BATCH: je1a04 USER: jeh69 DIV: @xyv04/data1/CLS_pj/GRP_je/JOB_i01/DIV_je0301747 DATE: October 17, 2003 1 Vapor Pressures and Vaporization Enthalpies of the n-Alkanes from 2 C21 to C30 at T ) 298.15 K by Correlation Gas Chromatography 3 James S. Chickos* and William Hanshaw 4 Department of Chemistry and Biochemistry, University of MissourisSt. Louis, St. Louis, Missouri 63121 5 6 The temperature dependence of gas chromatographic retention times for n-heptadecane to n-triacontane 7 is reported. These data are used to evaluate the vaporization enthalpies of these compounds at T ) 298.15 8 K, and a protocol is described that provides vapor pressures of these n-alkanes from T ) 298.15 to 575 9 K. The vapor pressure and vaporization enthalpy results obtained are compared with existing literature 10 data where possible and found to be internally consistent. Sublimation enthalpies for n-C17 to n-C30 are 11 calculated by combining vaporization enthalpies with fusion enthalpies and are compared when possible 12 to direct measurements. 13 14 Introduction 15 The n-alkanes serve as excellent standards for the 16 measurement of vaporization enthalpies of hydrocarbons.1,2 17 Recently, the vaporization enthalpies of the n-alkanes 18 reported in the literature were examined and experimental 19 values were selected on the basis of how well their 20 vaporization enthalpies correlated with their enthalpies of 21 transfer from solution to the gas phase as measured by gas 22 chromatography.3 A plot of the vaporization enthalpies of 23 the n-alkanes as a function of the number of carbon atoms 24 is given in Figure 1. The plot is remarkably linear from C5 25 to C20 but does show some curvature above C20. This 26 curvature was explained on the basis of a systematic error 27 in adjusting the vaporization enthalpies of the n-alkanes, 28 C21 to C28 and C30, found in the literature, from the 29 temperature of measurement to T ) 298.15 K.3 Since these 30 n-alkanes exhibit very low vapor pressures at ambient 31 temperatures, vapor pressure measurement for most of 32 these materials were conducted at temperatures that 33 required a significant temperature adjustment to T ) Figure 1. Vaporization enthalpies of the n-alkanes; the straight 34 298.15 K. This temperature adjustment ranged from 9.3 -1 3 line represents the results obtained by a linear regression analysis 35 to 51.9 kJ‚mol . In view of this curvature and our 11 of the recommended vaporization enthalpies of n-C5 to C20. 36 continuing interest in using the larger n-alkanes as stan- 37 dards for correlation gas chromatography measurements standards have usually been chosen at T ) 298.15 K, but 55 38 (c-gc), we have reexamined these values and would like to the correlation works for other temperatures as well. The 56 39 report the results of our measurements of both vaporization g linear correlation that is observed between ∆sln Hm and 57 40 enthalpy and vapor pressure at T ) 298.15 K. The results g ∆l Hm is empirical and can be criticized as lacking a 58 41 of our c-gc experiments of the n-alkanes from C21 to C30 theoretical basis. In this article we would like to provide a 59 42 were obtained using a method best described as a steplad- simple mathematical basis for the linear correlation ob- 60 43 der extrapolation. The results of this stepladder approach served. The correlation is applied to the evaluation of vapor 61 g 44 are tested by comparison of ∆l Hm(Tm) values and vapor pressures and enthalpies of vaporization of the n-alkanes 62 45 pressures obtained by c-gc to those measured by other from C21 to C30 at T ) 298.15 K. 63 46 methods at temperatures where experimental data are 47 available. Discussion 64 48 Correlation gas chromatography has proven to be quite Enthalpies of transfer from solution to the vapor, 65 49 successful in providing vaporization enthalpies of both ∆ gH , are measured by gas chromatography by measur- 66 50 liquids and solids. The technique relies on the linear sln m ing the retention times of a mixture consisting of both 67 51 correlation observed between enthalpies of transfer from g standards and target solutes as a function of temperature. 