1.10: sp Hybrid Orbitals and the Structure of Acetylene
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In addition to forming single and double bonds by sharing two and four electrons, respectively, carbon can also form a triple bond by sharing six electrons. To account for the triple bond in a molecule such as acetylene, \(\mathrm{H}-\mathrm{C} \equiv \mathrm{C}-\mathrm{H}\), we need a third kind of hybrid orbital, an sp hybrid. Imagine that, instead of combining with two or three \(p\) orbitals, a carbon 2 s orbital hybridizes with only a single \(p\) orbital. Two \(s p\) hybrid orbitals result, and two \(p\) orbitals remain unchanged. The two \(s p\) orbitals are oriented \(180^{\circ}\) apart on the right-left \((x)\) axis, while the \(p\) orbitals are perpendicular on the up-down \((y)\) axis and the in-out \((z)\) axis, as shown in Figure 1.16.
When two sp-hybridized carbon atoms approach each other, sp hybrid orbitals on each carbon overlap head-on to form a strong sp–sp σ bond. At the same time, the pz orbitals from each carbon form a pz–pz π bond by sideways overlap, and the py orbitals overlap similarly to form a py–py π bond. The net effect is the sharing of six electrons and formation of a carbon–carbon triple bond. Each of the two remaining sp hybrid orbitals forms a σ bond with hydrogen to complete the acetylene molecule (Figure 1.17).
As suggested by sp hybridization, acetylene is a linear molecule with H–C–C bond angles of 180°. The C–H bonds have a length of 106 pm and a strength of 558 kJ/mol (133 kcal/mol). The C–C bond length in acetylene is 120 pm, and its strength is about 965 kJ/mol (231 kcal/mol), making it the shortest and strongest of any carbon–carbon bond. A comparison of sp, sp2, and sp3 hybridization is given in Table 1.2.
Table 1.2 Comparison of C−C and C−H Bonds in Methane, Ethane, Ethylene, and Acetylene
| Molecule | Bond | Bond strength | Bond length (pm) | |
|---|---|---|---|---|
| (kJ/mol) | (kcal/mol) | |||
| Methane, \(\mathrm{CH}_4\) | \(\left(s p^3\right) \mathrm{C}-\mathrm{H}\) | 439 | 105 | 109 |
| Ethane, \(\mathrm{CH}_3 \mathrm{CH}_3\) | \(\left(s p^3\right) C-C\left(s p^3\right)\) | 377 | 90 | 153 |
| \(\left(s p^3\right) \mathrm{C}-\mathrm{H}\) | 421 | 101 | 109 | |
| Ethylene, \(\mathrm{H}_2 \mathrm{C}=\mathrm{CH}_2\) | \(\left(s p^2\right) \mathrm{C}=\mathrm{C}\left(s p^2\right)\) | 728 | 174 | 134 |
| \(\left(s p^2\right) \mathrm{C}-\mathrm{H}\) | 464 | 111 | 109 | |
| Acetylene, \(\mathrm{HC} \equiv \mathrm{CH}\) | \((s p) \mathrm{C} \equiv \mathrm{C}(s p)\) | 965 | 231 | 120 |
| \((s p) \mathrm{C}-\mathrm{H}\) | 558 | 133 | 106 | |
Draw a line-bond structure for propyne, CH3C≡CH. Indicate the hybridization of the orbitals on each carbon, and predict a value for each bond angle.
- Answer
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The CH3 carbon is sp3; the triple-bond carbons are sp; the C≡C−C and H−C≡C bond angles are approximately 180°.