The Covalent Bond

<body> <p align="center"><a name="top"><font size="6"><b>Hybrid Atomic Orbitals</b></font></a></p> <div align="center"><center><table border="1" cellpadding="2" width="500"> <tr> <td align="center"><a href="#hybrid">Hybrid Atomic Orbitals</a></td> <td align="center"><a href="#geom">Geometries of Hybrid Orbitals</a></td> </tr> <tr> <td align="center"><a href="#distrib">Electron Distribution and Hybridization</a></td> <td align="center"><a href="#double">Molecules with Double and Triple Bonds</a></td> </tr> </table> </center></div><hr> <p align="center"><a name="hybrid"><em><b>Hybrid Atomic Orbitals </b></em></a></p> <p>It is difficult to explain the shapes of even the simplest molecules with atomic orbitals. A solution to this problem was proposed by Linus Pauling, who argued that the valence orbitals on an atom could be combined to form <b>hybrid atomic orbitals</b>.</p> <p>The geometry of a BeF<sub>2</sub> molecule can be explained, for example, by mixing the 2<i>s</i> orbital on the beryllium atom with one of the 2<i>p</i> orbitals to form a set of <i>sp</i> hybrid orbitals that point in opposite directions, as shown in the figure below. One of the valence electrons on the beryllium atom is then placed in each of these orbitals, and these orbitals are allowed to overlap with half-filled 2<i>p</i> orbitals on a pair of fluorine atoms to form a linear BeF<sub>2</sub> molecule.</p> <p align="center"><img src="graphics/fig8_27.gif" alt="Diagram" width="466" height="157" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/fig8_27.gif"></p> <p>Pauling also showed that the geometry of molecules such as BF<sub>3</sub> and the CO<sub>3</sub><sup>2-</sup> ion could be explained by mixing a 2<i>s</i> orbital with both a 2<i>p</i><sub>x</sub> and a 2<i>p</i><sub>y</sub> orbital on the central atom to form three <i>sp</i><sup>2</sup> hybrid orbitals that point toward the corners of an equilateral triangle. When he mixed a 2<i>s</i> orbital with all three 2<i>p</i> orbitals (2<i>p</i><sub>x</sub>, 2<i>p</i><sub>y</sub> and 2<i>p</i><sub>z</sub>), Pauling obtained a set of four <i>sp</i><sup>3</sup> orbitals that are oriented toward the corners of a tetrahedron. These <i>sp</i><sup>3</sup> hybrid orbitals are ideal for explaining the geometries of tetrahedral molecules such as CH<sub>4</sub> or the SO<sub>4</sub><sup>2-</sup> ion.</p> <p>The hybrid atomic orbital model can be extended to molecules whose shapes are based on trigonal bipyramidal or octahedral distributions of electrons by including valence-shell <i>d</i> orbitals. Pauling showed that when the 3<i>d</i><sub>z</sub><sup>2</sup> orbital is mixed with the 3<i>s</i>, 3<i>p</i><sub>x</sub>, 3<i>p</i><sub>y</sub> and 3<i>p</i><sub>z</sub> orbitals on an atom, the resulting <i>sp</i><sup>3</sup><i>d</i> hybrid orbitals point toward the corners of a trigonal bipyramid. When both the 3<i>d</i><sub>z</sub><sup>2</sup> and 3<i>d</i><sub>x</sub><sup>2</sup>-<sub>y</sub><sup>2</sup> orbitals are mixed with the 3<i>s</i>, 3<i>p</i><sub>x</sub>, 3<i>p</i><sub>y</sub> and 3<i>p</i><sub>z</sub> orbitals, the result is a set of six <i>sp</i><sup>3</sup><i>d</i><sup>2</sup> hybrid orbitals that point toward the corners of an octahedron. </p> <p align="center"><a href="#top"><strong><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/top.gif"></strong></a></p> <hr> <p align="center"><a name="geom"><strong>Geometries of Hybrid Orbitals</strong></a></p> <p>The geometries of the five different sets of hybrid atomic orbitals (<i>sp</i>, <i>sp</i><sup>2</sup>, <i>sp</i><sup>3</sup>, <i>sp</i><sup>3</sup><i>d</i> and <i>sp</i><sup>3</sup><i>d</i><sup>2</sup>) are shown in the figure below. </p> <p align="center"><img src="graphics/fig8_28.gif" alt="Orbitals" width="519" height="285" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/fig8_28.gif"></p> <p align="center"><a href="#top"><strong><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/top.gif"></strong></a></p> <hr> <p align="center"><a name="distrib"><em><b>The Relationship Between the Distribution of Electrons in an Atom and the Hybridization of That Atom</b></em></a></p> <p>The relationship between hybridization and the distribution of electrons in the valence shell of an atom is summarized in the table below.</p> <div align="center"><center><table border="0" cellpadding="2" width="500"> <tr> <td align="center" valign="bottom">Number of Places Where Electrons are Found</td> <td align="center" valign="bottom"> </td> <td align="center" valign="bottom">Molecular Geometry</td> <td align="center" valign="bottom"> </td> <td align="center" valign="bottom">Hybridization</td> <td align="center" valign="bottom"> </td> <td align="center" valign="bottom">Examples</td> </tr> <tr> <td align="center" colspan="7">¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯</td> </tr> <tr> <td align="center" valign="top">2</td> <td> </td> <td>linear</td> <td> </td> <td><i>sp</i></td> <td> </td> <td>BeF<sub>2</sub>, CO<sub>2</sub></td> </tr> <tr> <td align="center">3</td> <td> </td> <td>trigonal