{"id":495,"date":"2017-12-14T21:38:42","date_gmt":"2017-12-14T21:38:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-mcc-introductorychemistry\/chapter\/valence-bond-theory-and-hybrid-orbitals\/"},"modified":"2017-12-14T21:38:42","modified_gmt":"2017-12-14T21:38:42","slug":"valence-bond-theory-and-hybrid-orbitals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/chapter\/valence-bond-theory-and-hybrid-orbitals\/","title":{"raw":"Valence Bond Theory and Hybrid Orbitals","rendered":"Valence Bond Theory and Hybrid Orbitals"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul><li>Gain an understanding of valence bond theory.<\/li>\n\t<li>Gain an understanding of hybrid orbitals.<\/li>\n<\/ul><\/div>\n\u00a0\n<h2>Valence Bond Theory<\/h2>\nEarlier we saw that covalent bonding requires the sharing of electrons between two atoms, so that each atom can complete its valence shell. But how does this sharing process occur? Remember that we can only estimate the likelihood of finding an electron in a certain area as a probability. This probability is represented as a distribution in space that we call an <em>atomic orbital<\/em> (Figure 9.5 \"Representations of <em>s<\/em> and <em>p<\/em> atomic orbitals\")\n\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/1000px-S-p-Orbitals.svg_.png\"><img class=\"alignnone wp-image-2497\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213803\/1000px-S-p-Orbitals.svg_-1.png\" alt=\"Figure #.#. Representations of S and P atomic orbitals.\" height=\"133\" width=\"400\"\/><\/a>\n\n<span class=\"Apple-style-span\">Figure 9.5. Representations of\u00a0<em>s<\/em>\u00a0and\u00a0<em>p<\/em>\u00a0atomic orbitals.<\/span>[footnote]This illustration shows all <em>s<\/em> and <em>p<\/em>\u00a0atomic orbitals. By Sven\\CC-BY-SA-3.0[\/footnote]\n\n\u00a0\n\nThe valence bond theory states that atoms in a covalent bond share electron density through the overlapping of their valence atomic orbitals. This creates an area of electron pair density between the two atoms. Since these electrons are simultaneously attracted to both nuclei, the electron pair holds the two atoms together.\n\nLet\u2019s examine the simplest case of atomic overlap resulting in a covalent bond, the formation of H<sub>2<\/sub> from two hydrogen atoms (Figure 9.6 \"<span class=\"Apple-style-span\">A diagram showing the overlap of <em>s<\/em> orbitals of two hydrogen atoms to form H<sub>2<\/sub><\/span>\"). The 1<em>s<\/em> orbitals of the two\u00a0hydrogens approach each other and overlap to form a bond that\u00a0has cylindrical symmetry known as a <a class=\"glossary\">sigma bond (\u03c3 bond)<\/a>. Repulsion forces between the two nuclei and between the two electrons are also present. The optimal distance between atoms, which maximizes the attractive forces and minimizes the repulsive forces, gives the H-H sigma bond a length of 74 pm.\n\n[caption id=\"attachment_2500\" align=\"alignnone\" width=\"400\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/H2_orbital_overlap_.png\"><img class=\"wp-image-2500\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213805\/H2_orbital_overlap_-1.png\" alt=\"Figure #.#. A diagram illustrating the overlap of s orbitals of two hydrogen atoms to form H2.\" height=\"119\" width=\"400\"\/><\/a> Figure 9.6. A diagram showing the overlap of <em>s<\/em> orbitals of two hydrogen atoms to form H<sub>2<\/sub>.[\/caption]\n\nFor molecules that\u00a0contain double or triple bonds, one of these bonds is a sigma bond, and the remaining multiple bonds are a different type of bond known as a <a class=\"glossary\">pi bond (\u03c0 bond)<\/a>. Pi bonds result from the sideways overlap of <em>p<\/em> orbitals, placing electron density on opposite sides of the internuclear axis (Figure 9.7 \"Pi bond diagram showing sideways overlapping of <em>p<\/em> orbitals\").\n\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/adapted-pi-bond-diagram.jpg\"><img class=\"size-full wp-image-2504\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213807\/adapted-pi-bond-diagram-1.jpg\" alt=\"Figure #.#. Pi bond diagram showing side to side overlap of p orbitals.\" height=\"351\" width=\"263\"\/><\/a>\n\n<span class=\"Apple-style-span\">Figure 9.7. Pi bond diagram showing sideways overlap of\u00a0<em>p<\/em>\u00a0orbitals.