{"id":220091,"date":"2025-05-27T13:27:24","date_gmt":"2025-05-27T13:27:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220091"},"modified":"2025-05-27T13:27:27","modified_gmt":"2025-05-27T13:27:27","slug":"determine-the-lattice-energy-of-mx","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/27\/determine-the-lattice-energy-of-mx\/","title":{"rendered":"Determine the lattice energy of MX"},"content":{"rendered":"\n

Determine the lattice energy of MX
Consider an ionic compound, MX2, composed of generic metal M and generic, gaseous halogen X.<\/p>\n\n\n\n

The enthalpy of formation of MX2 is ?Hf = -975 kJ\/mol.<\/p>\n\n\n\n

The enthalpy of sublimation of M is ?Hsub = 133 kJ\/mol.<\/p>\n\n\n\n

The first and second ionization energies of M are IE1 = 751 and IE2 = 1412.<\/p>\n\n\n\n

The electron affinity of X is EA = -323 kJ\/mol.<\/p>\n\n\n\n

The bond energy of X2 is BE = 203 kJ\/mol.<\/p>\n\n\n\n

Determine the lattice energy of MX2.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine the lattice energy<\/strong> of the ionic compound MX\u2082<\/strong>, we use the Born-Haber cycle<\/strong>, which relates the enthalpy changes in the formation of an ionic compound from its elements.<\/p>\n\n\n\n

Given:<\/h3>\n\n\n\n
    \n
  • \u0394Hf (MX\u2082)<\/strong> = \u2013975 kJ\/mol (formation of MX\u2082 from M(s) and X\u2082(g))<\/li>\n\n\n\n
  • \u0394Hsub (M)<\/strong> = +133 kJ\/mol (sublimation of M(s) to M(g))<\/li>\n\n\n\n
  • IE\u2081 (M)<\/strong> = +751 kJ\/mol<\/li>\n\n\n\n
  • IE\u2082 (M)<\/strong> = +1412 kJ\/mol<\/li>\n\n\n\n
  • EA (X)<\/strong> = \u2013323 kJ\/mol (per atom)<\/li>\n\n\n\n
  • Bond Energy (X\u2082)<\/strong> = +203 kJ\/mol (per mole of X\u2082 molecules broken)<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Step-by-step Breakdown:<\/h3>\n\n\n\n

    Formation of MX\u2082:<\/strong><\/p>\n\n\n\n

      \n
    1. Sublimation of M(s)<\/strong> \u2192 M(g):
      \u2003\u0394H = +133 kJ\/mol<\/li>\n\n\n\n
    2. Ionization of M(g)<\/strong> \u2192 M\u00b2\u207a(g):
      \u2003IE\u2081 + IE\u2082 = 751 + 1412 = 2163 kJ\/mol<\/strong><\/li>\n\n\n\n
    3. Dissociation of X\u2082(g)<\/strong> \u2192 2 X(g):
      \u2003X\u2082 \u2192 2X:
      \u2003\u0394H = +\u00bd(203) = +101.5 kJ\/mol<\/strong><\/li>\n\n\n\n
    4. Electron gain by 2 X(g)<\/strong> \u2192 2 X\u207b(g):
      \u20032 \u00d7 EA = 2 \u00d7 (\u2013323) = \u2013646 kJ\/mol<\/strong><\/li>\n\n\n\n
    5. Formation of MX\u2082(s)<\/strong> from M\u00b2\u207a(g) and 2X\u207b(g):
      \u2003This is the lattice energy (U)<\/strong>, which we solve for.<\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      Use the Born-Haber cycle equation:<\/h3>\n\n\n\n

      \u0394Hf=\u0394Hsub+IE1+IE2+12BE+2EA+U\\Delta H_f = \\Delta H_{sub} + IE_1 + IE_2 + \\dfrac{1}{2}BE + 2EA + U<\/p>\n\n\n\n

      Plug in values: \u2212975=133+751+1412+101.5\u2212646+U-975 = 133 + 751 + 1412 + 101.5 – 646 + U \u2212975=1751.5+U-975 = 1751.5 + U U=\u2212975\u22121751.5=\u22122726.5 kJ\/molU = -975 – 1751.5 = \\boxed{-2726.5\\ \\text{kJ\/mol}}<\/p>\n\n\n\n

      \n\n\n\n

      Final Answer:<\/h3>\n\n\n\n

      Lattice Energy (U) of MX\u2082 = \u20132726.5 kJ\/mol<\/strong><\/p>\n\n\n\n

      \n\n\n\n

      Explanation <\/h3>\n\n\n\n

      Lattice energy is a measure of the strength of the forces between the ions in an ionic solid. It represents the energy released when one mole of an ionic compound forms from its gaseous ions. To determine it, we use the Born-Haber cycle, which breaks down the formation of the ionic compound into a series of energetic steps.<\/p>\n\n\n\n

      In this problem, we are given the enthalpy of formation of MX\u2082, along with the sublimation energy, ionization energies of the metal M, the bond energy of halogen X\u2082, and the electron affinity of X. Starting from the elements in their standard states, M (solid) and X\u2082 (gas), we proceed through the steps of sublimating M, ionizing it to M\u00b2\u207a, breaking X\u2082 into two atoms, and adding electrons to form two X\u207b ions. The total of these steps gives the energy required to produce the gaseous ions.<\/p>\n\n\n\n

      The final step is the combination of M\u00b2\u207a and 2 X\u207b into solid MX\u2082, which releases a large amount of energy \u2013 the lattice energy. By using the enthalpy of formation, we can rearrange the Born-Haber equation to solve for the unknown lattice energy. The result, \u20132726.5 kJ\/mol, indicates a highly exothermic process, which is typical for ionic compounds due to the strong electrostatic attraction between oppositely charged ions.<\/p>\n\n\n\n

      This lattice energy is crucial in understanding the stability, melting point, and solubility of the ionic compound. A more negative lattice energy generally means a more stable solid with stronger ionic bonds.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Determine the lattice energy of MXConsider an ionic compound, MX2, composed of generic metal M and generic, gaseous halogen X. The enthalpy of formation of MX2 is ?Hf = -975 kJ\/mol. The enthalpy of sublimation of M is ?Hsub = 133 kJ\/mol. The first and second ionization energies of M are IE1 = 751 and […]<\/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-220091","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220091","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=220091"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220091\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220091"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220091"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220091"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}