties of RP-1 Approx. formula C 12 H 23.4 Boiling range (F) Freezing point (F) -56 Flash point (F) 155 Net heating value (btu/lb) 18,650 Specific gravity (70F) Critical T (F) 770 Critical P (psia) 315 Preliminary composition n-paraffins (wt%) 2.1 i-paraffins 27.1 naphthenes 62.4 aromatics 8.4

Application of the GC method to a complex mixture For a mixture of i structurally related components, the following relationship applies: ln(t o /t 1 ) = ln(A 1 )-  sln g H m (T m ) 1 /RT ln(t o /t 2 ) = ln(A 2 )-  sln g H m (T m ) 2 /RT … ln(t o /t i ) = ln(A i )-  sln g H m (T m ) i /RT Multiplying each component by its mole fraction, n i and summing over all i components result in the following equation: ∑ n i  ln(t o /t i ) = ∑ n i  ln(A i )- ∑ n i   sln g H m (T m ) i /RT A plot of ∑ n i  ln(t o /t i ) versus 1/T should result in a straight line with a slope of -  sln g H m (T m ) mix. When several structurally related standards are included in the mixture, a plot of ln(t o /t i ) versus 1/T for each standard should also result in a linear plot. The  sln g H m (T m ) term for each standard can be correlated to its respective vaporization enthalpy. From the correlation equation and  sln g H m (T m ) mix of the mixture, the vaporization enthalpy of the ensemble,  l g H m (T m ) mix, can be determined. This assumes that the enthalpy of mixing is small

A GC Plot of RP-1 with 6 Standards RP-1 with standards: 1. n-octane 2. nonene 3. n-decane 4. naphthalene 5. n-dodecane 6. n-tridecane

A plot of natural logarithm of the reciprocal adjusted retention times for (top to bottom): ,n- octane; , nonene; , n-decane; , naphthalene; , n-dodecane; , n-tridecane.

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 )= ( /T) + ( ± 0.008) r 2 = nonene ln(t o /t a )= ( /T) + ( ± 0.010) r 2 = n-decane ln(t o /t a )= ( /T) + ( ± 0.010) r 2 = naphthalene ln(t o /t a )= ( /T) + ( ± 0.008) r 2 = n-dodecane ln(t o /t a )= ( /T) + ( ± 0.010) r 2 = n-tridecane ln(t o /t a )= ( /T) + ( ± 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

A demonstration of the application of the method for a 1:1 molar mixture of n-Octane and n-Tridecane A demonstration of the application of the method for a 1:1 molar mixture of n-Octane and n-Tridecane Vaporization enthalpy of n-Octane = 41560J/mol Vaporization enthalpy of n-Octane = 41560J/mol Vaporization enthalpy of n-Tridecane = 67062J/mol Vaporization enthalpy of 1:1 Mixture = 54120J/mol Vaporization enthalpy of 1:1 Mixture = 54120J/mol (assume ideal mixing) [0.5× ×67062] (assume ideal mixing) [0.5× ×67062]

For a 1:1 mixture of n-Octane and n Tridecane ∑n i ln(t o /t i )= ∑n i ln(A i )- ∑n i  sln g H m (T m ) i /RT ∑n i  ln(t o /t i )= ∑n i  ln(A i )- ∑n i   sln g H m (T m ) i /RT T/K (1/T) K -1 ln(t o /t a )  n i ln(1/t i ) (n i = 0.5) T/K (1/T) K -1 ln(t o /t a )  n i  ln(1/t i ) (n i = 0.5) n-octane n-decane n-octane/n- tridecane n-octane n-decane n-octane/n- tridecane

∑n i ln(t o /t i )= ± – 4954/T (1:1 octane: tridecane) ∑n i  ln(t o /t i )= ± – 4954/T (1:1 octane: tridecane)

 l g H m ( K) = (1.444  0.092)  sln g H m (368 K) – (4818  746); r 2 =  l g H m ( K) vs  sln g H m (368 K) for the remaining standards A plot of  l g H m ( K) vs  sln g H m (368 K) for the remaining standards dodecane naphthalene decane nonene