<\/span>[footnote]Adapted from Pi-bond.jpg by JoJan\\CC-BY-SA-3.0[\/footnote]\n\n\u00a0\n<h2>Hybrid Orbitals<\/h2>\n<h3><em>sp<\/em><sup>3<\/sup>\u00a0hybridization<\/h3>\nA problem arises when we apply the valence bond theory method of orbital overlap to even simple molecules like methane (CH<sub>4<\/sub>) (Figure 9.8 \"Methane\"). Carbon (1<em>s<\/em><sup>2<\/sup> 2<em>s<\/em><sup>2<\/sup> 2<em>p<\/em><sup>2<\/sup>) only has two unpaired valence electrons that\u00a0are available to be shared through orbital overlap, yet CH<sub>4<\/sub> has four C-H \u03c3 bonds!\n\n\u00a0\n\n[caption id=\"attachment_2523\" align=\"alignnone\" width=\"186\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/methane.png\"><img class=\"size-full wp-image-2523\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213808\/methane-1.png\" alt=\"Figure #.#. Methane.\" height=\"201\" width=\"186\"\/><\/a> Figure 9.8. Methane.[\/caption]\n\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/L_Pauling.jpg\"><img class=\"size-full wp-image-2510\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213810\/L_Pauling-1.jpg\" alt=\"Figure #.#. Photograph of Nobel laureate Linus Pauling.\" height=\"278\" width=\"229\"\/><\/a>\n\n<span class=\"Apple-style-span\">Figure 9.9. Nobel laureate Linus Pauling.<\/span>[footnote]L Pauling\\Public Domain[\/footnote]\n\nIn 1931, Linus Pauling (Figure\u00a09.9) proposed a mathematical mixing of atomic orbitals known as <a>hybridization<\/a>. The 2<em>s <\/em>and <em>three<\/em> 2<em>p<\/em> orbitals are averaged mathematically through hybridization to produce <em>four<\/em> degenerate <em>sp<\/em><sup>3<\/sup>\u00a0hybrid orbitals (Figure 9.10 \"<span class=\"Apple-style-span\">Hybridization of carbon to generate <em>sp<\/em><sup>3<\/sup>\u00a0orbitals\"<\/span>). Note that in hybridization, the number of atomic orbitals hybridized is equal to the number of hybrid orbitals generated.\n\n\u00a0\n\n[caption id=\"attachment_2511\" align=\"alignnone\" width=\"400\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/sp3_hybridization_of_carbon_2.png\"><img class=\"wp-image-2511\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213812\/sp3_hybridization_of_carbon_2-1.png\" alt=\"Figure #.#. Hybridization of carbon to generate sp3 orbitals.\" height=\"93\" width=\"400\"\/><\/a> Figure 9.10. Hybridization of carbon to generate <em>sp<\/em><sup>3<\/sup> orbitals.[\/caption]\n\n\u00a0\n\nThe<em> sp<\/em><sup>3<\/sup> orbitals, being a combination of a spherical <em>s<\/em> orbital and propeller- (or peanut-) shaped <em>p<\/em> orbital, give an unsymmetrical propeller shape where one lobe of the orbital is larger\u00a0(fatter) than the other (Figure 9.11 \"<span class=\"Apple-style-span\">An <em>sp<\/em><sup>3<\/sup>\u00a0hybridized atomic orbital\"<\/span>). This larger lobe is typically used for orbital overlap in covalent bonding.\n\n[caption id=\"attachment_2512\" align=\"alignnone\" width=\"268\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/sp3_orbital.png\"><img class=\"size-full wp-image-2512\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213814\/sp3_orbital-1.png\" alt=\"Figure #.#. Illustration of an sp3 hybridized atomic orbital.\" height=\"130\" width=\"268\"\/><\/a> Figure 9.11.\u00a0An <em>sp<\/em><sup>3<\/sup> hybridized atomic orbital.[\/caption]\n\n\u00a0\n\nAccording to VSEPR theory, the four degenerate orbitals will arrange as far apart from each other as possible, giving a tetrahedral geometry with each orbital 109.5<sup>o<\/sup> apart (Figure 9.12 \"<span class=\"Apple-style-span\">A\u00a0carbon atom's four tetrahedral <em>sp<\/em><sup>3<\/sup>\u00a0hybridized orbitals\"<\/span>).\n\n\u00a0\n\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/1000px-AE4h-jak-edit.png\"><img class=\"alignnone wp-image-2513\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213818\/1000px-AE4h-jak-edit-1.png\" alt=\"Figure #.#. Depiction of a tetrahedral carbon atom having four sp3 hybridized orbitals.\" height=\"358\" width=\"400\"\/><\/a>\n\n<span class=\"Apple-style-span\">Figure 9.12. A\u00a0carbon atom's four tetrahedral sp<sup>3<\/sup>\u00a0hybridized orbitals.