{"id":249601,"date":"2025-07-09T17:48:41","date_gmt":"2025-07-09T17:48:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249601"},"modified":"2025-07-09T17:48:45","modified_gmt":"2025-07-09T17:48:45","slug":"using-lcao-mo-theory-what-is-bond-order-of-c2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/using-lcao-mo-theory-what-is-bond-order-of-c2\/","title":{"rendered":"Using LCAO-MO theory, what is bond order of C2-"},"content":{"rendered":"\n<p>Using LCAO-MO theory, what is bond order of C2- (the one minus ion)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The bond order of the C2\u2212\\text{C}_2^-C2\u2212\u200b ion can be determined using the Molecular Orbital (MO) theory and the Linear Combination of Atomic Orbitals (LCAO) approach.<\/p>\n\n\n\n<p>First, let&#8217;s review the molecular orbitals formed by the combination of atomic orbitals of carbon atoms. Each carbon atom has 6 electrons, so in the neutral C2\\text{C}_2C2\u200b molecule, the total number of electrons is 12. The molecular orbitals are filled in increasing energy levels based on the order of their formation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">For C2\u2212\\text{C}_2^-C2\u2212\u200b (the C2\\text{C}_2C2\u200b ion with one extra electron):<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The total number of electrons in C2\u2212\\text{C}_2^-C2\u2212\u200b is 13 (12 from the neutral molecule and 1 extra due to the negative charge).<\/li>\n\n\n\n<li>The molecular orbitals for C2\\text{C}_2C2\u200b in order of increasing energy are:\n<ul class=\"wp-block-list\">\n<li>\u03c31s\\sigma_{1s}\u03c31s\u200b, \u03c31s\u2217\\sigma^*_{1s}\u03c31s\u2217\u200b (from the 1s atomic orbitals),<\/li>\n\n\n\n<li>\u03c32s\\sigma_{2s}\u03c32s\u200b, \u03c32s\u2217\\sigma^*_{2s}\u03c32s\u2217\u200b (from the 2s atomic orbitals),<\/li>\n\n\n\n<li>\u03c32pz\\sigma_{2p_z}\u03c32pz\u200b\u200b, \u03c02px\\pi_{2p_x}\u03c02px\u200b\u200b, \u03c02py\\pi_{2p_y}\u03c02py\u200b\u200b, \u03c02px\u2217\\pi^*_{2p_x}\u03c02px\u200b\u2217\u200b, \u03c02py\u2217\\pi^*_{2p_y}\u03c02py\u200b\u2217\u200b, and \u03c32pz\u2217\\sigma^*_{2p_z}\u03c32pz\u200b\u2217\u200b (from the 2p atomic orbitals).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Electron configuration of C2\u2212\\text{C}_2^-C2\u2212\u200b:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The electrons are filled into the molecular orbitals as follows:\n<ul class=\"wp-block-list\">\n<li>\u03c31s2\\sigma_{1s}^2\u03c31s2\u200b, \\sigma^*_{1s}^2 (2 electrons each),<\/li>\n\n\n\n<li>\u03c32s2\\sigma_{2s}^2\u03c32s2\u200b, \\sigma^*_{2s}^2 (2 electrons each),<\/li>\n\n\n\n<li>\u03c32pz2\\sigma_{2p_z}^2\u03c32pz\u200b2\u200b,<\/li>\n\n\n\n<li>\u03c02px2\\pi_{2p_x}^2\u03c02px\u200b2\u200b, \u03c02py2\\pi_{2p_y}^2\u03c02py\u200b2\u200b (4 electrons total in the degenerate \u03c0\\pi\u03c0 orbitals),<\/li>\n\n\n\n<li>\\pi^*_{2p_x}^1 (1 electron in the anti-bonding \u03c0\u2217\\pi^*\u03c0\u2217 orbital).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Calculation of bond order:<\/h3>\n\n\n\n<p>Bond order is given by the formula:Bond&nbsp;Order=12(Number&nbsp;of&nbsp;bonding&nbsp;electrons\u2212Number&nbsp;of&nbsp;anti-bonding&nbsp;electrons)\\text{Bond Order} = \\frac{1}{2} \\left( \\text{Number of bonding electrons} &#8211; \\text{Number of anti-bonding electrons} \\right)Bond&nbsp;Order=21\u200b(Number&nbsp;of&nbsp;bonding&nbsp;electrons\u2212Number&nbsp;of&nbsp;anti-bonding&nbsp;electrons)<\/p>\n\n\n\n<p>From the configuration, the bonding electrons are those in \u03c31s\\sigma_{1s}\u03c31s\u200b, \u03c32s\\sigma_{2s}\u03c32s\u200b, \u03c32pz\\sigma_{2p_z}\u03c32pz\u200b\u200b, and \u03c02px\\pi_{2p_x}\u03c02px\u200b\u200b, \u03c02py\\pi_{2p_y}\u03c02py\u200b\u200b orbitals, giving us:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bonding electrons: 2(\u03c31s)+2(\u03c32s)+2(\u03c32pz)+4(\u03c02px+\u03c02py)=102 (\\sigma_{1s}) + 2 (\\sigma_{2s}) + 2 (\\sigma_{2p_z}) + 4 (\\pi_{2p_x} + \\pi_{2p_y}) = 102(\u03c31s\u200b)+2(\u03c32s\u200b)+2(\u03c32pz\u200b\u200b)+4(\u03c02px\u200b\u200b+\u03c02py\u200b\u200b)=10<\/li>\n\n\n\n<li>Anti-bonding electrons: 2(\u03c31s\u2217)+2(\u03c32s\u2217)+1(\u03c02px\u2217)=52 (\\sigma^*_{1s}) + 2 (\\sigma^*_{2s}) + 1 (\\pi^*_{2p_x}) = 52(\u03c31s\u2217\u200b)+2(\u03c32s\u2217\u200b)+1(\u03c02px\u200b\u2217\u200b)=5<\/li>\n<\/ul>\n\n\n\n<p>So, the bond order is:Bond&nbsp;Order=12(10\u22125)=12\u00d75=2.5\\text{Bond Order} = \\frac{1}{2} \\left( 10 &#8211; 5 \\right) = \\frac{1}{2} \\times 5 = 2.5Bond&nbsp;Order=21\u200b(10\u22125)=21\u200b\u00d75=2.5<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The bond order of the C2\u2212\\text{C}_2^-C2\u2212\u200b ion is 2.5, which indicates a bond that is stronger than a single bond but not as strong as a double bond, reflecting the presence of the extra electron in an anti-bonding orbital.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner9-1.jpeg\" alt=\"\" class=\"wp-image-249602\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Using LCAO-MO theory, what is bond order of C2- (the one minus ion) The Correct Answer and Explanation is: The bond order of the C2\u2212\\text{C}_2^-C2\u2212\u200b ion can be determined using the Molecular Orbital (MO) theory and the Linear Combination of Atomic Orbitals (LCAO) approach. First, let&#8217;s review the molecular orbitals formed by the combination of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-249601","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249601","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=249601"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/249601\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=249601"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=249601"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=249601"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}