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Liquid Sulfur 101 S20, S15>S18>S11, S13, S14, S16, S17, S21, S22>S23. Larger rings, though present, could not be determined quantitatively [93]. The chemical equilibria S8 Ð8=nSn ð12Þ are governed by the Gibbs energy DGo=DHoT·DSo. At higher temperatures the entropy term favors the rings smaller than S8 since DSo will be positive in these cases and T·DSo overcompensates the always positive term DHo re- sulting in a negative value of DGo. The rings larger than S8 are thermody- namically unfavorable and their concentrations remain small at all tempera- tures; only the entropy of mixing may work in favor of them. However, since a large number of different ring sizes is possible including an increasing number of different conformations of the same ring size they cumulatively contribute substantially to the concentration of p-sulfur. The missing “rest” of the 100% assay in the last column of Table 3 is attributed to the soluble rings with more than 23 atoms as well as to analytical errors [93]. In principle, one would also expect the homocyclic S5 to be present in hot sulfur melts but this species may be too unstable to survive the quenching and extraction procedure since never has ever a peak at the expected reten- tion time been observed. However, according to Rau et al. [94] saturated sul- fur vapor contains only 0.7 mol% S5 but 20% S6 and 12% S7 at 200 C. At higher temperatures the melt will also contain traces of S4, S3 and S2 [61]; see also the next section. The sum of the concentrations of the non-S8 rings at 116 C is 4.87%, practically identical to the concentration of p-sulfur as de- rived from the freezing point depression (see above), thus confirming the re- liability of the HPLC analysis. The data in Table 3 have been used to calculate the enthalpies of forma- tion of the various rings in liquid sulfur from S8 using Eq. (12). From these enthalpies the mean bond energies of the sulfur homocycles were derived. The differences of these mean bond energies to the value of S8 (266.6 kJ mol1 [95]) are shown in Fig. 3 [93]. As can be seen, S12 and the rings larger than S17 are most stable (besides S8) with mean bond energies of just 1 kJ mol1 below that of S8. Of the smaller rings S6 seems to be most strained but even in this case the difference in bond energies of ca. 4 kJ mol1 is only 1.5% of the total bond energy. Density functional calcula- tions confirmed that the mean bond energies of sulfur rings larger than S12 are practically identical [96]. Ludwig et al. have tried to model the composition of liquid sulfur by quantum-chemical calculations [97] which is not accurately possible since the polymeric molecules—a major component above 159 C—cannot be cal- culated. Therefore, the results are of little use and no novel insights were achieved. The critical parameters of sulfur have been determined as follows: Tc=1313 K, pc=179.7 atm (18.2 MPa), rc=0.563 g cm3 [98]; Tc=1313 K, pc=20.3 MPa, rc=0.58 g cm3 [99].PDF Image | Topics in Current Chemistry
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