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CORRESPONDENCE Comment on “Critical Properties, Normal Boiling Temperatures, and Acentric Factors of Fifty Ionic Liquids” Robert G. Jones,* Peter Licence, Kevin R. J. Lovelock, and Ignacio J. Villar-Garcia Department of Physical Chemistry, School of Chemistry, UniVersity of Nottingham, UniVersity Park, Nottingham, NG7 2RD, United Kingdom Sir: In the paper by Valderrama and Robles1 (this set of authors is abbreviated hereafter as VR), the critical properties, normal boiling temperatures, and acentric factors of 50 ionic liquids (ILs) have been determined using an extended group contribution method that is based on the concepts of Lydersen2 and Jaback and Reid3 and modified by Alvarez and Valderrama.4 In this correspondence, we compare seven of the boiling temperatures calculated by VR with values derived from the heats of vaporization experimentally determined by Jones and Licence (abbreviated hereafter as JL),5 which have only recently become available. This comparison indicates that the boiling temperatures of ILs are not well-predicted by the method used by VR, and, by inference, the critical properties and acentric factors are also likely to be in error. The reason is thought to be non-inclusion of the Coulombic energy in IL. JL determined the heats of vaporization (∆vapH298) of eight ILs, using line-of-sight mass spectroscopy to monitor the temperature programmed desorption profiles of thin films of the ILs under ultrahigh vacuum (UHV) (p < 10-9 mbar). The desorption profiles exhibited zero-order desorption kinetics, as expected for multilayer desorption, and the subsequent analysis yielded the enthalpies of vaporization, corrected to 298 K. Table 1 shows these ∆vapH298 values, together with the temperatures at which the zero-order desorption peak for each IL reached a maximum pressure (Tpeak). (These pressures were in the region of 10-7 mbar.) Although the exact value of Tpeak is dependent on the thickness of the IL thin film, it is indicative of the boiling temperature, under UHV conditions. The normal boiling points calculated by VR for seven of these ILs are also shown in Table 1. A comparison of the experimental Tpeak(JL) values with the Tb(VR) values shows that the Tb(VR) values do not correlate with the behavior of the Tpeak values. For instance, for [C8MIm]BF4,6 the calculated Tb value (576.1 K) is only 27 K higher than the experimental Tpeak value of 549 K, whereas, for [C8MIM]Tf2N,6 the highest calculated Tb value (943.4 K) is some 455 K above the experimental Tpeak value of 488 K. The small difference between the boiling temperature in UHV (Tpeak) and the calculated boiling temperature (Tb(VR)) for [C8MIM]BF4 is particularly surprising, because the boiling point of a liquid is pressure-dependent and the normal boiling point given by VR is defined at an applied pressure of 1 atm. Therefore, we have an apparent increase in boiling temperature of only 27 K for a factor of 1012-1015 * To whom correspondence should be addressed. Tel.: 44 (0)115 9513468. Fax: 44 (0)115 9513562: E-mail: robert.g.jones@ nottingham.ac.uk.
Table 1. From ref 5 (JL) cationa
aniona
[C2MIm]+
EtSO4Tf2NTf2NTf2NTf2NBF4PF6CF3SO3-
[C2MIm]+ [C4MIm]+ [C6MIm]+ [C8MIm]+ [C8MIm]+ [C8MIm]+ [C8MIm]+ a
Tb (K)
∆vapH298 Tpeak from from ref 5 (JL) (kJ/mol) (K) ((5 K) ref 1 (VR) ((10%) 164(4) 134(2) 134(3) 139(2) 149(2) 162(3) 169(4) 151(3)
523 445 476 484 488 549 555 527
702.1 806.1 851.8 897.6 943.4 576.1 635.5
1070 910 910 930 990 1060 1100 1000
See ref 6 for key to acronyms.
increase in pressure, which is not physically possible for any reasonable value for the heat of vaporization. We now estimate the Tb values from the experimental ∆vapH298 values of JL for comparison with the Tb(VR) values. Trouton’s rule7-9 relates the normal boiling point at a pressure of 1 atm to the enthalpy of vaporization at the normal boiling point (∆vapHTb) and Trouton’s constant (∼85 J K-1) mol-1.