<\/span>[footnote]Adapted from AE4h by Jfmelero\\CC-BY-SA-3.0 [\/footnote]\n\n\u00a0\n<h3><em>sp<\/em><sup>2<\/sup>\u00a0hybridization<\/h3>\nLet\u2019s examine another simple molecule, ethene (C<sub>2<\/sub>H<sub>4<\/sub>) (Figure\u00a09.13 \"Ethene\"). Each carbon of ethene is bonded to two hydrogens and a carbon. There is also a double bond between the two carbons.\n\n\u00a0\n\n[caption id=\"attachment_2525\" align=\"alignnone\" width=\"230\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/ethene.png\"><img class=\"size-full wp-image-2525\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213820\/ethene-1.png\" alt=\"Figure #.#. Ethene.\" height=\"188\" width=\"230\"\/><\/a> Figure 9.13. Ethene.[\/caption]\n\nBoth the unhybridized atomic orbitals of carbon and the <em>sp<\/em><sup>3<\/sup> hybridization we just examined do not explain\u00a0the bonding observed in ethene. In this case, only the 2<em>s<\/em> and <em>two <\/em>of the 2<em>p<\/em> orbitals hybridize to give three new <em>sp<\/em><sup>2<\/sup> hybridized orbitals capable of forming the three \u03c3 bonds of each carbon in ethene (Figure 9.14 \"<span class=\"Apple-style-span\">Hybridization of carbon to generate <em>sp<\/em><sup>2<\/sup>\u00a0orbitals\"<\/span>).\n\n\u00a0\n\n[caption id=\"attachment_2526\" align=\"alignnone\" width=\"400\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/carbon_sp2_hybridization.png\"><img class=\"wp-image-2526\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213822\/carbon_sp2_hybridization-1.png\" alt=\"Figure #.#. sp2 hybridization of carbon.\" height=\"100\" width=\"400\"\/><\/a> Figure 9.14. Hybridization of carbon to generate<em> sp<\/em><sup>2<\/sup> orbitals.[\/caption]\n\n\u00a0\n\nThe three hybridized orbitals arrange in a trigonal planar structure with a bond angle of 120<sup>o<\/sup> following VSEPR (Figure 9.15 \"<span class=\"Apple-style-span\">A\u00a0carbon atom's trigonal planar \u00a0<em>sp<\/em><sup>2<\/sup>\u00a0hybridized orbitals\"<\/span>).\n\n\u00a0\n\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/1000px-AE3h-jak-edit.png\"><img class=\"alignnone wp-image-2527\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213827\/1000px-AE3h-jak-edit-1.png\" alt=\"Figure #.#. Depiction of a trigonal planar carbon atom having three sp2 hybridized orbitals.\" height=\"339\" width=\"400\"\/><\/a>\n\n<span class=\"Apple-style-span\">Figure 9.15. A\u00a0carbon atom's trigonal planar \u00a0<em>sp<\/em><sup>2<\/sup>\u00a0hybridized orbitals.<\/span>[footnote]Adapted from AE3h by Jfmelero\\CC BY-SA 3.0 [\/footnote]\n\n\u00a0\n\nThe unhybridized 2<em>p<\/em> orbital in both carbons are left available to form the double bond\u2019s \u03c0 bond.\n\n\u00a0\n<h3><em>sp<\/em>\u00a0hybridization<\/h3>\nThe final example of hybridization we will examine is the molecule ethyne (C<sub>2<\/sub>H<sub>2<\/sub>) (Figure 9.16 \"Ethyne\").\n\n[caption id=\"attachment_4538\" align=\"alignnone\" width=\"400\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Ethyne.png\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213829\/Ethyne-1.png\" alt=\"Figure #.#. Ethyne.\" width=\"400\" height=\"35\" class=\"wp-image-4538\"\/><\/a> Figure 9.16. Ethyne.[\/caption]\n\n\u00a0\n\nThe carbons in ethyne are each sigma bonded to a single hydrogen, but triple bonded to each other. Again, the models of hybridization we have looked at so far are insufficient to explain the bonding pattern observed. In ethyne, only the 2<em>s<\/em> and <em>one <\/em>of the 2<em>p<\/em> orbitals hybridize to give two new <em>sp<\/em> hybridized orbitals capable of forming the two \u03c3 bonds of each carbon in ethyne (Figure 9.17 \"<span class=\"Apple-style-span\">Hybridization of carbon to generate\u00a0<em>sp<\/em>\u00a0orbitals\"<\/span>).\n\n\u00a0\n\n[caption id=\"attachment_2530\" align=\"alignnone\" width=\"400\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/carbon_sp_hybridization.png\"><img class=\"wp-image-2530\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213832\/carbon_sp_hybridization-1.png\" alt=\"Figure #.#. Hybridization of carbon to generate sp orbitals.\" height=\"106\" width=\"400\"\/><\/a> Figure 9.17. Hybridization of carbon to generate <em>sp<\/em> orbitals.[\/caption]\n\nThe two hybridized <em>sp<\/em> orbitals arrange linearly with a bond angle of 180<sup>o<\/sup> following VSEPR (Figure 9.18 \"<span class=\"Apple-style-span\">A\u00a0carbon atom's linear\u00a0<em>sp<\/em>\u00a0hybridized orbitals\"<\/span>).