68 52 solution to the vapor, ∆sln Hm, as measured by gas chro- g The retention times, t, are adjusted for the dead volume of 69 53 matography and the vaporization enthalpy (∆l Hm)ofa the column by measuring the retention time of an unre- 70 54 series of standards. The vaporization enthalpies of the tained solute, usually the solvent. Since the retention time 71 * To whom correspondence should be addressed. E-mail: [email protected]. of the unretained solute is governed by the flow rate of the 72 Phone: 314 516 5377. carrier, its retention time as a function of temperature 73 10.1021/je0301747 CCC: $27.50 © xxxx American Chemical Society Published on Web 00/00/0000 PAGE EST: 8.8 BATCH: je1a04 USER: jeh69 DIV: @xyv04/data1/CLS_pj/GRP_je/JOB_i01/DIV_je0301747 DATE: October 17, 2003 B Journal of Chemical and Engineering Data 74 behaves differently from those of the other solutes. The In this equation, nc refers to the number of carbon atoms. 129 75 viscosity of the carrier gas, usually He in our experiments, This equation takes the general form mnc + b. Although 130 76 increases with temperature. Thus, the retention time of this equation was derived for vaporization enthalpies at 131 77 the nonretained reference, tnrr, increases while that for the T ) 298.15 K, the temperature selection is arbitrary and 132 78 other solutes decreases with temperature. This observation it is reasonable to assume that a similar equation of the 133 79 is useful in ensuring a reliable measurement of the time same type, m′nc + b′, could also be derived for vaporization 134 80 needed to traverse the column at each temperature. The enthalpies at T ) Tm, where m′ and b′ are appropriate 135 6,7 81 adjusted retention time, ta ) t - tnrr, measures the amount constants. Vaporization enthalpies at T ) 298.15 K differ 136 82 of time the solute spends on the stationary phase, and this from those at T ) Tm by differences in the heat capacities 137 83 time is inversely proportional to the compound’s vapor of the liquid and gas phases, and both properties are known 138 8,9 84 pressure above the condensed phase. A plot of ln(1/ta) to be modeled by group additivity. In addition, vaporiza- 139 -1 85 versus 1/T (K ) results in a linear plot with a slope equal tion enthalpies at both T ) 298.15 K and T ) Tm could be 140 g 86 to -∆ slnHm(Tm)/R. This technique has been used by others, modeled exactly by these equations by simply allowing the 141 87 notably the work of Fuchs et al.,4 who pioneered the use of intercepts, b and b′, to vary. Enthalpies of solution are 142 88 enthalpies of transfer in conjunction with enthalpies of small in comparison to vaporization enthalpies10 and also 143 89 solution to evaluate vaporization enthalpies. can be modeled by group additivity, m′′nc + b′′. This 144 g 90 The term ∆ slnHm(Tm) can be equated in a thermody- modeling can also be exact if b′′ is allowed to vary. 145 91 namic cycle to the sum of the vaporization enthalpy Substituting these linear functions into eq 3 and combining 146 92 measured at T ) Tm and the enthalpy of solution or similar terms results in eq 5, where msln ) (m′ + m′′) and 147 93 adsorption (∆slnHm) of each solute on the stationary phase bsln ) (b′ + b′′). 148 94 of the column as shown below. The sensitivity of the flame 95 ionization detector ensures dilute concentrations of solute, ) + + slope [mslnnc bsln]/[mnc b] (5) 96 and since the solute dissolves in the stationary phase, the 97 same thermodynamic cycle applies to both solids and As long as bsln and b are small in comparison to mslnnc and 149 98 liquids. g mnc, respectively, the correlation of ∆sln Hm(Tm) with 150 ∆ gH (298.15 K) will be linear because the ratio [m n + 151 ∆g H (T ) ) ∆g H (T ) + ∆ H (T ) (1) l m sln c sln m m l m m sln m m bsln]tranfer/[mnc + b]vap is a hyperbolic function approaching 152 its asymptote, msln/m. Similar arguments can also be made 153 g 99 Peacock and Fuchs measured ∆ slnHm(Tm) values of a for hydrocarbon derivatives containing a single functional 154 100 series of compounds by gas chromatography and adjusted group or multiple functional groups provided the number 155 101 the results for temperature. They combined enthalpies of and type of functional groups in the correlation are kept 156 102 vaporization and solution in the liquid stationary phase constant. Alternatively, the hydrocarbon portion can be 157 103 of the column, DC 200, and compared their results to kept constant and the number of identical functional 158 g ) 104 ∆ slnHm(Tm) values adjusted for temperature to T 298.15 groups varied. In either of these instances, it would be 159 105 K. The thermochemical cycle yielded results that were not necessary to define nc differently. 160 106 exactly identical but were very similar and were linearly 4 107 correlated. Experimental Section 161 g 108 In correlation gas chromatography, ∆ slnHm(Tm) values All n-alkanes were purchased from the Aldrich Chemical 162 109 are correlated directly with the vaporization enthalpies of Co.