∆vapHTb ≈ 85 Tb
(1)
To convert the experimental values of ∆vapH298 to ∆vapHTb requires the difference in heat capacity at constant pressure (∆gl CP ) CP,g - CP,l) between the IL in the vapor (CP,g) and liquid (CP,l) phases. This value has been estimated at -94 J K-1 mol-1 for [C4MIm]Tf2N.10 Using this constant value for all the ILs and inserting into Trouton’s rule gives
∆vapH298 - 94(Tb - 298) ≈ 85 Tb
(2)
Solving eq 2 for Tb using the appropriate ∆vapH298 values for the eight ILs gives the Tb(JL) values shown in Table 1. It is difficult to estimate the error in these Tb values; however, it will be in the region of (10%. There is very little correlation between the Tb(VR) and Tb(JL) values. In particular, the Tb(JL) values always exceed the corresponding Tb(VR) values; however, the difference can be as little as ∼30 K (for [C6MIm]Tf2N) or as large as ∼480 K (for [C8MIm]BF4). Note that, for highly ordered liquids, such as molten salts, Trouton’s constant is expected to be larger,11 reaching a value of perhaps 100 J K-1 mol-1. This has the effect of reducing the calculated Tb values by ∼10%. Because of the fact that 10% is approximately
10.1021/ie070413+ CCC: $37.00 © 2007 American Chemical Society Published on Web 06/23/2007
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Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007
the level of error in the Tb(JL) values, the choice of Trouton’s constant is already within the error of our calculation. We now inquire about the cause of the discrepancy in the boiling temperatures. JL have shown5 that the internal energy of vaporization, ∆vapU (expressed in units of kJ/mol) can be written as follows:
by the Lydersen-Joback-Reid method. If the LydersenJoback-Reid method can be adapted to incorporate the Coulombic interactions in ILs, then this method may yet prove to be useful in predicting the true normal boiling points, critical properties, and acentric parameters of ILs.
∆vapU ) ∆UC,0.85 + ∆Uvdw )
Literature Cited
(
)
21.967 7.9385 × 104 1+ ∆Uvdw (3) (r+ + r-) (r+ + r-) where (r+ + r-), given in units of picometers (pm), in eq 3 is given by
(r+ + r-) ) 3
x
Vm VNA3
(4)
∆UC,0.85 is the electrostatic or Coulomb contribution to the heat of vaporization and ∆Uvdw is due to the non-Coulombic contributions, which have been pulled together into one overall van der Waals contribution. The numerical value of (r+ + r-) is derived from the molar volume (Vm) of the IL and the number of ions in the molecular formula, V (for the ILs considered here, V ) 2). ∆UC,0.85 contributes 73%-95% of the value of ∆vapU for the eight ILs in Table 1,5 illustrating rather convincingly that the major cohesive energy in these ILs is Coulombic. However, the parametrized Lydersen-Joback-Reid method used by VR to estimate Tb is based on chemical groupings, with no explicit recognition of the ionic nature of the bonding in ILs. We suggest that this is the reason for the discrepancies between the Tb(VR) values and Tb(JL) values determined from the experimentally measured ∆vapH298 values. Note that the trend to increasing Tb when going from [C2MIm]Tf2N to [C8MIm]Tf2N in the JL data is reproduced in the VR data, because this is primarily an effect of increasing van der Waals interactions as the alkyl chains become longer, which is modeled quite well
(1) Valderrama, J. O.; Robles, P. A. Critical Properties, Normal Boiling Temperatures, and Acentric Factors of Fifty Ionic Liquids. Ind. Eng. Chem. Res. 2007, 46, 1338-1344. (2) Lydersen, A. L. Estimation of Critical Properties of Organic Compounds. Report 3; University of Wisconsin, College of Engineering, Engineering Experimental Station: Madison, WI, 1955. (3) Joback, K. K.; Reid, R. Estimation of Pure Component Properties from Group Contributions. Chem. Eng. Commun. 1987, 57, 233-247. (4) Alvarez, V. H.; Valderrama, J. O. A modified Lydersen-JobackReid method to estimate the critical properties of biomolecules. Alimentaria 2004, 254, 55-66. (5) Armstrong, J. P.; Hurst, C.; Jones, R. G.; Licence, P.; Lovelock, K. R. J.; Satterley, C. J.; Villar-Garcia, I. J. Vapourisation of ionic liquids. Phys. Chem. Chem. Phys. 2007, 9, 982-990. (6) [C2MIm]+ refers to the 1-ethyl-3-methylimidazolium cation. In the general [CnMIm]+ notation n ) 2, 4, 6, and 8 refers to ethyl, butyl, hexyl, and octyl groups, respectively, in the imidazolium cation. Tf2N- is the bis(trifluoromethylsulfonyl)imide ) (CF3SO2)2N- anion. (7) Atkins, P.; de Paula, J. Atkins’ Physical Chemistry, 7th Edition; Oxford University Press: Oxford, U.K., 2002; p 101. (8) Trouton, F. On a relation existing between the latent heats, specific heats, and relative volumes of volatile bodies. Nature 1883, 27, 292. (9) Trouton, F. On molecular latent heat. Philos. Mag. 1884, 18, 5456. (10) Paulechka, Y. U.; Zaitsau, Dz. H.; Kabo, G. J.; Strechan, A. A. Vapor pressure and thermal stability of ionic liquid 1-butyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)amide. Thermochim. Acta 2005, 439, 158-160. (11) Glasstone, S. Textbook of Physical Chemistry, 2nd Edition; MacMillan: New York, 1946; p 457, table 70. (Note: Trouton’s constant for KCl is 100 J K-1mol-1.)
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