Each of the carbons in ethane is surrounded by four atoms in a roughly tetrahedral geometry; each carbon in ethene is surrounded by three atoms in a trigonal planar geometry and each carbon in acetylene by two atoms in a linear geometry. These structures can be rationalized by suggesting that the valence 2s and 2p orbitals of carbon are able to combine either to produce four equivalent sp³ hybrids directed toward the four corners of a tetrahedron, or three equivalent sp² hybrids directed toward the corners of an equilateral triangle with a p orbital left over, or two equivalent sp hybrids directed along a line with two p orbitals left over. The 2p atomic orbitals extend farther from carbon than the 2s orbital. Therefore, sp³ hybrids will extend farther than sp² hybrids, which in turn will extend farther than sp hybrids. As a consequence, bonds made with sp³ hybrids should be longer than those made with sp² hybrids, which should in turn be longer than those made with sp hybrids.

a. Obtain equilibrium geometries for ethane, ethene, and acetylene using the HF/6-31G* model. Is the ordering in C―H bond lengths what you expect on the basis of the hybridization arguments? Using the C―H bond length in ethane as a standard, what is the percent reduction in C―H bond lengths in ethene? In acetylene?

b. Obtain equilibrium geometries for cyclopropane, cyclobutane, cyclopentane, and cyclohexane using the HF/6-31G* model. Are the C―H bond lengths in each of these molecules consistent with their Incorporating sp³-hybridized carbons? Note any exceptions.

c. Obtain equilibrium geometries for propane, propene, and propyne using the HF/6-31G* model. Is the ordering of bond lengths the same as that observed for the C―H bond lengths in ethane, ethene, and acetylene? Are the percent reductions in bond lengths from the standard (propane) similar (±10%) to those seen for ethene and acetylene (relative to ethane)?