\n\n\u00a0\n\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/AE2h-jak-edit.png\"><img class=\"alignnone wp-image-2531\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213836\/AE2h-jak-edit-1.png\" alt=\"Figure #.#. Depiction of a carbon atom's linear sp hybridized orbitals.\" height=\"292\" width=\"400\"\/><\/a>\n\n<span class=\"Apple-style-span\">Figure 9.18. A\u00a0carbon atom's linear\u00a0<em>sp<\/em>\u00a0hybridized orbitals.<\/span>[footnote]Adapted from AE2h by Jfmelero\\CC BY-SA 3.0[\/footnote]\n\nThe two remaining unhybridized 2<em>p<\/em> orbitals in both carbons are left available to form the triple bond\u2019s two \u03c0 bonds.\n<h3>\n\u00a0Other hybridizations<\/h3>\nOther hybridizations are possible, allowing us to apply valence bond theory to explain the bonding patterns observed in most real molecules. Some additional hybridizations are summarized in Table 9.5 \"Hybrid Orbitals and Geometry.\"\n\n[caption id=\"attachment_2538\" align=\"alignnone\" width=\"400\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/Hybrid_Orbitals_and_Geometry.jpg\"><img class=\"wp-image-2538\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213840\/Hybrid_Orbitals_and_Geometry-1.jpg\" alt=\"Table #.#. Hybrid orbitals and geometries.\" height=\"517\" width=\"400\"\/><\/a> Table\u00a09.5. Hybrid orbitals and geometries.[\/caption]\n\n[footnote]Hybrid orbital and geometries by Chem507f10grp4\\public domain.[\/footnote]\n\n\u00a0\n<div class=\"bcc-box bcc-success\">\n<h3>Key Takeaways<\/h3>\n<ul><li>Valence bond theory explains bonding through the overlap of atomic orbitals.<\/li>\n\t<li>Atomic orbitals can be hybridized mathematically to better explain actual bonding patterns.<\/li>\n<\/ul><\/div>\n\u00a0","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Gain an understanding of valence bond theory.<\/li>\n<li>Gain an understanding of hybrid orbitals.<\/li>\n<\/ul>\n<\/div>\n<p>\u00a0<\/p>\n<h2>Valence Bond Theory<\/h2>\n<p>Earlier we saw that covalent bonding requires the sharing of electrons between two atoms, so that each atom can complete its valence shell. But how does this sharing process occur? Remember that we can only estimate the likelihood of finding an electron in a certain area as a probability. This probability is represented as a distribution in space that we call an <em>atomic orbital<\/em> (Figure 9.5 &#8220;Representations of <em>s<\/em> and <em>p<\/em> atomic orbitals&#8221;)<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/1000px-S-p-Orbitals.svg_.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2497\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213803\/1000px-S-p-Orbitals.svg_-1.png\" alt=\"Figure #.#. Representations of S and P atomic orbitals.\" height=\"133\" width=\"400\" \/><\/a><\/p>\n<p><span class=\"Apple-style-span\">Figure 9.5. Representations of\u00a0<em>s<\/em>\u00a0and\u00a0<em>p<\/em>\u00a0atomic orbitals.<\/span><a class=\"footnote\" title=\"This illustration shows all s and p\u00a0atomic orbitals. By Sven\\CC-BY-SA-3.0\" id=\"return-footnote-495-1\" href=\"#footnote-495-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>\u00a0<\/p>\n<p>The valence bond theory states that atoms in a covalent bond share electron density through the overlapping of their valence atomic orbitals. This creates an area of electron pair density between the two atoms. Since these electrons are simultaneously attracted to both nuclei, the electron pair holds the two atoms together.<\/p>\n<p>Let\u2019s examine the simplest case of atomic overlap resulting in a covalent bond, the formation of H<sub>2<\/sub> from two hydrogen atoms (Figure 9.6 &#8220;<span class=\"Apple-style-span\">A diagram showing the overlap of <em>s<\/em> orbitals of two hydrogen atoms to form H<sub>2<\/sub><\/span>&#8220;). The 1<em>s<\/em> orbitals of the two\u00a0hydrogens approach each other and overlap to form a bond that\u00a0has cylindrical symmetry known as a <a class=\"glossary\">sigma bond (\u03c3 bond)<\/a>. Repulsion forces between the two nuclei and between the two electrons are also present. The optimal distance between atoms, which maximizes the attractive forces and minimizes the repulsive forces, gives the H-H sigma bond a length of 74 pm.