{"id":245,"date":"2017-08-21T04:48:20","date_gmt":"2017-08-21T04:48:20","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/chemistry\/?page_id=245"},"modified":"2017-09-19T15:46:56","modified_gmt":"2017-09-19T15:46:56","slug":"hybridization-and-molecular-orbital-theory","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/chemistry\/hybridization-and-molecular-orbital-theory\/","title":{"rendered":"Hybridization and Molecular Orbital Theory"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\">\n<p><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/vsepr\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/chemical-naming-and-structure\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/comparison-of-properties\">Next Lesson \u27a1<\/a><\/p>\n<\/div>\n<p><!-- UPDATE NEXT\/PREVIOUS ABOVE --><\/p>\n<p><!-- CONTENT STARTS HERE --><\/p>\n<h1 id=\"title\">Chemical Naming and Structure: Hybridization and Molecular Orbital Theory<\/h1>\n<h4>Objective<\/h4>\n<p>We will review how atomic orbitals may be combined within an atom to form hybrid orbitals, or combined between two atoms to form molecular orbitals.<\/p>\n<h4>Previously we covered&#8230;<\/h4>\n<ul>\n<li>Because pairs of valence electrons are negatively charged, they will repel each other and move as far apart as possible. This allows us to predict the shape of a molecule from its Lewis structure.<\/li>\n<li>In VSEPR, single, double and triple bonds all behave as only one region of electron density.<\/li>\n<li>Molecules whose central atoms obey the Octet Rule may have shapes that are linear, trigonal planar, tetrahedral, trigonal pyramidal, or bent.<\/li>\n<li>Molecules whose central atoms have more than eight valence electrons may have shapes that are trigonal bipyramidal, see-saw, T-shaped, linear, octahedral, square pyramidal, or square planar.<\/li>\n<li>If a molecule has more than one central atom, we only consider one central atom at a time.<\/li>\n<\/ul>\n<section>\n<h3>Why Hybrid Orbitals?<\/h3>\n<p>You may remember that we often describe electrons in an atom by the orbital in which they reside. Nitrogen for example, has two electrons in the 1s orbital, two electrons in its 2s orbital and three electrons spread out among its three 2p orbitals. We often show this in the form of an electron configuration, which for nitrogen would look like this: 1s<sup>2<\/sup> 2s<sup>2<\/sup> 2p<sup>3<\/sup>. These orbitals are derived for individual atoms and thus may be referred to more specifically as atomic orbitals.<\/p>\n<p>It is important to remember that atomic orbitals are not physical objects, but rather they are simply regions of space defined relative to the nucleus of the atom. When atoms bond covalently, they must share electrons. Since these shared electrons must continue to belong to their original atoms, they must remain in their original orbitals. But since they must now also belong to a new atom, they must also now reside in an orbital for that atom as well. The only solution to this problem is that an orbital of one atom must overlap with an orbital of another atom in order to form a covalent bond.<\/p>\n<p>The reason for this background is to remind us that atomic orbitals are useful in describing electron behavior in atoms. They are less useful when those atoms begin to bond with each other to form molecules. For example, we know that carbon will bond with hydrogen to form methane, CH<sub>4<\/sub>. In order for these bonds to form, the orbitals containing carbon\u2019s valence electrons (2s and 2p) must overlap with each hydrogen\u2019s valence orbital (1s). The molecule formed is predicted to be tetrahedral in shape, with bond angles of approximately 109.5\u00ba. But p orbitals are 90\u00ba apart from each other and the s orbital is superimposed upon those p orbitals.<\/p>\n<p>We can resolve this contradiction by the use of hybrid orbitals. Since atomic orbitals are simply mathematical equations that successfully describe electron behavior, we can combine the equations to get new orbitals. By combining the 2s and the three 2p orbitals for carbon, we get four new orbitals which we will call sp<sup>3<\/sup> orbitals. Fortunately, these four orbitals are arranged in a tetrahedral pattern. In the figure below, we see the 2s orbitals and then the three 2p orbitals. On the right we see, the four sp<sup>3<\/sup> hybrid orbitals superimposed upon one another on the right.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization2.2s_2p_sp3.gif\" \/><\/center>Because there are only two regions of electron density around the central atom (carbon), they would move directly across the carbon atom from each other to get as far apart as possible. This is shown in the figure below. This shape is described as \u201clinear\u201d and the bond angle is 180\u00ba.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/VSEPR2.linear_bond_angle.gif\" \/><\/center>Boron trihydride, BH<sub>3<\/sub>, has a Lewis structure as shown below. Since there are only three regions of electron density, they will move 120\u00ba apart, forming a triangular pattern within a two-dimensional plane. This shape is described as \u201ctrigonal planar\u201d with a bond angle of 120\u00ba.