planar</td> <td> </td> <td><i>sp</i><sup>2</sup></td> <td> </td> <td>BF<sub>3</sub>, CO<sub>3</sub><sup>2-</sup></td> </tr> <tr> <td align="center">4</td> <td> </td> <td>tetrahedral</td> <td> </td> <td><i>sp</i><sup>3</sup></td> <td> </td> <td>CH<sub>4</sub>, SO<sub>4</sub><sup>2-</sup></td> </tr> <tr> <td align="center">5</td> <td> </td> <td>trigonal bipyramidal</td> <td> </td> <td><i>sp</i><sup>3</sup><i>d</i></td> <td> </td> <td>PF<sub>5</sub></td> </tr> <tr> <td align="center">6</td> <td> </td> <td>octahedral</td> <td> </td> <td><i>sp</i><sup>3</sup><i>d</i><sup>2</sup></td> <td> </td> <td>SF<sub>6</sub></td> </tr> </table> </center></div><p><a name="prob8"></a></p> <div align="center"><center><table border="5" cellpadding="10" width="100%" bordercolor="#B87333"> <tr> <td width="100%"><em><strong>Practice Problem 8:</strong></em><p>Use the table above to determine the hybridization of the central atom in the following compounds. </p> <blockquote> </blockquote> <blockquote> </blockquote> <blockquote> </blockquote> <blockquote> </blockquote> <p align="center"><img src="graphics/exer8_9.gif" alt="Structures" width="310" height="114" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/exer8_9.gif"></p> <p><a href="http://chemed.chem.purdue.edu/~genchem/topicreview/bp/ch8/problems/ex8_9a.html"><em><strong>Click here to check your answer to Practice Problem 8</strong></em></a></p> </td> </tr> </table> </center></div><p align="center"><a href="#top"><strong><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/top.gif"></strong></a></p> <hr> <p align="center"><a name="double"><em><b>Molecules with Double and Triple Bonds </b></em></a></p> <p>The hybrid atomic orbital model can also be used to explain the formation of double and triple bonds. </p> <p>Example: Let's consider the bonding in formaldehyde (H<sub>2</sub>CO), for example, which has the following Lewis structure.</p> <p align="center"><img src="graphics/h2co.gif" alt="Structure" width="77" height="53" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/h2co.gif"></p> <p>There are three places where electrons can be found in the valence shell of both the carbon and oxygen atoms in this molecule. As a result, the VSEPR theory predicts that the valence electrons on these atoms will be oriented toward the corners of an equilateral triangle. Let's assume, for the sake of argument, that the formaldehyde molecule lies in the <i>XY</i> plane of a coordinate system. We can create a set of <i>sp</i><sup>2</sup> hybrid orbitals on the carbon and oxygen atoms that lie in this plane by mixing the 2<i>s</i>, 2<i>p</i><sub>x</sub> and 2<i>p</i><sub>y</sub> orbitals on each atom.</p> <p>There are four valence electrons on a neutral carbon atom. One of these electrons is placed in each of the three <i>sp</i><sup>2</sup> hybrid orbitals. The fourth electron is placed in the 2<i>p</i><sub>z</sub> orbital that wasn't used during hybridization. </p> <p>There are six valence electrons on a neutral oxygen atom. A pair of these electrons is placed in each of two of the <i>sp</i><sup>2</sup> hybrid orbitals. One electron is then placed in the <i>sp</i><sup>2</sup> hybrid orbital that points toward the carbon atom, and another is placed in the unhybridized 2<i>p</i><sub>z</sub> orbital. </p> <p>The C-H bonds are formed when the electrons in two of the <i>sp</i><sup>2</sup> hybrid orbitals on carbon interact with a 1<i>s</i> electron on a hydrogen atom, as shown in the figure below.. A C-O bond is formed when the electron in the other <i>sp</i><sup>2</sup> hybrid orbital on carbon interacts with the unpaired electron in the <i>sp</i><sup>2</sup> hybrid orbital on the oxygen atom. These bonds are called <b>sigma (s) bonds</b> because they look like an <i>s</i> orbital when viewed along the bond.</p> <p align="center"><img src="graphics/fig8_29.gif" alt="Diagram" width="294" height="153" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/fig8_29.gif"></p> <p>The electron in the 2<i>p</i><sub>z</sub> orbital on the carbon atom then interacts with the electron in the 2<i>p</i><sub>z</sub> orbital on the oxygen atom to form a second covalent bond between these atoms. This is called a <b>pi (p) bond</b> because its looks like a <i>p</i> orbital when viewed along the bond.</p> <p>Double bonds occur most often in compounds that contain C, N, O, P, or S atoms. There are two reasons for this. First, double bonds by their very nature are covalent bonds. They are therefore most likely to be found among the elements that form covalent compounds. Second, the interaction between <i>p</i><sub>z</sub> orbitals to form a <i>p</i> bond requires that the atoms come relatively close together, so these bonds tend to be the strongest for atoms that are relatively small. </p> <p align="center"><a href="#top"><strong><img src="graphics/top.gif" alt="Return to Top of Page" border="0" width="226" height="36" sgi_fullpath="/disk2/chemistry/genchem/public_html/topicreview/bp/ch8/graphics/top.gif"></strong></a></p> <hr> <p><img src="http://chemed.chem.purdue.edu/Count.cgi?df=topicrevhybrid.dat"></p> </body>