Knowledge Bank

Tentative vibrational frequency assignments have been made for a number of polymethylbenzenes so that the thermodynamic functions of systems containing these compounds could be computed by statistical mechanical methods. All of the methylbenzenes for which vibrational assignments had not previously been made were included: namely, 1, 2, 3-trimethylbenzene, 1, 2, 4-trimethylbenzene, the three tetra-methylbenzene isomers, pentamethylbenzene and hexamethylbenzene. A minor change in the assignment of the 1,2$\cdot$dimethylbenzene frequencies by Pitzer was also made. Pitzer’s modification of the Teller$\cdot$Redlich product rule (Pitzer and Scott, JACS, 65, 803 (1943)) was employed extensively to aid in all of the assignments. The translational and free rotational contributions to the various thermodynamic functions were computed according to the method outlined by Taylor (Taylor, Wagman, Williams, Pitzer and Rossini, J. Res. N.B.S., 37, 95 (1946)). The vibrational contributions were calculated on the IBM 650 electronic computer using the harmonic oscillator expressions given by Taylor and Glasstone (""""Treatise on Physical Chemistry"""" p. 654 (1942)). These data were then combined to yield the thermodynamic functions uncorrected for the effect of restricted rotation. The value of the barrier assigned by Taylor, et al., for isolated methyl groups in methylbenzene, 1,3-dimethylbenzene and 1,4-dimethylbenzene (750 cal./mole) was accepted. The value of 2100 cal./mole assigned to adjacent methyl groups (as in 1,2-dimethylbenzene) appears to be too high based upon our vibrational assignment for 1,2,4-trimethylbenzene and the recent experimental entropy for this compound by Kilpatrick (Southwest Regional Meeting ACS, Houston, Texas (Dec. 1955)). A value of 1400 cal./mole appears to be more reasonable. Employing this barrier for the outside methyl groups in 1,2,3-trimethylbenzene and the experimental entropy for this compound by Kilpatrick one obtains a barrier of 3200 cal./mole for the central methyl group. This is to be contrasted with the value of 750 cal./mole for this methyl group assumed by Taylor, et al. These barriers were employed to obtain the restricted rotation contributions for the three tetramethylbenzenes, pentamethylbenzene and hexamethylbenzene (e.g., six 3200 cal./mole barriers were used for hexamethylbenzene). On the basis of these assignments thermodynamic equilibria were calculated for the tri-and tetramethylbenzenes at several temperatures. The calculated equilibria are compared with experimental data at two temperatures below: [FIGURE] Although no definitive estimates of error have yet been made, it is believed that the differences shown above will fall within these error limits and that further refinements in the vibrational assignments would not affect the results significantly.