<\/p>\n<p><center><img decoding=\"async\" class=\"centerimg\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/VSEPR2.lewis_dot_BH3.gif\" \/><\/center><\/p>\n<h3>Hybridizations and the Octet Rule<\/h3>\n<p>There are three hybridization schemes or types of hybrid orbitals that can form when atoms obey the Octet Rule. It is easiest to recognize them from a Lewis structure of the molecule. Just as we did in VSEPR, we will look at the number of regions of electron density around a central atom. Remember that double bonds or triple bonds still count as only one region.<\/p>\n<h3>sp<sup>3<\/sup> hybridization<\/h3>\n<p>We have already seen that four regions of electron density, like that of CH<sub>4<\/sub>, will cause the 2s and the three 2p orbitals to hybridize and form four sp<sup>3<\/sup> hybrids. This is true even if any of the regions are lone pairs, therefore molecules such as H<sub>2<\/sub>O and NH<sub>3<\/sub> are also sp<sup>3<\/sup> hybridized.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/VSEPR2.lewis_dot_CH4.gif\" \/><\/center><\/p>\n<h3>sp<sup>2<\/sup> hybridization<\/h3>\n<p>When a molecule has three regions of electron density around a central atom, such as C<sub>2<\/sub>H<sub>4<\/sub>, the s orbital and only two p orbitals will combine to form three sp<sup>2<\/sup> hybrid orbitals. These new orbitals are 120\u00ba apart, which is the same as predicted by VSEPR. The figure shows the three sp<sup>2<\/sup> hybrid orbitals superimposed upon one another.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization3.sp2_hybrid_orbital.gif\" \/><\/center><\/p>\n<h3>sp hybridization<\/h3>\n<p>A molecule with only two regions of electron density around a central atom, such as C<sub>2<\/sub>H<sub>2<\/sub>, will combine its s orbital with only one p orbital, forming two sp hybrid orbitals. These orbitals are 180\u00ba apart, so they form linear molecules as predicted by VSEPR. The figure below shows the two sp hybrid orbitals superimposed upon one another.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization3.lewis_dot_C2H2.png\" \/><\/center><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization3.sp_hybrid_orbital.gif\" \/><\/center><\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Which of the following is the correct hybridization for the nitrogen atom in methylamine, CH<sub>3<\/sub>NH<sub>2<\/sub>?<\/p>\n<ol>\n<li>sp<\/li>\n<li>sp<sup>2<\/sup><\/li>\n<li>sp<sup>3<\/sup><\/li>\n<li>Cannot be determined<\/li>\n<\/ol>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">The correct answer is C. In the Lewis structure of CH<sub>3<\/sub>NH<sub>2<\/sub>, nitrogen  has four regions of electron density (a single bond to the carbon atom, two single bonds to hydrogen atoms and a lone pair of electrons). This is consistent with sp<sup>3<\/sup> hybridization.<\/p>\n<\/section>\n<h3>Hybridization beyond the Octet Rule<\/h3>\n<p>You may recall that in order for an atom to have more than eight valence electrons, it must use one or more d orbitals. If we combine it (or them) with the s and p orbitals, we will make hybrid orbitals that correspond to the shapes that we saw previously when discussing VSEPR.<\/p>\n<p>Five regions of electron density will result in dsp<sup>3 <\/sup>hybrid orbitals. These orbitals are arranged in exactly the same fashion as the trigonal bipyramidal shape\u2014three are equatorial and 120\u00ba from each other in a triangular plane while two are axial, each perpendicular to the plane of the equatorial orbitals, one above and one below. The figure below shows the five dsp<sup>3<\/sup> hybrid orbitals superimposed upon one another.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization4.dsp3_hybrid_orbital.gif\" \/><\/center>Six regions of electron density will result in d<sup>2<\/sup>sp<sup>3<\/sup> hybrid orbitals. These orbitals are arranged in an octahedral pattern, with 90\u00ba angles between them. The figure below shows the six d<sup>2<\/sup>sp<sup>3 <\/sup>hybrid orbitals superimposed upon one another.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization4.d2sp3_hybrid_orbital.gif\" \/><\/center><\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Which of the following is the correct hybridization for the sulfur atom in sulfur tetrachloride, SCl<sub>4<\/sub>?<\/p>\n<ol>\n<li>sp<sup>3<\/sup><\/li>\n<li>dsp<sup>3<\/sup><\/li>\n<li>d<sup>3<\/sup>sp<sup>2<\/sup><\/li>\n<li>Cannot be determined<\/li>\n<\/ol>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">The correct answer is B. In the Lewis structure of SCl<sub>4<\/sub>, sulfur has five regions of electron density (four single bonds to chlorine atoms and a lone pair of electrons). This is consistent with dsp<sup>3<\/sup> hybridization.<\/p>\n<\/section>\n<h3>Molecular Orbital Theory<\/h3>\n<p>As we just saw in hybrid orbital theory, atomic orbitals in a given atom can combine with each other to make new orbitals. These new hybrid orbitals then overlap with other orbitals to form covalent bonds. Another way to compensate for the inability of atomic orbitals to describe electrons in a molecule is to use <abbr title=\"A bonding theory in which electrons occupy orbitals that belong to the entire molecule rather than just a single atom\">molecular orbital theory<\/abbr>. In this theory, the atomic orbitals from one atom combine with the atomic orbitals of another atom to form <abbr title=\"An orbital, formed by combining atomic orbitals from separate atoms, that belongs to an entire molecule rather than just a single atom\">molecular orbitals<\/abbr>.