<\/p>\n<div id=\"attachment_2500\" style=\"width: 410px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/H2_orbital_overlap_.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2500\" class=\"wp-image-2500\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213805\/H2_orbital_overlap_-1.png\" alt=\"Figure #.#. A diagram illustrating the overlap of s orbitals of two hydrogen atoms to form H2.\" height=\"119\" width=\"400\" \/><\/a><\/p>\n<p id=\"caption-attachment-2500\" class=\"wp-caption-text\">Figure 9.6. A diagram showing the overlap of <em>s<\/em> orbitals of two hydrogen atoms to form H<sub>2<\/sub>.<\/p>\n<\/div>\n<p>For molecules that\u00a0contain double or triple bonds, one of these bonds is a sigma bond, and the remaining multiple bonds are a different type of bond known as a <a class=\"glossary\">pi bond (\u03c0 bond)<\/a>. Pi bonds result from the sideways overlap of <em>p<\/em> orbitals, placing electron density on opposite sides of the internuclear axis (Figure 9.7 &#8220;Pi bond diagram showing sideways overlapping of <em>p<\/em> orbitals&#8221;).<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/adapted-pi-bond-diagram.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2504\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213807\/adapted-pi-bond-diagram-1.jpg\" alt=\"Figure #.#. Pi bond diagram showing side to side overlap of p orbitals.\" height=\"351\" width=\"263\" \/><\/a><\/p>\n<p><span class=\"Apple-style-span\">Figure 9.7. Pi bond diagram showing sideways overlap of\u00a0<em>p<\/em>\u00a0orbitals.<\/span><a class=\"footnote\" title=\"Adapted from Pi-bond.jpg by JoJan\\CC-BY-SA-3.0\" id=\"return-footnote-495-2\" href=\"#footnote-495-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>\u00a0<\/p>\n<h2>Hybrid Orbitals<\/h2>\n<h3><em>sp<\/em><sup>3<\/sup>\u00a0hybridization<\/h3>\n<p>A problem arises when we apply the valence bond theory method of orbital overlap to even simple molecules like methane (CH<sub>4<\/sub>) (Figure 9.8 &#8220;Methane&#8221;). Carbon (1<em>s<\/em><sup>2<\/sup> 2<em>s<\/em><sup>2<\/sup> 2<em>p<\/em><sup>2<\/sup>) only has two unpaired valence electrons that\u00a0are available to be shared through orbital overlap, yet CH<sub>4<\/sub> has four C-H \u03c3 bonds!<\/p>\n<p>\u00a0<\/p>\n<div id=\"attachment_2523\" style=\"width: 196px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/methane.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2523\" class=\"size-full wp-image-2523\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213808\/methane-1.png\" alt=\"Figure #.#. Methane.\" height=\"201\" width=\"186\" \/><\/a><\/p>\n<p id=\"caption-attachment-2523\" class=\"wp-caption-text\">Figure 9.8. Methane.<\/p>\n<\/div>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/L_Pauling.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-2510\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213810\/L_Pauling-1.jpg\" alt=\"Figure #.#. Photograph of Nobel laureate Linus Pauling.\" height=\"278\" width=\"229\" \/><\/a><\/p>\n<p><span class=\"Apple-style-span\">Figure 9.9. Nobel laureate Linus Pauling.<\/span><a class=\"footnote\" title=\"L Pauling\\Public Domain\" id=\"return-footnote-495-3\" href=\"#footnote-495-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a><\/p>\n<p>In 1931, Linus Pauling (Figure\u00a09.9) proposed a mathematical mixing of atomic orbitals known as <a>hybridization<\/a>. The 2<em>s <\/em>and <em>three<\/em> 2<em>p<\/em> orbitals are averaged mathematically through hybridization to produce <em>four<\/em> degenerate <em>sp<\/em><sup>3<\/sup>\u00a0hybrid orbitals (Figure 9.10 &#8220;<span class=\"Apple-style-span\">Hybridization of carbon to generate <em>sp<\/em><sup>3<\/sup>\u00a0orbitals&#8221;<\/span>). Note that in hybridization, the number of atomic orbitals hybridized is equal to the number of hybrid orbitals generated.<\/p>\n<p>\u00a0<\/p>\n<div id=\"attachment_2511\" style=\"width: 410px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/sp3_hybridization_of_carbon_2.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2511\" class=\"wp-image-2511\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213812\/sp3_hybridization_of_carbon_2-1.png\" alt=\"Figure #.#. Hybridization of carbon to generate sp3 orbitals.