Vaporization enthalpies calculated for the standards and for 1:1 mixture of n-Octane/n-Tridecane a  sln g H m (368 K)  l g H m ( K) lit  l g H m ( K) Calcd [eq (2)] nonene ±5.0 decane ±5.2 naphthalene ±5.3 dodecane ±5.7 1:1 mixture of n-octane/ n-tridecane ± b  l g H m ( K) = (1.444  0.092)  sln g H m (368 K) – (4.82  3.7); r 2 = (2)  l g H m ( K) = (1.444  0.092)  sln g H m (368 K) – (4.82  3.7); r 2 = (2) a enthalpies in kJ /mol a enthalpies in kJ /mol b calculated for a 1:1 mixture of n-octane/n-tridecane b calculated for a 1:1 mixture of n-octane/n-tridecane

Approximation of the Mol Fraction 8 C 13C FID detector response is proportional to the number of carbon atoms

DETECTOR BIAS The observed correlation between the number of carbon atoms present in the standards and the natural logarithm of their adjusted retention time at T = 364 K. The point that falls off the line is naphthalene, all others are n-alkanes/alkenes. The area of each peak was adjusted for carbon number based on its retention time. mol fraction = area(i)/[N c (i)/Σ i area i /N c (i) where N c = ln(1/t a )

The slopes, intercepts, enthalpies of transfer, and enthalpies of vaporization of the standards and those calculated for RP-1; enthalpies in kJ. mol -1 a adjusted for detector bias SlopeIntercept  sln g H m (368 K)  l g H m ( K) lit  l g H m (298.15K) calcd octane   nonene   decane   naphthalene   dodecane   tridecane   RP    1.2 RP-1 a    1.2  l g H m ( K)/kJmol -1 = (1.472  0.041)  sln g H m (368 K) –(5.145  0.59); r 2 =0.9970

STANDARDS CHOSEN FOR JP-7 Samples of JP-7 and JP-8 already contain substantial amounts of n-alkanes as identified by GCMS and retention time studies. n-Undecane, n-dodecane, n- tridecane, and n-tetradecane were identified and used as internal standards for JP-7 C 11 C 12 C 13 C 14

STANDARDS CHOSEN FOR JP-8 n-decane through to n-pentadecane were similarly identified and used as standards in JP-8. Similar in composition to Jet A used in commercial aviation C 11 C 12 C 13 C 14 C 15

 l g H m ( K) kJ. mol -1 Approximate Formula Mass a g. mol -1  l g H m ( K) kJ. kg -1 calcd  l g H m ( K) kJ. kg -1 (lit) RP-1 C 12 H , 246 b JP-7 C 12 H c JP-8 C 11 H A comparison of vaporization enthalpies of RP-1, JP-7, and JP-8 with literature values a reference Edwards, T. “Kerosene Fuels for Aerospace Propulsion-Composition and Properties” b reference CPIA Liquid Propellant Manual c reference “Aviation Fuel Properties” CRC Report No 530, Society of Automotive Engineers, Inc.

The vaporization enthalpy of JP-10, A High Energy Density Rocket Fuel

The enthalpies of vaporization and sublimation of exo- and endo- tetrahydrodicyclopentadienes at T = 298:15K Chickos,J. S.; Hillesheim, D.; Nichols, G. J. Chem. Thermodyn. 2002, 34, 1647–1658. ∆ g l H m ( K) exo-THDCPD49.1 ± 2.3 endo-THDCPD50.2 ± 2.3

RJ-4 A High Energy Density Rocket Fuel Standards Used decane exo-tetrahydrodicyclopentadiene endo-tetrahydrodicyclopentadiene n-tetradecane  l g H m ( K) = 55.3 ± 1.0 kJ/mol Chickos, J.S. Wentz, A. E.; Hillesheim-Cox, D. Zehe, M. J. Ind. Eng. Chem. 2003, 42,

Acknowledgments Tim Edwards, Wright Patterson Air Force Base W. Hanshaw, P. Umnahanant, and D. Hillesheim-Cox Solutia STARS program support for A. E. Wentz. Fundacāo para a Ciệncis e a Tecnologia (Portugal) support for D. Hillesheim-Cox NASA NASA