<\/p>\n<p>Molecular orbital theory can be quite complex, so we will only consider a few simple aspects of it here. One important point is that any time orbitals are combined, the number of orbitals is conserved. You may recall that when we combined an s orbital with a single p orbital, we formed two sp hybrid orbitals. Since we started with two orbitals, we ended with two orbitals. This will also apply to molecular orbitals. If we combine two 1s orbitals from two different atoms, we will form two new molecular orbitals. These are traditionally called the 1\u03c3 orbital and the 1\u03c3* orbital.<\/p>\n<p>The 1\u03c3 orbital is lower in energy than either of the 1s orbitals used in its making. It has its greatest electron density between the nuclei of the atoms. Filling this orbital with two electrons contributes the possibility of forming a bond between the atoms, so it is called a <abbr title=\"A molecular orbital that has high electron density between the nuclei and contributes to bond formation\">bonding orbital<\/abbr>.<\/p>\n<p>The 1\u03c3* orbital is higher in energy than either of the 1s orbitals used in its making. It has two regions of electron density, each on the side of one nucleus opposite the other nucleus. Putting electrons in these positions destabilizes a bond, so this type of orbital is called an <abbr title=\"A molecular orbital that has high electron density away from the center of the nuclei and destabilizes bond formation\">antibonding orbital<\/abbr>. A picture of two 1s orbitals combining to form the 1\u03c3 and 1\u03c3* orbitals is shown below.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/hybridization5.1s_to_1sigma_orbitals.gif\" \/><\/center><\/p>\n<h3>Bond Order<\/h3>\n<p>Bond order can be determined by assuming that a pair of electrons in a bonding orbital creates a bond and a pair of electrons in an antibonding orbital destroys a bond. The formula for determining bond order is as follows:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s5_001.gif\" \/><\/center>Let\u2019s consider the hydrogen molecule, H<sub>2<\/sub>. The molecule has two valence electrons, both of which will occupy the lowest orbital possible, which is the 1\u03c3. There are no electrons to go into the 1\u03c3*. Our calculation of bond order would be:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s5_002.gif\" \/><\/center>This means that H<sub>2<\/sub> has a bond order of one\u2014a single bond. By comparison, consider the hypothetical possibility of He<sub>2<\/sub>. There are four valence electrons, so two will occupy the 1\u03c3 and two will occupy the 1\u03c3*. The bond order of this molecule is:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s5_003.gif\" \/><\/center>Molecular orbital theory predicts that two He atoms should not bond with each other.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>What is the hybridization of xenon in xenon difluoride, XeF<sub>2<\/sub>?<\/p>\n<ol>\n<li>sp<sup>2 <\/sup><\/li>\n<li>sp<sup>3 <\/sup><\/li>\n<li>dsp<sup>3<\/sup><\/li>\n<li>d<sup>2<\/sup>sp<sup>3<\/sup><\/li>\n<\/ol>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">The correct answer is C. The Lewis structure of XeF<sub>2<\/sub> has five regions of electron density around the xenon, consistent with dsp<sup>3<\/sup> hybridization.<\/p>\n<\/section>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>What is the hybridization of xenon in xenon tetrafluoride, XeF<sub>4<\/sub>?<\/p>\n<ol>\n<li>sp<sup>2 <\/sup><\/li>\n<li>sp<sup>3 <\/sup><\/li>\n<li>dsp<sup>3<\/sup><\/li>\n<li>d<sup>2<\/sup>sp<sup>3<\/sup><\/li>\n<\/ol>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">The correct answer is D. The Lewis structure XeF<sub>2<\/sub> has six regions of electron density around the xenon, consistent with d<sup>2<\/sup>sp<sup>3<\/sup> hybridization.<br \/>\n<img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/VSEPR7.lewis_dot_XeF4.gif\" \/><\/p>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<p><!-- UPDATE NEXT\/PREVIOUS BELOW --><\/p>\n<div class=\"advance\">\n<p><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/vsepr\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/chemical-naming-and-structure\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/comparison-of-properties\">Next Lesson \u27a1<\/a><\/p>\n<\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Chemical Naming and Structure: Hybridization and Molecular Orbital Theory Objective We will review how atomic orbitals may be combined within an atom to form hybrid orbitals, or combined between two atoms to form molecular orbitals. Previously we covered&#8230; Because pairs of valence electrons are negatively charged, they will repel [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-245","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/245","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/comments?post=245"}],"version-history":[{"count":14,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/245\/revisions"}],"predecessor-version":[{"id":858,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/245\/revisions\/858"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/media?parent=245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}