Thermodynamics

71. A recent article focuses on the energy required to rotate about a C=C bond. Kinetics studies give the activation enthalpy and entropy of the processes shown. [Note: rotation about the central double bond is made feasible by resonance stabilization of the 90°- twisted biradical.] Your task is to calculate the thermodynamics (deltaH) for 1 going to 2 and for 3 going to 4. Compare your calculated deltaH values with those in Tables III and IV of the reference. Note that structure 3 represents two compounds: a racemic isomer (in which the squiggle H is up) and a meso isomer (H down); these give, respectively, racemic 4 (H down) and meso 4 (H up).

89. Calculate deltaH for the thermal valence isomerization of 1,6-methano[10]annulene (the parent compound with both X's = H) to its tricyclic isomer. Do the same for the bridged compounds in which -X-X- is either -CH₂CH₂- or -CH=CH-. Discuss the variation in deltaH as a function of substituents; compare your answers with those given (calculated and experimental) in the cited article.

91. Heats of hydration of alkenes to alcohols provide the same information about the relative stability of alkenes as is obtained from heats of hydrogenation. Use MM to calculate deltaH for the following isomerizations, each of which is a measure of the relative energies of disubstituted vs. trisubstituted alkenes; do the calculation for the acyclic model and for the cyclic compounds in which n = 2, 3, or 4. Compare your answers with those in the article; discuss any differences.

114. Triquinacene (shown to the right) undergoes stepwise addition of three H₂ molecules. The first hydrogenation step is unexpectedly less exothermic than the second and third. The authors cited have done MM and other calculations in an effort to explain this. Your task is to do the MMX calculations on triquinacene and its di-, tetra-, and hexahydro derivatives; to compare your energies, bond distances, dihedral angles, etc. with those in the reference; and to see if you can explain the anomalous heat of hydrogenation.

118. A recent paper presents new heats of hydrogenation data for the complete hydrogenation of 1,3,5-hexatriene (E and Z) as well as for all of the hexadienes: 1,3- hexadiene, 1,4-hexadiene, 1,5-hexadiene, 2,4-hexadiene in all of their stereoisomeric forms. From these data are calculated new values for the heats of formation of these various conjugated and unconjugated compounds. This problem requires performing MMX calculations on all of these compounds (plus hexane, the common hydrogenation product) and from these determining the heats of formation and heats of hydrogenation. Compare your results with the experimental values and discuss any differences.

175. Shown to the right are 1,3,5-cycloheptatriene (tropilidene) and Z-1,3,5-hexatriene. A recent article uses heat of hydrogenation data to argue for 1,6-homoconjugation in the cyclic molecule. Compute the heats of formation for these compounds and for every one of their mono-, di-, and tri-hydrogenation products; compute, also, the heats of formation corrected for strain (see Table I in the article). Discuss the importance of 1,6-overlap in tropilidene.

229. A recent article describes models for fullerenes (of which the most famous is "Buckyball" C₆₀) that are fused six/five aromatic compounds. Compute the heats of hydrogenation (with one or two equivalents of H₂) for the aromatic compounds shown to the right, leading to compounds 1 or 2, 3 or 4, and 9 or 10 (these compound numbers coming from the cited reference). Compare your results with the published values.

239. A recent experimental study of heats of hydrogenation of styrene and its various mono- methyl derivatives allowed an accurate estimate of the heats of formation of these and related unsaturated compounds. Use MMX calculations to determine these heats of hydrogenation; compare your results with the experimental and calculated numbers in the cited article (Table 5).

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