\" height=\"93\" width=\"400\" \/><\/a><\/p>\n<p id=\"caption-attachment-2511\" class=\"wp-caption-text\">Figure 9.10. Hybridization of carbon to generate <em>sp<\/em><sup>3<\/sup> orbitals.<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p>The<em> sp<\/em><sup>3<\/sup> orbitals, being a combination of a spherical <em>s<\/em> orbital and propeller- (or peanut-) shaped <em>p<\/em> orbital, give an unsymmetrical propeller shape where one lobe of the orbital is larger\u00a0(fatter) than the other (Figure 9.11 &#8220;<span class=\"Apple-style-span\">An <em>sp<\/em><sup>3<\/sup>\u00a0hybridized atomic orbital&#8221;<\/span>). This larger lobe is typically used for orbital overlap in covalent bonding.<\/p>\n<div id=\"attachment_2512\" style=\"width: 278px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/sp3_orbital.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2512\" class=\"size-full wp-image-2512\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213814\/sp3_orbital-1.png\" alt=\"Figure #.#. Illustration of an sp3 hybridized atomic orbital.\" height=\"130\" width=\"268\" \/><\/a><\/p>\n<p id=\"caption-attachment-2512\" class=\"wp-caption-text\">Figure 9.11.\u00a0An <em>sp<\/em><sup>3<\/sup> hybridized atomic orbital.<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p>According to VSEPR theory, the four degenerate orbitals will arrange as far apart from each other as possible, giving a tetrahedral geometry with each orbital 109.5<sup>o<\/sup> apart (Figure 9.12 &#8220;<span class=\"Apple-style-span\">A\u00a0carbon atom&#8217;s four tetrahedral <em>sp<\/em><sup>3<\/sup>\u00a0hybridized orbitals&#8221;<\/span>).<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/1000px-AE4h-jak-edit.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2513\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213818\/1000px-AE4h-jak-edit-1.png\" alt=\"Figure #.#. Depiction of a tetrahedral carbon atom having four sp3 hybridized orbitals.\" height=\"358\" width=\"400\" \/><\/a><\/p>\n<p><span class=\"Apple-style-span\">Figure 9.12. A\u00a0carbon atom&#8217;s four tetrahedral sp<sup>3<\/sup>\u00a0hybridized orbitals.<\/span><a class=\"footnote\" title=\"Adapted from AE4h by Jfmelero\\CC-BY-SA-3.0\" id=\"return-footnote-495-4\" href=\"#footnote-495-4\" aria-label=\"Footnote 4\"><sup class=\"footnote\">[4]<\/sup><\/a><\/p>\n<p>\u00a0<\/p>\n<h3><em>sp<\/em><sup>2<\/sup>\u00a0hybridization<\/h3>\n<p>Let\u2019s examine another simple molecule, ethene (C<sub>2<\/sub>H<sub>4<\/sub>) (Figure\u00a09.13 &#8220;Ethene&#8221;). Each carbon of ethene is bonded to two hydrogens and a carbon. There is also a double bond between the two carbons.<\/p>\n<p>\u00a0<\/p>\n<div id=\"attachment_2525\" style=\"width: 240px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/ethene.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2525\" class=\"size-full wp-image-2525\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213820\/ethene-1.png\" alt=\"Figure #.#. Ethene.\" height=\"188\" width=\"230\" \/><\/a><\/p>\n<p id=\"caption-attachment-2525\" class=\"wp-caption-text\">Figure 9.13. Ethene.<\/p>\n<\/div>\n<p>Both the unhybridized atomic orbitals of carbon and the <em>sp<\/em><sup>3<\/sup> hybridization we just examined do not explain\u00a0the bonding observed in ethene. In this case, only the 2<em>s<\/em> and <em>two <\/em>of the 2<em>p<\/em> orbitals hybridize to give three new <em>sp<\/em><sup>2<\/sup> hybridized orbitals capable of forming the three \u03c3 bonds of each carbon in ethene (Figure 9.14 &#8220;<span class=\"Apple-style-span\">Hybridization of carbon to generate <em>sp<\/em><sup>2<\/sup>\u00a0orbitals&#8221;<\/span>).<\/p>\n<p>\u00a0<\/p>\n<div id=\"attachment_2526\" style=\"width: 410px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/carbon_sp2_hybridization.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2526\" class=\"wp-image-2526\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213822\/carbon_sp2_hybridization-1.png\" alt=\"Figure #.#. sp2 hybridization of carbon.\" height=\"100\" width=\"400\" \/><\/a><\/p>\n<p id=\"caption-attachment-2526\" class=\"wp-caption-text\">Figure 9.14. Hybridization of carbon to generate<em> sp<\/em><sup>2<\/sup> orbitals.<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p>The three hybridized orbitals arrange in a trigonal planar structure with a bond angle of 120<sup>o<\/sup> following VSEPR (Figure 9.15 &#8220;<span class=\"Apple-style-span\">A\u00a0carbon atom&#8217;s trigonal planar \u00a0<em>sp<\/em><sup>2<\/sup>\u00a0hybridized orbitals&#8221;<\/span>).<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/1000px-AE3h-jak-edit.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2527\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213827\/1000px-AE3h-jak-edit-1.png\" alt=\"Figure #.#. Depiction of a trigonal planar carbon atom having three sp2 hybridized orbitals.\" height=\"339\" width=\"400\" \/><\/a><\/p>\n<p><span class=\"Apple-style-span\">Figure 9.15. A\u00a0carbon atom&#8217;s trigonal planar \u00a0<em>sp<\/em><sup>2<\/sup>\u00a0hybridized orbitals.<\/span><a class=\"footnote\" title=\"Adapted from AE3h by Jfmelero\\CC BY-SA 3.0\" id=\"return-footnote-495-5\" href=\"#footnote-495-5\" aria-label=\"Footnote 5\"><sup class=\"footnote\">[5]<\/sup><\/a><\/p>\n<p>\u00a0<\/p>\n<p>The unhybridized 2<em>p<\/em> orbital in both carbons are left available to form the double bond\u2019s \u03c0 bond.<\/p>\n<p>\u00a0<\/p>\n<h3><em>sp<\/em>\u00a0hybridization<\/h3>\n<p>The final example of hybridization we will examine is the molecule ethyne (C<sub>2<\/sub>H<sub>2<\/sub>) (Figure 9.16 &#8220;Ethyne&#8221;).<\/p>\n<div id=\"attachment_4538\" style=\"width: 410px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Ethyne.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4538\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213829\/Ethyne-1.png\" alt=\"Figure #.#. Ethyne.\" width=\"400\" height=\"35\" class=\"wp-image-4538\" \/><\/a><\/p>\n<p id=\"caption-attachment-4538\" class=\"wp-caption-text\">Figure 9.16. Ethyne.<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p>The carbons in ethyne are each sigma bonded to a single hydrogen, but triple bonded to each other. Again, the models of hybridization we have looked at so far are insufficient to explain the bonding pattern observed. In ethyne, only the 2<em>s<\/em> and <em>one <\/em>of the 2<em>p<\/em> orbitals hybridize to give two new <em>sp<\/em> hybridized orbitals capable of forming the two \u03c3 bonds of each carbon in ethyne (Figure 9.17 &#8220;<span class=\"Apple-style-span\">Hybridization of carbon to generate\u00a0<em>sp<\/em>\u00a0orbitals&#8221;<\/span>).<\/p>\n<p>\u00a0<\/p>\n<div id=\"attachment_2530\" style=\"width: 410px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/carbon_sp_hybridization.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2530\" class=\"wp-image-2530\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213832\/carbon_sp_hybridization-1.png\" alt=\"Figure #.#. Hybridization of carbon to generate sp orbitals.\" height=\"106\" width=\"400\" \/><\/a><\/p>\n<p id=\"caption-attachment-2530\" class=\"wp-caption-text\">Figure 9.17. Hybridization of carbon to generate <em>sp<\/em> orbitals.<\/p>\n<\/div>\n<p>The two hybridized <em>sp<\/em> orbitals arrange linearly with a bond angle of 180<sup>o<\/sup> following VSEPR (Figure 9.18 &#8220;<span class=\"Apple-style-span\">A\u00a0carbon atom&#8217;s linear\u00a0<em>sp<\/em>\u00a0hybridized orbitals&#8221;<\/span>).<\/p>\n<p>\u00a0<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/AE2h-jak-edit.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2531\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213836\/AE2h-jak-edit-1.png\" alt=\"Figure #.#. Depiction of a carbon atom's linear sp hybridized orbitals.\" height=\"292\" width=\"400\" \/><\/a><\/p>\n<p><span class=\"Apple-style-span\">Figure 9.18. A\u00a0carbon atom&#8217;s linear\u00a0<em>sp<\/em>\u00a0hybridized orbitals.<\/span><a class=\"footnote\" title=\"Adapted from AE2h by Jfmelero\\CC BY-SA 3.0\" id=\"return-footnote-495-6\" href=\"#footnote-495-6\" aria-label=\"Footnote 6\"><sup class=\"footnote\">[6]<\/sup><\/a><\/p>\n<p>The two remaining unhybridized 2<em>p<\/em> orbitals in both carbons are left available to form the triple bond\u2019s two \u03c0 bonds.<\/p>\n<h3>\n\u00a0Other hybridizations<\/h3>\n<p>Other hybridizations are possible, allowing us to apply valence bond theory to explain the bonding patterns observed in most real molecules. Some additional hybridizations are summarized in Table 9.5 &#8220;Hybrid Orbitals and Geometry.&#8221;<\/p>\n<div id=\"attachment_2538\" style=\"width: 410px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/06\/Hybrid_Orbitals_and_Geometry.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2538\" class=\"wp-image-2538\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213840\/Hybrid_Orbitals_and_Geometry-1.jpg\" alt=\"Table #.#. Hybrid orbitals and geometries.\" height=\"517\" width=\"400\" \/><\/a><\/p>\n<p id=\"caption-attachment-2538\" class=\"wp-caption-text\">Table\u00a09.5. Hybrid orbitals and geometries.<\/p>\n<\/div>\n<p><a class=\"footnote\" title=\"Hybrid orbital and geometries by Chem507f10grp4\\public domain.\" id=\"return-footnote-495-7\" href=\"#footnote-495-7\" aria-label=\"Footnote 7\"><sup class=\"footnote\">[7]<\/sup><\/a><\/p>\n<p>\u00a0<\/p>\n<div class=\"bcc-box bcc-success\">\n<h3>Key Takeaways<\/h3>\n<ul>\n<li>Valence bond theory explains bonding through the overlap of atomic orbitals.<\/li>\n<li>Atomic orbitals can be hybridized mathematically to better explain actual bonding patterns.<\/li>\n<\/ul>\n<\/div>\n<p>\u00a0<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-495\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Chemistry- 1st Canadian Edition . <strong>Authored by<\/strong>: Jessie A. Key and David W. Ball. <strong>Provided by<\/strong>: BCCampus. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/opentextbc.ca\/introductorychemistry\/\">https:\/\/opentextbc.ca\/introductorychemistry\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. <strong>License Terms<\/strong>: Download this book for free at http:\/\/open.bccampus.ca<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-495-1\">This illustration shows all <em>s<\/em> and <em>p<\/em>\u00a0atomic orbitals. By Sven\\CC-BY-SA-3.0 <a href=\"#return-footnote-495-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-495-2\">Adapted from Pi-bond.jpg by JoJan\\CC-BY-SA-3.0 <a href=\"#return-footnote-495-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-495-3\">L Pauling\\Public Domain <a href=\"#return-footnote-495-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><li id=\"footnote-495-4\">Adapted from AE4h by Jfmelero\\CC-BY-SA-3.0  <a href=\"#return-footnote-495-4\" class=\"return-footnote\" aria-label=\"Return to footnote 4\">&crarr;<\/a><\/li><li id=\"footnote-495-5\">Adapted from AE3h by Jfmelero\\CC BY-SA 3.0  <a href=\"#return-footnote-495-5\" class=\"return-footnote\" aria-label=\"Return to footnote 5\">&crarr;<\/a><\/li><li id=\"footnote-495-6\">Adapted from AE2h by Jfmelero\\CC BY-SA 3.0 <a href=\"#return-footnote-495-6\" class=\"return-footnote\" aria-label=\"Return to footnote 6\">&crarr;<\/a><\/li><li id=\"footnote-495-7\">Hybrid orbital and geometries by Chem507f10grp4\\public domain. <a href=\"#return-footnote-495-7\" class=\"return-footnote\" aria-label=\"Return to footnote 7\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":23485,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Chemistry- 1st Canadian Edition \",\"author\":\"Jessie A. Key and David W. Ball\",\"organization\":\"BCCampus\",\"url\":\"https:\/\/opentextbc.ca\/introductorychemistry\/\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Download this book for free at http:\/\/open.bccampus.ca\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["jessie-a-key"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-495","chapter","type-chapter","status-publish","hentry","contributor-jessie-a-key"],"part":352,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/pressbooks\/v2\/chapters\/495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/wp\/v2\/users\/23485"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/pressbooks\/v2\/chapters\/495\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/pressbooks\/v2\/parts\/352"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/pressbooks\/v2\/chapters\/495\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/wp\/v2\/media?parent=495"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/pressbooks\/v2\/chapter-type?post=495"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/wp\/v2\/contributor?post=495"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-introductory-chemistry\/wp-json\/wp\/v2\/license?post=495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}